Finite Group Databasebeta

← #25965508

Subgroups — #25965508

Order 11008.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148330C211yesmaximal, characteristic, complemented
2#19147796C211yesmaximal, characteristic, complemented
3#19144887C212yesmaximal, complemented
4#19144839C212yesmaximal, complemented
5#19144826C212yesmaximal, complemented
6#19144781C212yesmaximal, complemented
7#19144747C212yesmaximal, complemented
8#19144706C212yesmaximal, complemented
9#19144656C212yesmaximal, complemented
10#19144615C212yesmaximal, complemented
11#19144528C211yesmaximal, characteristic, complemented
12C2×#14583224C211yesmaximal, characteristic, complemented
13#19144459C211yesmaximal, characteristic, complemented
14#19144448C211yesmaximal, characteristic, complemented
15#19144136C211yesmaximal, characteristic, complemented
16#19144136C211yesmaximal, characteristic, complemented
17#19143849C211yesmaximal, characteristic, complemented
18#19143817C211yesmaximal, characteristic, complemented
19#19143480C211yesmaximal, characteristic, complemented
20#19143472C211yesmaximal, characteristic, complemented
21#19143429C211yesmaximal, characteristic, complemented
22#19143429C211yesmaximal, characteristic, complemented
23C43×#2924C211yesmaximal, characteristic, complemented
24C22×#10621898C2211yescharacteristic
25C2×#13063353C2211yescharacteristic
26C2×#13063353C2211yescharacteristic
27C2×#13063347C2211yescharacteristic
28C2×#13063347C2211yescharacteristic
29#14583612—21no—
30#14583597—21no—
31#14583593—21no—
32#14583573—22no—
33#14583550—21no—
34#14583539—22no—
35#14583527C2211yescharacteristic, complemented
36#14583520C2212yes—
37#14583504C2212yes—
38#14583468C2211yescharacteristic, complemented
39#14583449C2212yescomplemented
40#14583433C2212yescomplemented
41#14583410C2211yescharacteristic
42C2×#13063299C2211yescharacteristic
43#14583380—21no—
44#14583380—21no—
45#14583379C2211yescharacteristic
46#14583379C2211yescharacteristic
47#14583379C2211yescharacteristic
48#14583379C2211yescharacteristic
49#14583379C2211yescharacteristic, complemented
50#14583376C2212yescomplemented
51#14583373C2211yescharacteristic, complemented
52#14583373C2212yescomplemented
53#14583372—22no—
54C4×#10621898C2212yescomplemented
55C4×#10621898C2212yescomplemented
56#14583367—22no—
57C2×#13063284C2211yescharacteristic
58#117×D43—21no—
59#117×D43—21no—
60#14583241C2212yescomplemented
61#14583241C2212yescomplemented
62#14583224C2212yes—
63#14583224C2212yes—
64#14583224C2212yescomplemented
65#14583224C2212yescomplemented
66#14583224C2212yescomplemented
67#14583224C2212yescomplemented
68#14583207C2212yescomplemented
69#14583207C2212yescomplemented
70#14583200C2212yescomplemented
71#14583200C2212yescomplemented
72#14583195C2212yescomplemented
73#14583190C2212yescomplemented
74#14583185C2212yescomplemented
75#14583180C2212yescomplemented
76#14583122C2212yescomplemented
77#14583122C2212yescomplemented
78#14583115C2212yescomplemented
79#14583115C2212yescomplemented
80#14583100C2212yescomplemented
81#14583100C2212yescomplemented
82#14583095C2212yescomplemented
83#14583095C2212yescomplemented
84#14583063C2211yescharacteristic, complemented
85#14583063C2211yescharacteristic, complemented
86#14583057C2211yescharacteristic, complemented
87#14583052C2211yescharacteristic, complemented
88#14583046C2212yes—
89#14583046C2212yes—
90#14583046C2211yescharacteristic, complemented
91#14583046C2211yescharacteristic, complemented
92#14583040C2212yes—
93#14583040C2211yescharacteristic, complemented
94#14583035C2212yes—
95#14583035C2211yescharacteristic, complemented
96#14583012C2212yescomplemented
97#14583012C2212yescomplemented
98#14583012C2212yescomplemented
99#14583007C2212yescomplemented
100#14583001C2212yescomplemented
101#14583001C2212yescomplemented
