Finite Group Databasebeta

← #25106405

Subgroups — #25106405

Order 11008.

1158 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583426C211yesmaximal, characteristic
2#19136998C211yesmaximal, characteristic, complemented
3#19136986C211yesmaximal, characteristic, complemented
4#19135578C212yesmaximal, complemented
5#19135429C212yesmaximal
6#19135054C211yesmaximal, characteristic, complemented
7#19135053C211yesmaximal, characteristic, complemented
8#19135051C211yesmaximal, characteristic, complemented
9#19134582C212yesmaximal, complemented
10#19134581C212yesmaximal, complemented
11C43×#1899C211yesmaximal, characteristic, complemented
12#14583426—21no—
13#14583426—21no—
14#14583426—21no—
15#14583426—21no—
16#14583426—21no—
17#14583426—21no—
18#14583426—21no—
19#14583426—21no—
20C2×#13063320C411yescharacteristic, complemented
21C2×#13063318C411yescharacteristic, complemented
22C2×#13063315C411yescharacteristic, complemented
23C2×#13063311C411yescharacteristic, complemented
24C2×#13063308C2211yescharacteristic
25C2×#13063302C2211yescharacteristic
26C2×#13063297C2211yescharacteristic
27C2×#13063290C411yescharacteristic, complemented
28C2×D4×Dic43C2211yescharacteristic
29C2×(C22⋊D43)⋊C4C411yescharacteristic, complemented
30C2×(C22⋊D43)⋊C4C2211yescharacteristic
31C2×#13063284C2211yescharacteristic
32C2×#13063283C411yescharacteristic, complemented
33C2×#13063281C411yescharacteristic, complemented
34C22×C4×Dic43C2211yescharacteristic
35C2×#13063240C2212yes—
36C2×#13063239C2212yes—
37C2×#13063239C2212yes—
38#14582768—21no—
39#14582766—21no—
40#14582764—21no—
41#14582763—21no—
42#14582762C2211yescharacteristic
43#14582757C2212yes—
44#14582757C2212yes—
45#14582757C2212yes—
46C4×Dic43⋊C4—21no—
47C4×Dic43⋊C4—21no—
48#14582750—21no—
49C22⋊C4×Dic43C2212yes—
50#14582744—21no—
51#14582666C2212yes—
52#14582665C2212yes—
53#14582665C2212yes—
54C2×#123×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C2×#99×C43C2212yes—
57C43×#381C2211yescharacteristic
58C43×#342C2212yes—
59C22×Dic86C2×C411yescharacteristic
60C22×C22⋊D43C2×C411yescharacteristic
61C22×C22⋊D43C2311yescharacteristic
62C23×Dic43C2×C411yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C22×C4×D43C2×C411yescharacteristic
66#13063320—21no—
67#13063320—21no—
68#13063320—21no—
69#13063320—21no—
70#13063318—21no—
71#13063318—21no—
72#13063318—21no—
73#13063318—21no—
74#13063315—21no—
75#13063315—21no—
76#13063315—21no—
77#13063315—21no—
78#13063311—21no—
79#13063311—21no—
80#13063311—21no—
81#13063311—21no—
82#13063308—21no—
83#13063308—21no—
84#13063308—21no—
85#13063308—21no—
86#13063302—21no—
87#13063302—21no—
88#13063302—21no—
89#13063302—21no—
90#13063297—21no—
91#13063297—21no—
92#13063297—21no—
93#13063297—21no—
94#13063290—21no—
95#13063290—21no—
96#13063290—21no—
97#13063290—21no—
98D4×Dic43—21no—
99D4×Dic43—21no—
100D4×Dic43—21no—
101D4×Dic43—21no—
102(C22⋊D43)⋊C4—21no—
103(C22⋊D43)⋊C4—21no—
104(C22⋊D43)⋊C4—21no—
105(C22⋊D43)⋊C4—21no—
106(C22⋊D43)⋊C4—21no—
107(C22⋊D43)⋊C4—21no—
108(C22⋊D43)⋊C4—21no—
109(C22⋊D43)⋊C4—21no—
110#13063284—42no—
111#13063283—21no—
112#13063283—21no—
113#13063283—21no—
114#13063283—21no—
115#13063281—21no—
116#13063281—21no—
117#13063281—21no—
118#13063281—21no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43C2×C411yescharacteristic
121C2×C4⋊Dic43C2×C411yescharacteristic
122C2×Dic43⋊C4—22no—
123C2×Dic43⋊C4—22no—
124C2×Dic43⋊C4—22no—
125C2×Dic43⋊C4C2×C411yescharacteristic
