Finite Group Databasebeta

← #25063639

Subgroups — #25063639

Order 11008.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148210C211yesmaximal, characteristic
2#19143239C211yesmaximal, characteristic, complemented
3#19133067C211yesmaximal, characteristic, complemented
4#19133058C211yesmaximal, characteristic, complemented
5#19133053C211yesmaximal, characteristic, complemented
6#19133041C211yesmaximal, characteristic, complemented
7#19133027C211yesmaximal, characteristic, complemented
8#19133023C211yesmaximal, characteristic, complemented
9#19133006C211yesmaximal, characteristic, complemented
10#19133001C211yesmaximal, characteristic, complemented
11#19132997C211yesmaximal, characteristic, complemented
12#19132989C211yesmaximal, characteristic, complemented
13#19132980C211yesmaximal, characteristic, complemented
14C2×#14582629C211yesmaximal, characteristic, complemented
15C43×#2990C211yesmaximal, characteristic, complemented
16#14583627C411yescharacteristic
17#14583622C411yescharacteristic
18#14583617—21no—
19#14583589C411yescharacteristic
20#14583589C411yescharacteristic
21#14583582—21no—
22#14583582—21no—
23D4×Dic86C411yescharacteristic
24#14583558C411yescharacteristic
25#14583558C411yescharacteristic
26#14583553C411yescharacteristic
27#14583548—21no—
28#14583456C2211yescharacteristic
29#14583453—21no—
30#14583433C2211yescharacteristic
31#14583433C2211yescharacteristic
32#14583429—21no—
33#14583429—21no—
34C4×#10621898C2211yescharacteristic
35C4×#10621900—21no—
36C2×C4×Dic86C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38#14582960—21no—
39#14582960—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582926—21no—
45#14582866—21no—
46C4×#10621877C2211yescharacteristic
47C2×C4×C43⋊C8C2211yescharacteristic
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582629C2211yescharacteristic
51#14582629C2211yescharacteristic
52#14582629C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582629C2211yescharacteristic
56#14582629C2211yescharacteristic
57#14582629C2211yescharacteristic
58#14582629C2211yescharacteristic
59#14582629C2211yescharacteristic
60#14582626C2211yescharacteristic
61#14582626C2211yescharacteristic
62#14582626C2211yescharacteristic
63#14582626C2211yescharacteristic
64C4×#41×C43C2211yescharacteristic
65C43×#446—21no—
66C43×#435—21no—
67C43×#435—21no—
68C8×D4×C43—21no—
69C43×#432C2211yescharacteristic
70C43×#432C2211yescharacteristic
71C43×#431C2211yescharacteristic
72C43×#423C2211yescharacteristic
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×#10621900—21no—
77C22×Dic86C2×C411yescharacteristic
78C22×Dic86C2×C411yescharacteristic
79C2×#10621877—21no—
80C22×C43⋊C8—21no—
81#13063325C2×C411yescharacteristic
82#13063325C2×C411yescharacteristic
83#13063324—21no—
84#13063323—21no—
85#13063320—21no—
86#13063320—21no—
87#13063319—21no—
88#13063319—21no—
89#13063318—21no—
90#13063318—21no—
91#13063317—21no—
92#13063317C2×C411yescharacteristic
93#13063317C2×C411yescharacteristic
94#13063315—21no—
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063313C2×C411yescharacteristic
99#13063313C2×C411yescharacteristic
100#13063311—21no—
101#13063311—21no—
102#13063309—21no—
103#13063309—21no—
104#13063308—21no—
105#13063308—21no—
106#13063306—21no—
107#13063306—21no—
108#13063305—21no—
109#13063304—21no—
110#13063304C2×C411yescharacteristic
111#13063304C2×C411yescharacteristic
112#13063304C2×C411yescharacteristic
113#13063304C2×C411yescharacteristic
114#13063303—21no—
115#13063303—21no—