102#14583001C2212yescomplemented
103#14583001C2212yescomplemented
104C4×Dic172C2212yescomplemented
105C4×#10621873C2212yescomplemented
106C4×#10621873C2212yescomplemented
107C4×#10621873C2212yescomplemented
108C4×#10621873C2212yescomplemented
109C4×D344C2212yescomplemented
110C4×D344C2212yescomplemented
111C4×D344C2212yescomplemented
112#14582941C2211yescharacteristic, complemented
113#14582941C2211yescharacteristic, complemented
114C2×#13063259C2211yescharacteristic, complemented
115C2×#13063257C2211yescharacteristic, complemented
116#14582901C2211yescharacteristic
117#14582901C2211yescharacteristic
118#14582901C2211yescharacteristic, complemented
119#14582901C2211yescharacteristic, complemented
120#14582896C2211yescharacteristic
121#14582896C2211yescharacteristic
122C2×#13063247C2211yescharacteristic, complemented
123C2×#13063247C2211yescharacteristic, complemented
124C2×#117×C43C2211yescharacteristic
125C43×#433C2212yescomplemented
126C43×#433C2212yescomplemented
127C43×#432C2212yescomplemented
128C43×#431C2212yescomplemented
129C43×#424C2211yescharacteristic, complemented
130C43×#424C2211yescharacteristic, complemented
131C43×#407C2211yescharacteristic
132C2×C22⋊C8×C43C2211yescharacteristic
133C43×#405C2211yescharacteristic, complemented
134C43×#405C2211yescharacteristic, complemented
135C2×#10621898—21no—
136C2×#10621898—21no—
137C2×#10621898—24no—
138C2×#10621898—24no—
139C2×#10621898—22no—
140C2×#10621898C2311yescharacteristic
141C2×#10621898C2311yescharacteristic
142C2×#10621898C2311yescharacteristic
143C2×#10621898C2311yescharacteristic
144C2×#10621898C2311yescharacteristic
145C22×Dic86C2311yescharacteristic
146C22×D172C2311yescharacteristic
147C22×D172C2311yescharacteristic
148C22×C22⋊D43—21no—
149C22×C22⋊D43—21no—
150C22×C4×D43—21no—
151#13063353—24no—
152#13063353—24no—
153#13063347—24no—
154#13063347—24no—
155C2×Dic172C2311yescharacteristic
156C2×Dic172C2311yescharacteristic
157C2×#10621873C2312yes—
158C2×#10621873C2312yes—
159C2×#10621873C2311yescharacteristic
160C2×#10621873C2311yescharacteristic
161C2×#10621873C2311yescharacteristic
162C2×#10621873C2311yescharacteristic
163C2×D344C2312yes—
164C2×D344C2312yes—
165C2×D344C2311yescharacteristic
166C2×D344C2311yescharacteristic
167#13063325C2312yes—
168#13063324—21no—
169#13063322C2312yes—
170#13063320—22no—
171#13063319—22no—
172#13063317C2312yes—
173#13063316—21no—
174#13063313—22no—
175#13063313C2312yes—
176#13063311—22no—
177#13063310—22no—
178#13063310—22no—
179#13063308—21no—
180#13063308—22no—
181#13063307—22no—
182#13063304C2311yescharacteristic
183#13063304C2311yescharacteristic
184#13063303—22no—
185#13063302—22no—
186#13063300—21no—
187#13063300—21no—
188#13063299—21no—
189#13063299—21no—
190#13063299—22no—
191#13063299C2312yes—
192#13063299C2311yescharacteristic
193#13063299C2312yes—
194#13063299C2311yescharacteristic
195#13063298—22no—
196#13063298—22no—
197#13063295—22no—
198#13063294—21no—
199C4×Dic86C2312yes—
200C4×Dic86C2312yes—
201C4×Dic86C2312yes—
202C4×Dic86C2312yes—
203C4×Dic86C2312yes—
204#13063290—22no—
205#13063290—22no—
206C4×D172—22no—
207C4×D172C2312yes—
208C4×D172C2312yes—
209C4×D172C2312yes—
210C4×D172C2312yes—
211C4×D172C2312yes—
212C4×D172C2312yes—
213C4×D172C2312yes—
214#13063287—21no—
215#13063287—21no—
216#13063287—22no—
217#13063287—22no—
218C4×C22⋊D43—21no—
219C4×C22⋊D43—21no—
220C4×C22⋊D43—22no—
221C4×C22⋊D43—22no—
222C4×C22⋊D43—22no—
223C4×C22⋊D43—22no—
224C4×C22⋊D43—22no—
225(C22⋊D43)⋊C4—22no—
226(C22⋊D43)⋊C4—22no—
227(C22⋊D43)⋊C4—22no—
228(C22⋊D43)⋊C4—22no—
229(C22⋊D43)⋊C4—22no—
230#13063284—21no—
231#13063284—21no—
232#13063284C2312yes—
233#13063284C2312yes—
234#13063284C2311yescharacteristic
235#13063283—21no—
236#13063283—21no—
237#13063283—21no—
238#13063283—21no—