126C2×Dic43⋊C4C2×C411yescharacteristic
127C2×Dic43⋊C4C2×C411yescharacteristic
128C2×Dic43⋊C4C2×C411yescharacteristic
129C2×Dic43⋊C4C2×C411yescharacteristic
130C2×Dic43⋊C4C2×C411yescharacteristic
131C2×C22⋊Dic43C2×C411yescharacteristic
132C2×C22⋊Dic43C2×C411yescharacteristic
133C2×C22⋊Dic43C2312yes—
134C2×C22⋊Dic43C2312yes—
135C2×C22⋊Dic43C2311yescharacteristic
136C2×(C2×D43)⋊C4C2×C411yescharacteristic
137C2×(C2×D43)⋊C4C2×C411yescharacteristic
138C2×(C2×D43)⋊C4C2×C411yescharacteristic
139C2×(C2×D43)⋊C4C2×C411yescharacteristic
140C2×C4×Dic43—21no—
141C2×C4×Dic43—22no—
142C2×C4×Dic43C2×C411yescharacteristic
143C2×C4×Dic43C2×C411yescharacteristic
144C2×C4×Dic43C2×C411yescharacteristic
145C2×C4×Dic43C2×C411yescharacteristic
146C2×C4×Dic43C2×C411yescharacteristic
147C2×C4×Dic43C2×C411yescharacteristic
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43D411yescharacteristic
151C2×C4×Dic43D411yescharacteristic
152C2×C4×Dic43D411yescharacteristic
153C2×C4×Dic43D411yescharacteristic
154C2×C4×Dic43D411yescharacteristic
155C2×C4×Dic43D411yescharacteristic
156#13063240—42no—
157#13063239—42no—
158#13063239—42no—
159C43⋊#95—21no—
160C43⋊#95—21no—
161C43⋊#95—22no—
162C43⋊#95—22no—
163C43⋊#95—22no—
164C43⋊#95—22no—
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167#123×C43—21no—
168#123×C43—21no—
169#123×C43—21no—
170#123×C43—21no—
171#117×C43—42no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2×C411yescharacteristic
174C2×C4⋊C4×C43C2×C411yescharacteristic
175C2×C22⋊C4×C43C2×C411yescharacteristic
176C2×C22⋊C4×C43C2×C411yescharacteristic
177C2×C22⋊C4×C43C2312yes—
178C2×C22⋊C4×C43C2312yes—
179C2×C22⋊C4×C43C2311yescharacteristic
180C2×C42×C43—21no—
181#99×C43—42no—
182#95×C43—21no—
183#95×C43—21no—
184C24×C43C22×C411yescharacteristic
185C24×C43C2411yescharacteristic
186C23×D43C22×C411yescharacteristic
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43C22×C411yescharacteristic
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C22×C411yescharacteristic
198C22×C4×C43C22×C411yescharacteristic
199C22×C4×C43C22×C411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C2×C22⋊D43—21no—
205C2×C22⋊D43—21no—
206C2×C22⋊D43—21no—
207C2×C22⋊D43—21no—
208C2×C22⋊D43—22no—
209C2×C22⋊D43—22no—
210C2×C22⋊D43—42no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—42no—
216C22×Dic43—42no—
217C22×Dic43—42no—
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C411yescharacteristic
220C22×Dic43C22×C411yescharacteristic
221C22×Dic43C22×C411yescharacteristic
222C22×Dic43C22×C411yescharacteristic
223C22×Dic43C22×C411yescharacteristic
224C22×Dic43C22×C411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—42no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—42no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—42no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—21no—
249C22⋊C4×C43—21no—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—22no—
254C42×C43—42no—
255C22⋊Dic43—21no—
256C22⋊Dic43—21no—
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261C22⋊Dic43—22no—
262C22⋊Dic43—22no—
263C22⋊Dic43—22no—
264C22⋊Dic43—22no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—42no—
278Dic43⋊C4—21no—
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—44no—
291Dic43⋊C4—44no—
292Dic43⋊C4—44no—
293C4×Dic43—21no—
294C4×Dic43—21no—
295C4×Dic43—21no—
296C4×Dic43—21no—
297C4×Dic43—44no—
298C4×Dic43—42no—
299C4×Dic43C22⋊C411yescharacteristic
300C4×Dic43C22⋊C411yescharacteristic
301C4×Dic43C22⋊C411yescharacteristic