116#13063302—21no—
117#13063302—21no—
118#13063301—21no—
119#13063299C2×C411yescharacteristic
120#13063299C2×C411yescharacteristic
121#13063297—21no—
122#13063297—21no—
123C4×Dic86—21no—
124C4×Dic86—21no—
125C4×Dic86—21no—
126C4×Dic86—21no—
127C4×Dic86—21no—
128C4×Dic86C2×C411yescharacteristic
129C4×Dic86C2×C411yescharacteristic
130C4×Dic86C2×C411yescharacteristic
131C4×Dic86C2×C411yescharacteristic
132C4×Dic86C2×C411yescharacteristic
133C4×Dic86C2311yescharacteristic
134C4×Dic86C2311yescharacteristic
135C4×Dic86C2311yescharacteristic
136#13063290—21no—
137C4×D172C2×C411yescharacteristic
138C4×D172C2311yescharacteristic
139D4×Dic43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144(C22⋊D43)⋊C4—21no—
145(C22⋊D43)⋊C4—21no—
146#13063284—21no—
147#13063284C2×C411yescharacteristic
148#13063283—21no—
149#13063282—21no—
150#13063282—21no—
151#13063282—21no—
152#13063281—21no—
153#13063281—21no—
154C2×C4⋊Dic43C2×C411yescharacteristic
155C2×C4⋊Dic43C2×C411yescharacteristic
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C2×C4×Dic43—21no—
159C2×C4×Dic43—21no—
160C42×D43—21no—
161C4⋊(C43⋊C8)—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)—21no—
168C22⋊(C43⋊C8)—21no—
169#13063236—21no—
170C4×C43⋊C8—21no—
171C4×C43⋊C8C2311yescharacteristic
172C4×C43⋊C8C2311yescharacteristic
173C4×C43⋊C8C2311yescharacteristic
174C4×C43⋊C8C2311yescharacteristic
175C2×#41×C43D411yescharacteristic
176C2×M16×C43—21no—
177C22×C8×C43—21no—
178C22×C8×C43—21no—
179C4×Q8×C43C2×C411yescharacteristic
180C4×Q8×C43D411yescharacteristic
181C4×D4×C43C2×C411yescharacteristic
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43C2×C411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187#117×C43D411yescharacteristic
188#117×C43D411yescharacteristic
189#117×C43D411yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43—21no—
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C4⋊C8×C43C2311yescharacteristic
197C4⋊C8×C43C2311yescharacteristic
198C4⋊C8×C43C2311yescharacteristic
199C4⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43—21no—
203#97×C43—21no—
204#97×C43—21no—
205C4×C8×C43—21no—
206#41×C43—42no—
207C2×Q8×C43C22⋊C411yescharacteristic
208C2×D4×C43C22⋊C411yescharacteristic
209C2×D4×C43C22⋊C411yescharacteristic
210C2×D4×C43C22⋊C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227#10621900—44no—
228#10621898—22no—
229#10621898—41no—
230C2×D172C22×C411yescharacteristic
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×Dic86—22no—
235C2×Dic86—22no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—41no—
240C2×Dic86—41no—
241C2×Dic86C22×C411yescharacteristic
242C2×Dic86C22×C411yescharacteristic
243C2×Dic86C22×C411yescharacteristic
244M16×C43—81no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—81no—
250C2×C8×C43—81no—
251C4⋊C4×C43C22⋊C411yescharacteristic
252C4⋊C4×C43C22⋊C411yescharacteristic
253C4⋊C4×C43C22⋊C411yescharacteristic
254C4⋊C4×C43C22⋊C411yescharacteristic
255C4⋊C4×C43C22⋊C411yescharacteristic
256C4⋊C4×C43C22⋊C411yescharacteristic
257C22⋊C4×C43C22⋊C411yescharacteristic
258C22⋊C4×C43C22⋊C411yescharacteristic
259C22⋊C4×C43C22⋊C411yescharacteristic
260C22⋊C4×C43C22⋊C411yescharacteristic
261C22⋊C4×C43C22⋊C411yescharacteristic
262C22⋊C4×C43C22⋊C411yescharacteristic
263C42×C43C22×C411yescharacteristic
264C42×C43C22×C411yescharacteristic
265C42×C43C22×C411yescharacteristic
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2×D411yescharacteristic
269C42×C43C2×D411yescharacteristic