239#13063283—21no—
240#13063282—22no—
241#13063282—22no—
242#13063282—22no—
243#13063281—22no—
244#13063281—22no—
245C2×C4⋊Dic43C2311yescharacteristic
246C2×C4⋊Dic43C2311yescharacteristic
247C2×C4⋊Dic43C2311yescharacteristic
248C4⋊C4×D43—21no—
249C4⋊C4×D43—21no—
250C4⋊C4×D43—21no—
251C4⋊C4×D43—21no—
252C4⋊C4×D43—21no—
253C2×C22⋊Dic43—21no—
254C2×(C2×D43)⋊C4—21no—
255C22⋊C4×D43—22no—
256C22⋊C4×D43—22no—
257C22⋊C4×D43—22no—
258C2×C4×Dic43—21no—
259C42×D43—22no—
260C42×D43—22no—
261#13063259C2312yes—
262#13063259C2312yes—
263#13063259C2312yes—
264#13063259C2312yes—
265#13063257C2312yes—
266#13063257C2312yes—
267#13063257C2312yes—
268#13063257C2312yes—
269#13063250C2312yes—
270#13063250C2312yes—
271#13063250C2311yescharacteristic
272#13063250C2311yescharacteristic
273#13063250C2311yescharacteristic
274#13063250C2311yescharacteristic
275#13063250C2312yes—
276#13063250C2312yes—
277#13063247C2312yes—
278#13063247C2312yes—
279#13063247C2311yescharacteristic
280#13063247C2311yescharacteristic
281#13063247C2311yescharacteristic
282#13063247C2311yescharacteristic
283#13063247C2312yes—
284#13063247C2312yes—
285#13063247C2312yes—
286#13063247C2312yes—
287#13063247C2312yes—
288#13063247C2312yes—
289C23×C4×C43C2311yescharacteristic
290C2×M16×C43C2311yescharacteristic
291C2×M16×C43C2311yescharacteristic
292C22×C8×C43C2311yescharacteristic
293C22×C8×C43C2311yescharacteristic
294#117×C43D412yes—
295#117×C43D411yescharacteristic
296#117×C43D411yescharacteristic
297#117×C43C2312yes—
298#117×C43C2311yescharacteristic
299#117×C43C2311yescharacteristic
300C2×C4⋊C4×C43D411yescharacteristic
301C2×C4⋊C4×C43D411yescharacteristic
302C2×C22⋊C4×C43D412yes—
303C2×C42×C43C2312yes—
304C4⋊C8×C43C2312yes—
305C4⋊C8×C43C2312yes—
306C4⋊C8×C43C2312yes—
307C4⋊C8×C43C2312yes—
308C22⋊C8×C43C2312yes—
309C22⋊C8×C43C2311yescharacteristic
310C22⋊C8×C43C2312yes—
311C22⋊C8×C43C2311yescharacteristic
312C22⋊C8×C43C2311yescharacteristic
313C22⋊C8×C43C2311yescharacteristic
314#97×C43C2312yes—
315#97×C43C2312yes—
316C4×C8×C43C2312yes—
317C4×C8×C43C2312yes—
318C24×C43C2×D411yescharacteristic
319C23×D43—21no—
320C23×D43—21no—
321C22×C4×C43—22no—
322C22×C4×C43—22no—
323C22×C4×C43C2×D411yescharacteristic
324C22×C4×C43C2×D411yescharacteristic
325C22×C4×C43C2×D411yescharacteristic
326C22×C4×C43C2×D412yes—
327C22×C4×C43C2×D412yes—
328C22×C4×C43C2411yescharacteristic
329C22×C4×C43C2411yescharacteristic
330C22×C4×C43C2411yescharacteristic
331C2×C22⋊D43—28no—
332C2×C22⋊D43—21no—
333C2×C22⋊D43—21no—
334C2×C22⋊D43—21no—
335C2×C22⋊D43—21no—
336C2×C22⋊D43—21no—
337C2×C22⋊D43—21no—
338C2×C22⋊D43—22no—
339C2×C22⋊D43—21no—
340C2×C22⋊D43—22no—
341C2×C22⋊D43—82no—
342C22×Dic43—21no—
343C22×Dic43—21no—
344C22×Dic43—21no—
345C22×Dic43—21no—
346#10621898—28no—
347#10621898—28no—
348#10621898—22no—
349#10621898—22no—
350#10621898—22no—
351#10621898—22no—
352#10621898—22no—
353#10621898—22no—
354#10621898—22no—
355#10621898—22no—
356#10621898—84no—
357#10621898#4114yescomplemented
358#10621898#4114yescomplemented
359C2×D172—21no—
360C2×D172—22no—
361C2×D172—22no—
362C2×D172—21no—
363C2×D172—22no—
364C2×D172—22no—
365C2×D172—22no—
366C2×D172—22no—
367C2×D172C2412yes—
368C2×D172C2411yescharacteristic
369C2×D172C2411yescharacteristic
370C2×D172C2411yescharacteristic
371C2×C4×D43—28no—
372C2×C4×D43—21no—
373C2×C4×D43—21no—
374C2×C4×D43—21no—
375C2×C4×D43—21no—
376C2×C4×D43—21no—
377C2×C4×D43—22no—
378C2×C4×D43—22no—
379C2×C4×D43—22no—
380C2×C4×D43—22no—
381C2×C4×D43—22no—
382C2×C4×D43—22no—
383C2×C4×D43—22no—
384C2×Dic86—21no—
385C2×Dic86—22no—
386C2×Dic86—22no—
387C2×Dic86—22no—
388C2×Dic86C2411yescharacteristic
389C2×Dic86C2411yescharacteristic
390C2×Dic86C2411yescharacteristic
391M16×C43—22no—
392M16×C43—22no—
393C2×C8×C43—22no—
394C2×C8×C43—22no—