302C4×Dic43C22⋊C411yescharacteristic
303C4×Dic43C22⋊C411yescharacteristic
304C4×Dic43C22⋊C411yescharacteristic
305C4×Dic43C22⋊C411yescharacteristic
306C4×Dic43C22⋊C411yescharacteristic
307C4×Dic43C22⋊C411yescharacteristic
308C4×Dic43C22⋊C411yescharacteristic
309C4×Dic43C22⋊C411yescharacteristic
310C4×Dic43C22⋊C411yescharacteristic
311C4×Dic43C22⋊C411yescharacteristic
312C4×Dic43C22⋊C411yescharacteristic
313C4×Dic43C22⋊C411yescharacteristic
314C4×Dic43C22⋊C411yescharacteristic
315C23×C43—21no—
316C23×C43—22no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43C23×C411yescharacteristic
322C23×C43C22×D411yescharacteristic
323C23×C43C22×D411yescharacteristic
324C23×C43H(5,𝔽2)12yes—
325C23×C432−1+412yes—
326C22×D43—21no—
327C22×D43—22no—
328C22×D43—41no—
329C22×D43—41no—
330D4×C43—41no—
331D4×C43—41no—
332D4×C43—42no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—22no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—42no—
348C2×C4×C43—42no—
349C2×C4×C43—42no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43—42no—
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C2×C22⋊C411yescharacteristic
357C22⋊D43—42no—
358C22⋊D43—41no—
359C22⋊D43—41no—
360C22⋊D43—42no—
361C22⋊D43—42no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—22no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—42no—
379C2×Dic43—42no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—42no—
383C2×Dic43—42no—
384C2×Dic43—42no—
385C2×Dic43—42no—
386C2×Dic43—42no—
387C2×Dic43—42no—
388C2×Dic43C2×C22⋊C411yescharacteristic
389C2×Dic43C2×C22⋊C411yescharacteristic
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394C2×Dic43C2×C22⋊C411yescharacteristic
395C2×Dic43C2×C22⋊C411yescharacteristic
396C4×D43—42no—
397C4×D43—42no—
398Dic86—42no—
399Dic86—42no—
400#21875—431nomaximal, Sylow
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—42no—
408C22×C43—42no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—82no—
413C22×C43C22×C22⋊C411yescharacteristic
414C22×C43#52012yes—
415C22×C43#53511yescharacteristic
416C22×C43#53611yescharacteristic
417C22×C43#53712yes—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—82no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—41no—
427C4×C43—41no—
428C4×C43—41no—
429C4×C43—82no—
430C4×C43—82no—
431Dic43—21no—
432Dic43—21no—
433Dic43—21no—
434Dic43—21no—
435Dic43—21no—
436Dic43—21no—
437Dic43—41no—
438Dic43—41no—
439Dic43—41no—
440Dic43—82no—
441Dic43—82no—
442Dic43#41012yes—
443Dic43#41012yes—
444C2×#529—431no—
445#2285—431no—
446#2283—431no—
447#1996—432no—
448#1964—432no—
449#1899—431no—
450#1899—431no—
451#1899—431no—
452#1899D4311yescharacteristic, complemented
453#1799—432no—
454#1799—432no—
455C2×C43—21no—
456C2×C43—22no—
457C2×C43—22no—
458C2×C43—21no—
459C2×C43—81no—
460C2×C43#231111yescharacteristic
461C2×C43C2×#41011yescharacteristic
462C2×C43C2×#41011yescharacteristic
463D43—81no—
464#529—861no—
465#529—861no—
466#529—861no—
467#529—861no—
468#529—861no—
469#529—861no—
470#529—861no—
471#529—861no—
472C2×#126—431no—
473C2×#126—431no—
474C2×#125—431no—
475C2×#124—431no—
476C2×#123—431no—
477C2×#123C2×D4311yescharacteristic
478C2×C22⋊Q8—431no—
479C2×#121—431no—
480C2×C4×Q8—431no—
481C2×C4×D4—431no—
482C2×C4×D4—431no—
483C2×C4×D4—431no—
484C2×#117—431no—
485C2×#117—431no—
486C2×#117—431no—
487C2×#117C2×D4311yescharacteristic
488C22×C42—431no—
489C2×#99—432no—
490C2×#99—432no—
491C2×#99—432no—
492C2×#99C2×D4312yes—
493#384—861no—