270C42×C43C2×D411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2411yescharacteristic
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43C22×C411yescharacteristic
292C4⋊Dic43C22×C411yescharacteristic
293C4⋊Dic43C22×C411yescharacteristic
294C4⋊Dic43C22×C411yescharacteristic
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320#10621877—42no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—42no—
326C23×C43C2×C22⋊C411yescharacteristic
327C23×C43C2×C22⋊C411yescharacteristic
328C23×C43C2×C22⋊C411yescharacteristic
329C22×D43—21no—
330Q8×C43—41no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—41no—
334C2×C4×C43—22no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C2×C22⋊C411yescharacteristic
357C2×C4×C43C2×C22⋊C411yescharacteristic
358C2×C4×C43C23×C411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C22⋊D43—42no—
362C22⋊D43—42no—
363C22⋊D43—42no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—21no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—42no—
374C2×Dic43—42no—
375D172—21no—
376D172—21no—
377C4×D43—42no—
378C4×D43—42no—
379C4×D43—41no—
380C4×D43—41no—
381Dic86—21no—
382Dic86—21no—
383Dic86—21no—
384Dic86—21no—
385Dic86—21no—
386Dic86—42no—
387Dic86—42no—
388Dic86—42no—
389Dic86#13112yes—
390C8×C43—41no—
391C8×C43—41no—
392C8×C43—41no—
393C8×C43—41no—
394C43⋊C8—41no—
395C43⋊C8—41no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398#17524—431nomaximal, Sylow
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43#42112yes—
408C22×C43C22×C22⋊C411yescharacteristic
409C2×D43—41no—
410C2×D43—41no—
411C2×D43—41no—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—21no—
422C4×C43C2×#13111yescharacteristic
423C4×C43#56811yescharacteristic
424C4×C43#57711yescharacteristic
425C4×C43#57811yescharacteristic
426Dic43—22no—
427Dic43—41no—
428Dic43—41no—
429Dic43—41no—
430Dic43—41no—
431Dic43—41no—
432Dic43—41no—
433#3482—431no—
434#2990D4311yescharacteristic, complemented
435#2922—431no—
436#1497—431no—
437#1495—431no—
438#1494—431no—
439#1491—431no—
440#1488—431no—
441#1487—431no—
442#1483—431no—
443#1482—431no—
444#1481—431no—
445#1479—431no—
446#1477—431no—
447C2×Q8⋊C8—431no—
448C2×C43—22no—
449C2×C43—41no—
450C2×C43—41no—
451C2×C43#288011yescharacteristic
452C2×C43#289811yescharacteristic
453C2×C43C2×#42111yescharacteristic
454D43—81no—
455#557—431no—
456#556—431no—
457#556—861no—
458#552—431no—
459#552—431no—
460#552—861no—
461#552—861no—
462D4×Q8—431no—
463#548—431no—
464#548—431no—
465#547—431no—
466#547—861no—
467#533—431no—
468#533—861no—
469#529—431no—
470#529—431no—
471#529—861no—
472#529—861no—
473C4×#41—431no—
474C4×#41—861no—
475C4×#41C2×D4311yescharacteristic
476C2×C4×Q8—431no—
477C2×C4×Q8—431no—
478#446—21no—
479#435—21no—
480#435—21no—
481C8×D4—21no—
482#433—861no—
483#433—861no—
484#432C2×D4311yescharacteristic
485#432C2×D4311yescharacteristic
486#431—431no—
487#431—431no—
488#431—431no—
489#431—431no—
490#431C2×D4311yescharacteristic
491#424—861no—
492#423C2×D4311yescharacteristic
493C2×C4⋊C8C2×D4311yescharacteristic
494C2×C4⋊C8C2×D4311yescharacteristic
495#408—861no—
496C4×M16—431no—
497C2×C4×C8—431no—
498Q8⋊C8—431no—
499Q8⋊C8—431no—
500Q8⋊C8—431no—
501Q8⋊C8—431no—
502Q8⋊C8—431no—
503Q8⋊C8—431no—
504Q8⋊C8—431no—
505Q8⋊C8—431no—
506Q8⋊C8—431no—
507Q8⋊C8—431no—
508Q8⋊C8—431no—
509Q8⋊C8—431no—
510D4⋊C8—431no—
511D4⋊C8—431no—
512D4⋊C8—431no—
513D4⋊C8—431no—
514C43#1752411yescharacteristic, complemented, Sylow
515C2×#41—431no—
516C2×#41—861no—
517C2×#41D17211yescharacteristic