395C2×C8×C43C2411yescharacteristic
396C2×C8×C43C2411yescharacteristic
397C2×C8×C43C2412yes—
398C2×C8×C43C2412yes—
399C2×C8×C43C2411yescharacteristic
400C2×C8×C43C2411yescharacteristic
401C4⋊C4×C43C2×D411yescharacteristic
402C4⋊C4×C43C2×D411yescharacteristic
403C4⋊C4×C43C2×D411yescharacteristic
404C4⋊C4×C43C2×D411yescharacteristic
405C4⋊C4×C43C2×D412yes—
406C4⋊C4×C43C2×D412yes—
407C22⋊C4×C43C2×D412yes—
408C22⋊C4×C43C2×D412yes—
409C22⋊C4×C43C2×D412yes—
410C22⋊C4×C43C2×D412yes—
411C42×C43C2×D412yes—
412C42×C43C2×D412yes—
413C42×C43C2412yes—
414C42×C43C2412yes—
415C22⋊Dic43—22no—
416C22⋊Dic43—21no—
417C22⋊Dic43—22no—
418C22⋊Dic43—21no—
419C22⋊Dic43—21no—
420(C2×D43)⋊C4—22no—
421(C2×D43)⋊C4—22no—
422(C2×D43)⋊C4—22no—
423(C2×D43)⋊C4—22no—
424(C2×D43)⋊C4—22no—
425(C2×D43)⋊C4—22no—
426(C2×D43)⋊C4—22no—
427(C2×D43)⋊C4—22no—
428(C2×D43)⋊C4—22no—
429(C2×D43)⋊C4—22no—
430(C2×D43)⋊C4—21no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—21no—
433C4⋊Dic43—21no—
434C4⋊Dic43—21no—
435C4⋊Dic43—21no—
436C4⋊Dic43—22no—
437C4⋊Dic43C2412yes—
438C4⋊Dic43C2412yes—
439C4⋊Dic43C2412yes—
440C4⋊Dic43C2411yescharacteristic
441C4⋊Dic43C2411yescharacteristic
442Dic43⋊C4—22no—
443Dic43⋊C4—22no—
444Dic43⋊C4—22no—
445Dic43⋊C4—22no—
446Dic43⋊C4—22no—
447Dic43⋊C4—21no—
448Dic43⋊C4—22no—
449Dic43⋊C4—22no—
450Dic43⋊C4—21no—
451C4×Dic43—22no—
452C4×Dic43—22no—
453C4×Dic43—22no—
454C4×Dic43—22no—
455C4×Dic43—22no—
456C4×Dic43—22no—
457C4×Dic43—22no—
458C4×Dic43—21no—
459Dic172—22no—
460Dic172—22no—
461D344—22no—
462D344—22no—
463D344—24no—
464D344—24no—
465#10621873—22no—
466#10621873—22no—
467#10621873—22no—
468#10621873—22no—
469#10621873—24no—
470#10621873—24no—
471C23×C43—22no—
472C23×C43—41no—
473C23×C43—41no—
474C23×C43C22×D411yescharacteristic
475C23×C43C22×D411yescharacteristic
476C23×C43C22×D411yescharacteristic
477C22×D43—21no—
478C22×D43—21no—
479C22×D43—24no—
480C22×D43—22no—
481C22×D43—21no—
482C22×D43—42no—
483C22×D43—81no—
484C22×D43—81no—
485C22×D43—81no—
486C22×D43—81no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—21no—
491C2×C4×C43—21no—
492C2×C4×C43—21no—
493C2×C4×C43—21no—
494C2×C4×C43—42no—
495C2×C4×C43—42no—
496C2×C4×C43C22×D411yescharacteristic
497C2×C4×C43C22×D412yes—
498C2×C4×C43C22×D411yescharacteristic
499C2×C4×C43C22×D412yes—
500C2×C4×C43C22×D412yes—
501C2×C4×C43C22×D412yes—
502C2×C4×C43C22×D411yescharacteristic
503C2×C4×C43C2×#4112yes—
504C2×C4×C43C2×#4112yes—
505C2×C4×C43C2511yescharacteristic
506C22⋊D43—24no—
507C22⋊D43—24no—
508C22⋊D43—24no—
509C22⋊D43—24no—
510C22⋊D43—42no—
511C22⋊D43—44no—
512C22⋊D43—42no—
513C22⋊D43—81no—
514C22⋊D43—82no—
515C2×Dic43—24no—
516C2×Dic43—21no—
517C2×Dic43—21no—
518C2×Dic43—22no—
519C2×Dic43—22no—
520C2×Dic43—21no—
521C2×Dic43—21no—
522C2×Dic43—22no—
523C2×Dic43—21no—
524C2×Dic43—81no—
525C2×Dic43—81no—
526C2×Dic43—81no—
527D172—24no—
528D172—21no—
529D172—21no—
530D172—22no—
531D172—22no—
532D172—21no—
533D172—21no—
534D172—42no—
535D172—82no—
536D172—82no—
537D172C2×#4112yes—
538D172C2×#4112yes—
539C4×D43—24no—
540C4×D43—24no—
541C4×D43—24no—
542C4×D43—24no—
543C4×D43—42no—
544C4×D43—82no—
545C4×D43—82no—
546C4×D43—82no—
547C4×D43—82no—
548C4×D43—82no—
549C4×D43—82no—
550C4×D43—82no—
551Dic86—24no—
552Dic86—21no—
553Dic86—21no—
554Dic86—21no—
555Dic86—21no—
556Dic86—82no—
557Dic86C2×#4112yes—
558Dic86C2×#4112yes—
559C8×C43—21no—
560C8×C43—21no—
561C8×C43—22no—
562C8×C43—22no—
563C8×C43—21no—
564C8×C43—21no—
565#60587—431nomaximal, Sylow
566C22×C43—21no—
567C22×C43—21no—
568C22×C43—21no—
569C22×C43—21no—
570C22×C43—21no—
571C22×C43—21no—
572C22×C43—21no—
573C22×C43—21no—
574C22×C43—82no—
575C22×C43#52512yes—
576C22×C43C23×D411yescharacteristic
577C2×D43—22no—
578C2×D43—22no—
579C2×D43—41no—
580C2×D43—41no—
581C2×D43—41no—
582C2×D43—41no—