494#383—861no—
495#382—861no—
496#382—861no—
497#381—431no—
498#381C2×D4311yescharacteristic
499#380—432no—
500#380—432no—
501#380—432no—
502C4×C4⋊C4—861no—
503C4×C4⋊C4—861no—
504C4×C4⋊C4—861no—
505C4×C22⋊C4—432no—
506#376—861no—
507#342—432no—
508#342—432no—
509#342—432no—
510#342C2×D4312yes—
511C43#2187511yescharacteristic, complemented, Sylow
512C22×Q8—431no—
513C22×D4—431no—
514C22×D4—431no—
515C22×D4C22×D4311yescharacteristic
516C23×C4—431no—
517C23×C4—431no—
518C23×C4—431no—
519C23×C4—431no—
520C23×C4C22×D4311yescharacteristic
521#126—861no—
522#126—861no—
523#126—861no—
524#126—861no—
525#126—861no—
526#126—861no—
527#126—861no—
528#126—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125—861no—
533#124—861no—
534#124—861no—
535#124—861no—
536#124—861no—
537#123—21no—
538#123—21no—
539#123—21no—
540#123—21no—
541#123—861no—
542#123—861no—
543#123—861no—
544#123—861no—
545C22⋊Q8—861no—
546C22⋊Q8—861no—
547C22⋊Q8—861no—
548C22⋊Q8—861no—
549#121—861no—
550#121—861no—
551#121—861no—
552#121—861no—
553C4×Q8—861no—
554C4×Q8—861no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×D4—861no—
558C4×D4—861no—
559C4×D4—861no—
560C4×D4—861no—
561C4×D4—861no—
562C4×D4—861no—
563C4×D4—861no—
564C4×D4—861no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—861no—
568C4×D4—861no—
569#117—42no—
570#117—861no—
571#117—861no—
572#117—861no—
573#117—861no—
574#117—861no—
575#117—861no—
576#117—861no—
577#117—861no—
578#117—1722no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—431no—
581C2×C4⋊C4—431no—
582C2×C4⋊C4—431no—
583C2×C4⋊C4—431no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—431no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—862no—
589C2×C4⋊C4—862no—
590C2×C4⋊C4—862no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4C4×D4311yescharacteristic
593C2×C4⋊C4C4×D4311yescharacteristic
594C2×C22⋊C4—431no—
595C2×C22⋊C4—431no—
596C2×C22⋊C4—431no—
597C2×C22⋊C4—431no—
598C2×C22⋊C4—431no—
599C2×C22⋊C4—431no—
600C2×C22⋊C4—431no—
601C2×C22⋊C4—432no—
602C2×C22⋊C4—432no—
603C2×C22⋊C4C4×D4311yescharacteristic
604C2×C22⋊C4C4×D4311yescharacteristic
605C2×C22⋊C4C22×D4312yes—
606C2×C22⋊C4C22×D4312yes—
607C2×C22⋊C4C22×D4311yescharacteristic
608C2×C42—21no—
609C2×C42—431no—
610C2×C42—431no—
611C2×C42—431no—
612C2×C42—431no—
613C2×C42—431no—
614C2×C42—431no—
615C2×C42—431no—
616C2×C42—431no—
617C2×C42—431no—
618C2×C42—431no—
619C2×C42—431no—
620C2×C42—431no—
621C2×C42—431no—
622C2×C42—431no—
623C2×C42—862no—
624C2×C42—861no—
625#99—42no—
626#99—1722no—
627#99—1722no—
628#99—1722no—
629#95—21no—
630#95—21no—
631#95—862no—
632#95—862no—
633#95—862no—
634#95—862no—
635#95—861no—
636#95—861no—
637C24—431no—
638C24C2×C4×D4311yescharacteristic
639C24C23×D4311yescharacteristic
640C2×Q8—861no—
641C2×Q8—861no—
642C2×Q8—1722no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—862no—
652C2×D4—862no—
653C2×D4—1722no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—862no—
678C22×C4—862no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4—1722no—
683C22×C4C2×C4×D4311yescharacteristic
684C22×C4C2×C4×D4311yescharacteristic
685C22×C4C2×C4×D4311yescharacteristic
686C22×C4C2×C4×D4311yescharacteristic
687C22×C4C2×C4×D4311yescharacteristic
688C22×C4D4×D4311yescharacteristic
689C22×C4D4×D4311yescharacteristic
690C22×C4D4×D4311yescharacteristic
691C22×C4D4×D4311yescharacteristic
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—42no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—1722no—