518C22×Q8—431no—
519C22×Q8—431no—
520C2×M16—21no—
521C2×M16—861no—
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—861no—
525C4⋊Q8—431no—
526C4⋊Q8—431no—
527C4⋊Q8—861no—
528C4⋊Q8—861no—
529#126—861no—
530#126—861no—
531#126—861no—
532#126—861no—
533#126—861no—
534#126—861no—
535#125—431no—
536#125—431no—
537#125—861no—
538#125—861no—
539#125—861no—
540#125—861no—
541#125—861no—
542#124—431no—
543#124—431no—
544#124—861no—
545#124—861no—
546#123—861no—
547#123—861no—
548#123—861no—
549#123—861no—
550#123—861no—
551#123—861no—
552C22⋊Q8—431no—
553C22⋊Q8—431no—
554C22⋊Q8—431no—
555C22⋊Q8—431no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561C22⋊Q8—861no—
562C22⋊Q8—861no—
563#121—431no—
564#121—431no—
565#121—861no—
566#121—861no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—431no—
571C4×Q8—431no—
572C4×Q8—431no—
573C4×Q8—431no—
574C4×Q8—431no—
575C4×Q8—861no—
576C4×Q8—861no—
577C4×Q8—861no—
578C4×Q8—861no—
579C4×Q8—861no—
580C4×Q8—861no—
581C4×Q8C4×D4311yescharacteristic
582C4×Q8C22⋊D4311yescharacteristic
583C4×D4—431no—
584C4×D4—431no—
585C4×D4—861no—
586C4×D4—861no—
587C4×D4—861no—
588C4×D4—861no—
589C4×D4—861no—
590C4×D4—861no—
591C4×D4—861no—
592C4×D4C4×D4311yescharacteristic
593C4×D4C4×D4311yescharacteristic
594C4×D4C4×D4311yescharacteristic
595C4×D4C22⋊D4311yescharacteristic
596C4×D4C22⋊D4311yescharacteristic
597C4×D4C22⋊D4311yescharacteristic
598#117—431no—
599#117—861no—
600#117—861no—
601#117—861no—
602#117—861no—
603#117—861no—
604#117—861no—
605#117—861no—
606#117D17211yescharacteristic
607#117D17211yescharacteristic
608#117D17211yescharacteristic
609C2×C4⋊C4—431no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4—861no—
613C2×C42—861no—
614C2×C42—861no—
615C2×C42—861no—
616C2×C42C22×D4311yescharacteristic
617C2×C42C22×D4311yescharacteristic
618C2×C42C22×D4311yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622C4⋊C8—861no—
623C4⋊C8—861no—
624C4⋊C8—861no—
625C4⋊C8—861no—
626C4⋊C8C22×D4311yescharacteristic
627C4⋊C8C22×D4311yescharacteristic
628C4⋊C8C22×D4311yescharacteristic
629C4⋊C8C22×D4311yescharacteristic
630C22⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—861no—
634C22⋊C8—861no—
635C22⋊C8—861no—
636C22⋊C8—861no—
637#97—21no—
638#97—21no—
639#97—861no—
640C4×C8—21no—
641C4×C8—431no—
642C4×C8—431no—
643C4×C8—431no—
644C4×C8—431no—
645C4×C8—861no—
646#41—42no—
647#41—862no—
648#41—1721no—
649#41—1724no—
650C2×Q8—431no—
651C2×Q8—431no—
652C2×Q8—431no—
653C2×Q8—862no—
654C2×Q8—862no—
655C2×Q8—861no—
656C2×Q8—861no—
657C2×Q8—861no—
658C2×Q8—1721no—
659C2×Q8—1721no—
660C2×Q8(C2×D43)⋊C411yescharacteristic
661C2×D4—431no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4(C2×D43)⋊C411yescharacteristic
666C2×D4(C2×D43)⋊C411yescharacteristic
667C2×D4(C2×D43)⋊C411yescharacteristic
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4C2×C4×D4311yescharacteristic
676C22×C4C2×C4×D4311yescharacteristic
677C22×C4C2×C4×D4311yescharacteristic
678C22×C4C2×D17211yescharacteristic
679C22×C4C2×D17211yescharacteristic
680C22×C4C2×D17211yescharacteristic
681C22×C4C2×C22⋊D4311yescharacteristic
682C22×C4C2×C22⋊D4311yescharacteristic
683C22×C4C2×C22⋊D4311yescharacteristic
684M16—81no—
685M16—1722no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—81no—
691C2×C8—81no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—1722no—
697C4⋊C4—431no—
698C4⋊C4—431no—
699C4⋊C4—431no—
700C4⋊C4—431no—
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—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4(C2×D43)⋊C411yescharacteristic