583C2×D43—42no—
584C2×D43—41no—
585C2×D43—42no—
586C2×D43—41no—
587C2×D43—42no—
588C2×D43—41no—
589C2×D43—84no—
590C2×D43—162no—
591C4×C43—22no—
592C4×C43—22no—
593C4×C43—22no—
594C4×C43—22no—
595C4×C43—21no—
596C4×C43—21no—
597C4×C43#52512yes—
598C4×C43C22×#4111yescharacteristic
599C4×C43C22×#4111yescharacteristic
600Dic43—22no—
601Dic43—22no—
602Dic43—42no—
603Dic43—41no—
604Dic43—41no—
605Dic43—42no—
606Dic43—42no—
607Dic43—41no—
608#3494—431no—
609#3428—431no—
610#3126—432no—
611#3122—432no—
612#3121—432no—
613#3118—432no—
614#3115—432no—
615#3111—432no—
616#3106—432no—
617#3102—432no—
618#3093—431no—
619C2×#482—431no—
620#3084—431no—
621#3083—431no—
622#3045—431no—
623#3045—431no—
624#3006—431no—
625#3002—431no—
626#2952—431no—
627#2951—431no—
628#2946—431no—
629#2946—431no—
630#2924D4311yescharacteristic, complemented
631C2×C43—22no—
632C2×C43—41no—
633C2×C43—41no—
634C2×C43C2×#52511yescharacteristic
635C2×C43#358411yescharacteristic
636C2×C43#358511yescharacteristic
637D43—42no—
638D43—42no—
639D43—81no—
640D43—82no—
641C22×#41—431no—
642C2×AGL(1,ℤ/8)—431no—
643C2×AGL(1,ℤ/8)—431no—
644C2×#135—431no—
645C2×#135—431no—
646#555—861no—
647#553—861no—
648#553—861no—
649#551—862no—
650#547—861no—
651#546—862no—
652#544—431no—
653#542—432no—
654#540—432no—
655#535—431no—
656#532—432no—
657#529—432no—
658#525—431no—
659C2×#121—431no—
660#520—431no—
661#520—431no—
662#520—431no—
663#520—431no—
664#520—431no—
665#520—861no—
666#520—861no—
667#519—432no—
668#518—432no—
669#518—431no—
670#518—862no—
671C4×#41—432no—
672C4×#41—432no—
673C4×#41—862no—
674C2×#117—431no—
675C2×#117—861no—
676C2×#117—861no—
677C2×#117C2×D4311yescharacteristic
678#485—432no—
679#485—432no—
680#482—432no—
681#482—432no—
682#482—432no—
683#482—432no—
684#482—432no—
685#482—432no—
686#479—432no—
687#479—432no—
688#478—432no—
689#478—432no—
690#477—432no—
691#476—432no—
692#475—432no—
693#474—432no—
694#464—432no—
695#464—432no—
696#463—432no—
697#463—432no—
698#460—432no—
699#460—432no—
700#459—432no—
701#459—432no—
702#452—431no—
703#452—431no—
704#451—431no—
705#450—431no—
706#449—432no—
707#449—432no—
708#449—431no—
709#449—431no—
710#448—432no—
711#448—431no—
712#447—432no—
713#447—431no—
714#442—432no—
715#442—432no—
716#442—432no—
717#441—432no—
718#440—432no—
719#440—432no—
720#440—432no—
721#440—432no—
722C4×Q16—432no—
723C4×SD16—432no—
724C4×SD16—432no—
725C4×SD16—432no—
726C4×SD16—432no—
727C4×D8—432no—
728C4×D8—432no—
729C4×D8—432no—
730#433C2×D4312yescomplemented
731#433C2×D4312yescomplemented
732#432C2×D4312yescomplemented
733#431C2×D4312yescomplemented
734#428—431no—
735#428—431no—
736C2×#107—431no—
737C2×#106—431no—
738#424C2×D4311yescharacteristic, complemented
739#424C2×D4311yescharacteristic, complemented
740#417—431no—
741#417—431no—
742#417—431no—
743#417—431no—
744#416—431no—
745#416—431no—
746C2×#102—431no—
747C2×#102—431no—
748#407C2×D4311yescharacteristic
749C2×C22⋊C8C2×D4311yescharacteristic
750#405C2×D4311yescharacteristic, complemented
751#405C2×D4311yescharacteristic, complemented
752C43#6058711yescharacteristic, complemented, Sylow
753C2×#41—431no—
754C2×#41—431no—
755C2×#41—431no—
756C2×#41—431no—
757C2×#41—431no—
758C2×#41—864no—
759C2×#41—864no—
760C2×#41—861no—
761C2×#41—861no—
762C2×#41—862no—
763C22×Q8—431no—
764C22×D4—431no—
765C22×D4—431no—
766C22×D4—861no—
767C22×D4—861no—
768C23×C4—861no—
769C23×C4C22×D4311yescharacteristic
770AGL(1,ℤ/8)—864no—
771AGL(1,ℤ/8)—864no—
772#135—864no—
773#135—864no—
774C2×Q16—431no—
775C2×Q16—431no—
776C2×SD16—431no—
777C2×SD16—431no—
778C2×SD16—431no—
779C2×SD16—431no—
780C2×SD16—432no—
781C2×SD16—432no—
782C2×D8—431no—
783C2×D8—431no—
784C2×D8—432no—
785C2×D8—432no—
786C2×M16C22×D4311yescharacteristic
787C2×M16C22×D4311yescharacteristic