714C4⋊C4—1724no—
715C4⋊C4—1724no—
716C4⋊C4—1724no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C22⋊C4—861no—
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C22⋊C4—861no—
741C22⋊C4—862no—
742C22⋊C4—862no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C42—42no—
746C42—431no—
747C42—431no—
748C42—431no—
749C42—431no—
750C42—431no—
751C42—431no—
752C42—431no—
753C42—431no—
754C42—431no—
755C42—431no—
756C42—431no—
757C42—431no—
758C42—431no—
759C42—431no—
760C42—431no—
761C42—431no—
762C42—861no—
763C42—861no—
764C42—861no—
765C42—861no—
766C42—1722no—
767C42—1724no—
768C23—21no—
769C23—22no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—862no—
775C23—861no—
776C23—1721no—
777C23—1721no—
778C23C22×C4×D4311yescharacteristic
779C23C2×D4×D4311yescharacteristic
780C23C2×D4×D4311yescharacteristic
781C23#1306337012yes—
782C23#1306337212yes—
783Q8—1722no—
784Q8—1722no—
785D4—41no—
786D4—41no—
787D4—42no—
788D4—1722no—
789D4—1722no—
790D4—1721no—
791D4—1721no—
792D4—1722no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—431no—
814C2×C4—431no—
815C2×C4—431no—
816C2×C4—431no—
817C2×C4—431no—
818C2×C4—431no—
819C2×C4—431no—
820C2×C4—431no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—861no—
828C2×C4—861no—
829C2×C4—861no—
830C2×C4—862no—
831C2×C4—1722no—
832C2×C4—1722no—
833C2×C4—1722no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4—1721no—
839C2×C4—1721no—
840C2×C4—1722no—
841C2×C4—1722no—
842C2×C4—1722no—
843C2×C4—1722no—
844C2×C4—1722no—
845C2×C4—1722no—
846C2×C4—1722no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4C22⋊C4×D4311yescharacteristic
850C2×C4C22⋊C4×D4311yescharacteristic
851C2×C4C22⋊C4×D4311yescharacteristic
852C2×C4C22⋊C4×D4311yescharacteristic
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—82no—
865C22—3442no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22C2×C22⋊C4×D4311yescharacteristic
870C22#1458337812yes—
871C22#1458346411yescharacteristic
872C22#1458347111yescharacteristic
873C22#1458347612yes—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—82no—
882C4—82no—
883C4—432no—
884C4—432no—
885C4—861no—
886C4—861no—
887C4—861no—
888C4—861no—
889C4—861no—
890C4—861no—
891C4—3442no—
892C4—3442no—
893C4—1721no—
894C4—1721no—
895C4—1721no—
896C2—21no—
897C2—22no—
898C2—22no—
899C2—21no—
900C2—81no—
901C2—3441no—
902C2#1913718211yescharacteristic
903C2#410×D4311yescharacteristic
904C2#410×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1899C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063297C22
cosocleC24×C43C24
hypercenter#1899D43
hypocenterC43#21875
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

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

NH ≅ G/Ntype
2. #19136998C2semidirect
3. #19136986C2semidirect
4. #19135578C2semidirect
6. #19135054C2semidirect
7. #19135053C2semidirect
8. #19135051C2semidirect
9. #19134582C2semidirect
10. #19134581C2semidirect
11. C43×#1899C2semidirect
20. C2×#13063320C4semidirect
21. C2×#13063318C4semidirect
22. C2×#13063315C4semidirect
23. C2×#13063311C4semidirect
27. C2×#13063290C4semidirect
29. C2×(C22⋊D43)⋊C4C4semidirect
32. C2×#13063283C4semidirect
33. C2×#13063281C4semidirect
452. #1899D43semidirect
511. C43#21875semidirect

Maximal subgroups

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

subgroupindex
C2×#145834262
#191369982
#191369862
#191355782
#191354292
#191350542
#191350532
#191350512
#191345822
#191345812
C43×#18992
#2187543