788C22×C8C22×D4311yescharacteristic
789C22×C8C22×D4311yescharacteristic
790C4⋊Q8—432no—
791C4⋊Q8—861no—
792#127—432no—
793#126—862no—
794#126—862no—
795#125—432no—
796#125—861no—
797#124—432no—
798#124—862no—
799#124—862no—
800#123—861no—
801#123—862no—
802#123—862no—
803#123—862no—
804#123—862no—
805C22⋊Q8—431no—
806C22⋊Q8—431no—
807C22⋊Q8—862no—
808C22⋊Q8—862no—
809#121—432no—
810#121—432no—
811#121—431no—
812#121—431no—
813#121—861no—
814#121—861no—
815#121—862no—
816#121—861no—
817#121—861no—
818#121—862no—
819#121—862no—
820#120—861no—
821#120—862no—
822C4×Q8—432no—
823C4×Q8—432no—
824C4×Q8—432no—
825C4×Q8—432no—
826C4×Q8—432no—
827C4×Q8—862no—
828C4×Q8—862no—
829C4×D4—432no—
830C4×D4—432no—
831C4×D4—432no—
832C4×D4—432no—
833C4×D4—432no—
834C4×D4—432no—
835C4×D4—432no—
836C4×D4—862no—
837C4×D4—862no—
838C4×D4—862no—
839C4×D4—862no—
840C4×D4—861no—
841C4×D4—861no—
842C4×D4—862no—
843C4×D4—862no—
844C4×D4—862no—
845C4×D4—861no—
846C4×D4—861no—
847C4×D4—862no—
848C4×D4—862no—
849C4×D4—862no—
850C4×D4—862no—
851C4×D4—862no—
852C4×D4—862no—
853#117—432no—
854#117—432no—
855#117—431no—
856#117—861no—
857#117—861no—
858#117—861no—
859#117—861no—
860#117—861no—
861#117—861no—
862#117—861no—
863#117—862no—
864#117—862no—
865#117—862no—
866#117—862no—
867#117—862no—
868#117D17211yescharacteristic
869#117D17211yescharacteristic
870#117D17212yes—
871#117C22×D4312yes—
872#117C22×D4311yescharacteristic
873#117C22×D4311yescharacteristic
874C2×C4⋊C4—431no—
875C2×C4⋊C4—431no—
876C2×C4⋊C4—431no—
877C2×C4⋊C4—861no—
878C2×C4⋊C4—861no—
879C2×C4⋊C4—861no—
880C2×C4⋊C4—861no—
881C2×C4⋊C4—861no—
882C2×C4⋊C4D17211yescharacteristic
883C2×C4⋊C4D17211yescharacteristic
884C2×C22⋊C4—861no—
885C2×C22⋊C4—861no—
886C2×C22⋊C4—862no—
887C2×C22⋊C4—862no—
888C2×C22⋊C4—862no—
889C2×C22⋊C4D17212yes—
890C2×C42—861no—
891C2×C42—862no—
892C2×C42—862no—
893C2×C42C22×D4312yes—
894#107—432no—
895#107—432no—
896#107—432no—
897#107—432no—
898#106—432no—
899#106—432no—
900#106—432no—
901#106—432no—
902C4⋊C8C22×D4312yes—
903C4⋊C8C22×D4312yes—
904C4⋊C8C22×D4312yes—
905C4⋊C8C22×D4312yes—
906#103—431no—
907#103—431no—
908#103—431no—
909#103—431no—
910#103—432no—
911#103—432no—
912#103—432no—
913#103—432no—
914#102—432no—
915#102—432no—
916#102—432no—
917#102—432no—
918#102—431no—
919#102—431no—
920#102—431no—
921#102—431no—
922#102—432no—
923#102—432no—
924#102—432no—
925#102—432no—
926C22⋊C8C22×D4311yescharacteristic
927C22⋊C8C22×D4311yescharacteristic
928C22⋊C8C22×D4311yescharacteristic
929C22⋊C8C22×D4311yescharacteristic
930C22⋊C8C22×D4312yes—
931C22⋊C8C22×D4312yes—
932#97C22×D4312yes—
933#97C22×D4312yes—
934C4×C8C22×D4312yes—
935C4×C8C22×D4312yes—
936C24—861no—
937C24—861no—
938C24C2×D17211yescharacteristic
939#41—434no—
940#41—434no—
941#41—862no—
942#41—862no—
943#41—862no—
944#41—862no—
945#41—868no—
946#41—868no—
947#41—862no—
948#41—862no—
949#41—862no—
950#41—862no—
951#41—3444no—
952C2×Q8—431no—
953C2×Q8—431no—
954C2×Q8—431no—
955C2×Q8—862no—
956C2×Q8—862no—
957C2×Q8—861no—
958C2×Q8—862no—
959C2×D4—431no—
960C2×D4—431no—
961C2×D4—432no—
962C2×D4—431no—
963C2×D4—862no—
964C2×D4—862no—
965C2×D4—868no—
966C2×D4—861no—
967C2×D4—861no—
968C2×D4—861no—
969C2×D4—861no—
970C2×D4—861no—
971C2×D4—862no—
972C2×D4—861no—
973C2×D4—861no—
974C2×D4—862no—
975C2×D4—861no—
976C2×D4—862no—
977C2×D4—862no—
978C2×D4—861no—
979C2×D4—862no—
980C2×D4—862no—
981C2×D4—3442no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—868no—
985C22×C4—861no—
986C22×C4—861no—
987C22×C4—861no—
988C22×C4—861no—
989C22×C4—861no—
990C22×C4—861no—
991C22×C4—861no—
992C22×C4—861no—
993C22×C4—862no—
994C22×C4—862no—
995C22×C4—862no—
996C22×C4—862no—
997C22×C4—862no—
998C22×C4—862no—
999C22×C4—862no—
1000C22×C4—861no—
1001C22×C4C2×D17211yescharacteristic
1002C22×C4C2×D17211yescharacteristic
1003C22×C4C2×D17211yescharacteristic
1004C22×C4C2×D17212yes—
1005C22×C4C2×D17212yes—
1006C22×C4C23×D4311yescharacteristic
1007C22×C4C23×D4311yescharacteristic
1008C22×C4C23×D4311yescharacteristic
1009Q16—862no—
1010Q16—862no—
1011SD16—862no—
1012SD16—862no—
1013SD16—862no—
1014SD16—862no—
1015SD16—864no—
1016SD16—864no—
1017D8—862no—
1018D8—862no—
1019D8—864no—
1020D8—864no—
1021M16—22no—
1022M16—22no—
1023C2×C8—22no—
1024C2×C8—22no—
1025C2×C8C23×D4311yescharacteristic
1026C2×C8C23×D4311yescharacteristic
1027C2×C8C23×D4312yes—
1028C2×C8C23×D4312yes—
1029C2×C8C23×D4311yescharacteristic
1030C2×C8C23×D4311yescharacteristic
1031C4⋊C4—432no—
1032C4⋊C4—432no—
1033C4⋊C4—432no—
1034C4⋊C4—431no—
1035C4⋊C4—431no—
1036C4⋊C4—861no—
1037C4⋊C4—861no—
1038C4⋊C4—861no—
1039C4⋊C4—862no—
1040C4⋊C4—862no—
1041C4⋊C4—862no—
1042C4⋊C4—862no—
1043C4⋊C4—862no—
1044C4⋊C4—861no—
1045C4⋊C4—862no—
1046C4⋊C4—862no—
1047C4⋊C4—862no—
1048C4⋊C4—861no—
1049C4⋊C4C2×D17211yescharacteristic
1050C4⋊C4C2×D17211yescharacteristic
1051C4⋊C4C2×D17211yescharacteristic
1052C4⋊C4C2×D17211yescharacteristic
1053C4⋊C4C2×D17212yes—
1054C4⋊C4C2×D17212yes—
1055C22⋊C4—862no—
1056C22⋊C4—861no—
1057C22⋊C4—862no—
1058C22⋊C4—861no—
1059C22⋊C4—861no—
1060C22⋊C4—862no—
1061C22⋊C4—862no—
1062C22⋊C4—862no—
1063C22⋊C4—862no—
1064C22⋊C4—862no—
1065C22⋊C4—862no—
1066C22⋊C4—862no—
1067C22⋊C4—862no—
1068C22⋊C4—862no—
1069C22⋊C4—862no—
1070C22⋊C4—861no—
1071C22⋊C4—862no—
1072C22⋊C4—861no—
1073C22⋊C4C2×D17212yes—
1074C22⋊C4C2×D17212yes—
1075C22⋊C4C2×D17212yes—
1076C22⋊C4C2×D17212yes—
1077C42—862no—
1078C42—862no—
1079C42—862no—
1080C42—862no—
1081C42—862no—
1082C42—862no—
1083C42—861no—
1084C42—862no—
1085C42C2×D17212yes—
1086C42C2×D17212yes—
1087C42C23×D4312yes—
1088C42C23×D4312yes—
1089C23—22no—
1090C23—41no—
1091C23—41no—
1092C23—864no—
1093C23—861no—
1094C23—861no—
1095C23—862no—
1096C23—861no—
1097C23—3441no—
1098C23—3441no—
1099C23—3441no—
1100C23—3441no—
1101C23—1722no—
1102C23C22×D17211yescharacteristic
1103C23C22×D17211yescharacteristic
1104C23C22×D17211yescharacteristic
1105Q8—432no—
1106Q8—432no—
1107Q8—864no—
1108Q8—861no—
1109Q8—861no—
1110Q8—861no—
1111Q8—861no—
1112Q8—3442no—
1113D4—432no—
1114D4—432no—
1115D4—864no—
1116D4—864no—
1117D4—864no—
1118D4—864no—
1119D4—864no—
1120D4—861no—
1121D4—861no—
1122D4—862no—
1123D4—862no—
1124D4—861no—
1125D4—861no—
1126D4—3442no—
1127D4—3442no—
1128D4—3442no—
1129D4—3441no—
1130D4—1724no—
1131D4—1722no—
1132D4—1722no—
1133D4—1722no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—864no—
1144C2×C4—864no—
1145C2×C4—864no—
1146C2×C4—861no—
1147C2×C4—861no—
1148C2×C4—864no—
1149C2×C4—864no—
1150C2×C4—862no—
1151C2×C4—862no—
1152C2×C4—861no—
1153C2×C4—861no—
1154C2×C4—861no—
1155C2×C4—862no—
1156C2×C4—3442no—
1157C2×C4—3442no—
1158C2×C4—3442no—
1159C2×C4—3442no—
1160C2×C4—3442no—
1161C2×C4—3442no—
1162C2×C4—3442no—
1163C2×C4—3441no—
1164C2×C4—3441no—
1165C2×C4—3441no—
1166C2×C4—1722no—
1167C2×C4C22×D17211yescharacteristic
1168C2×C4C22×D17212yes—
1169C2×C4C22×D17211yescharacteristic
1170C2×C4C22×D17212yes—
1171C2×C4C22×D17212yes—
1172C2×C4C22×D17212yes—
1173C2×C4C22×D17211yescharacteristic
1174C2×C4#41×D4312yes—
1175C2×C4#41×D4312yes—
1176C2×C4C24×D4311yescharacteristic
1177C8—21no—
1178C8—21no—
1179C8—21no—
1180C8—21no—
1181C8—22no—
1182C8—22no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—82no—
1192C22—862no—
1193C22—862no—
1194C22—3444no—
1195C22—1722no—
1196C22—1721no—
1197C22—1721no—
1198C22—1722no—
1199C22—1721no—
1200C22—1722no—
1201C22—1721no—
1202C22—1721no—
1203C22—1721no—
1204C22—1721no—
1205C22—6882no—
1206C22#1458341112yes—
1207C22C23×D17211yescharacteristic
1208C4—22no—
1209C4—22no—
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—22no—
1214C4—862no—
1215C4—862no—
1216C4—1722no—
1217C4—1721no—
1218C4—1721no—
1219C4—1722no—
1220C4—1722no—
1221C4—1721no—
1222C4#1458341112yes—
1223C4C2×#41×D4311yescharacteristic
1224C4C2×#41×D4311yescharacteristic
1225C2—22no—
1226C2—41no—
1227C2—41no—
1228C2—3442no—
1229C2—3441no—
1230C2—1722no—
1231C2—1722no—
1232C2C2×#1458341111yescharacteristic
1233C2#1914936911yescharacteristic
1234C2#1914937611yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2924C2
socleC22×C43C23×D4
hypercenter#2924D43
hypocenterC43#60587
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19148330C2semidirect
2. #19147796C2semidirect
3. #19144887C2semidirect
4. #19144839C2semidirect
5. #19144826C2semidirect
6. #19144781C2semidirect
7. #19144747C2semidirect
8. #19144706C2semidirect
9. #19144656C2semidirect
10. #19144615C2semidirect
11. #19144528C2semidirect
12. C2×#14583224C2semidirect
13. #19144459C2semidirect
14. #19144448C2semidirect
15. #19144136C2semidirect
16. #19144136C2semidirect
17. #19143849C2semidirect
18. #19143817C2semidirect
19. #19143480C2semidirect
20. #19143472C2semidirect
21. #19143429C2semidirect
22. #19143429C2semidirect
23. C43×#2924C2semidirect
35. #14583527C22semidirect
38. #14583468C22semidirect
39. #14583449C22semidirect
40. #14583433C22semidirect
49. #14583379C22semidirect
50. #14583376C22semidirect
51. #14583373C22semidirect
52. #14583373C22semidirect
54. C4×#10621898C22semidirect
55. C4×#10621898C22semidirect
60. #14583241C22semidirect
61. #14583241C22semidirect
64. #14583224C22semidirect
65. #14583224C22semidirect
66. #14583224C22semidirect
67. #14583224C22semidirect
68. #14583207C22semidirect
69. #14583207C22semidirect
70. #14583200C22semidirect
71. #14583200C22semidirect
72. #14583195C22semidirect
73. #14583190C22semidirect
74. #14583185C22semidirect
75. #14583180C22semidirect
76. #14583122C22semidirect
77. #14583122C22semidirect
78. #14583115C22semidirect
79. #14583115C22semidirect
80. #14583100C22semidirect
81. #14583100C22semidirect
82. #14583095C22semidirect
83. #14583095C22semidirect
84. #14583063C22semidirect
85. #14583063C22semidirect
86. #14583057C22semidirect
87. #14583052C22semidirect
90. #14583046C22semidirect
91. #14583046C22semidirect
93. #14583040C22semidirect
95. #14583035C22semidirect
96. #14583012C22semidirect
97. #14583012C22semidirect
98. #14583012C22semidirect
99. #14583007C22semidirect
100. #14583001C22semidirect
101. #14583001C22semidirect
102. #14583001C22semidirect
103. #14583001C22semidirect
104. C4×Dic172C22semidirect
105. C4×#10621873C22semidirect
106. C4×#10621873C22semidirect
107. C4×#10621873C22semidirect
108. C4×#10621873C22semidirect
109. C4×D344C22semidirect
110. C4×D344C22semidirect
111. C4×D344C22semidirect
112. #14582941C22semidirect
113. #14582941C22semidirect
114. C2×#13063259C22semidirect
115. C2×#13063257C22semidirect
118. #14582901C22semidirect
119. #14582901C22semidirect
122. C2×#13063247C22semidirect
123. C2×#13063247C22semidirect
125. C43×#433C22semidirect
126. C43×#433C22semidirect
127. C43×#432C22semidirect
128. C43×#431C22semidirect
129. C43×#424C22semidirect
130. C43×#424C22semidirect
133. C43×#405C22semidirect
134. C43×#405C22semidirect
357. #10621898#41semidirect
358. #10621898#41semidirect
630. #2924D43semidirect
730. #433C2×D43semidirect
731. #433C2×D43semidirect
732. #432C2×D43semidirect
733. #431C2×D43semidirect
738. #424C2×D43semidirect
739. #424C2×D43semidirect
750. #405C2×D43semidirect
751. #405C2×D43semidirect
752. C43#60587semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191483302
#191477962
#191448872
#191448392
#191448262
#191447812
#191447472
#191447062
#191446562
#191446152
#191445282
C2×#145832242
#191444592
#191444482
#191441362
#191438492
#191438172
#191434802
#191434722
#191434292
C43×#29242
#6058743