723C4⋊C4(C2×D43)⋊C411yescharacteristic
724C4⋊C4(C2×D43)⋊C411yescharacteristic
725C4⋊C4(C2×D43)⋊C411yescharacteristic
726C4⋊C4(C2×D43)⋊C411yescharacteristic
727C4⋊C4(C2×D43)⋊C411yescharacteristic
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(C2×D43)⋊C411yescharacteristic
742C22⋊C4(C2×D43)⋊C411yescharacteristic
743C22⋊C4(C2×D43)⋊C411yescharacteristic
744C22⋊C4(C2×D43)⋊C411yescharacteristic
745C22⋊C4(C2×D43)⋊C411yescharacteristic
746C22⋊C4(C2×D43)⋊C411yescharacteristic
747C42—861no—
748C42—861no—
749C42—861no—
750C42—861no—
751C42—861no—
752C42—861no—
753C42—861no—
754C42—861no—
755C42—861no—
756C42C2×C4×D4311yescharacteristic
757C42C2×C4×D4311yescharacteristic
758C42C2×C4×D4311yescharacteristic
759C42C2×D17211yescharacteristic
760C42C2×D17211yescharacteristic
761C42C2×D17211yescharacteristic
762C42C2×C22⋊D4311yescharacteristic
763C42C2×C22⋊D4311yescharacteristic
764C42C2×C22⋊D4311yescharacteristic
765C42C23×D4311yescharacteristic
766C23—861no—
767C23C2×(C2×D43)⋊C411yescharacteristic
768C23C2×(C2×D43)⋊C411yescharacteristic
769C23C2×(C2×D43)⋊C411yescharacteristic
770Q8—41no—
771Q8—432no—
772Q8—861no—
773Q8—861no—
774Q8—861no—
775Q8—861no—
776Q8—861no—
777Q8—1722no—
778Q8—1722no—
779Q8—1722no—
780D4—22no—
781D4—22no—
782D4—41no—
783D4—861no—
784D4—861no—
785D4—1722no—
786D4—1722no—
787D4—1722no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4—1722no—
813C2×C4—1722no—
814C2×C4—1722no—
815C2×C4—1722no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4C2×(C2×D43)⋊C411yescharacteristic
819C2×C4C2×(C2×D43)⋊C411yescharacteristic
820C2×C4C2×(C2×D43)⋊C411yescharacteristic
821C2×C4C2×(C2×D43)⋊C411yescharacteristic
822C2×C4C2×(C2×D43)⋊C411yescharacteristic
823C2×C4C2×(C2×D43)⋊C411yescharacteristic
824C2×C4C2×(C2×D43)⋊C411yescharacteristic
825C2×C4C2×(C2×D43)⋊C411yescharacteristic
826C2×C4C2×(C2×D43)⋊C411yescharacteristic
827C2×C4C22×C4×D4311yescharacteristic
828C2×C4C22×C22⋊D4311yescharacteristic
829C2×C4C22×D17211yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—1721no—
835C8—1721no—
836C8—1721no—
837C8—1721no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—1721no—
847C22—1721no—
848C22—1721no—
849C22#1458291512yes—
850C22C22×(C2×D43)⋊C411yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—862no—
862C4—1721no—
863C4—1721no—
864C4—1721no—
865C4—1721no—
866C4—1721no—
867C4—1721no—
868C4#131×D4311yescharacteristic
869C4#1458366411yescharacteristic
870C4#1458371011yescharacteristic
871C4#1458371411yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—3441no—
876C2#1914304211yescharacteristic
877C2#1914312511yescharacteristic
878C2C2×#1458291511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2990C2
socleC22×C43C22×C22⋊C4
prime radical#19148210C2
cosocleC42×C43C24
hypercenter#2990D43
hypocenterC43#17524
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #19143239C2semidirect
3. #19133067C2semidirect
4. #19133058C2semidirect
5. #19133053C2semidirect
6. #19133041C2semidirect
7. #19133027C2semidirect
8. #19133023C2semidirect
9. #19133006C2semidirect
10. #19133001C2semidirect
11. #19132997C2semidirect
12. #19132989C2semidirect
13. #19132980C2semidirect
14. C2×#14582629C2semidirect
15. C43×#2990C2semidirect
434. #2990D43semidirect
514. C43#17524semidirect

Maximal subgroups

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

subgroupindex
#191482102
#191432392
#191330672
#191330582
#191330532
#191330412
#191330272
#191330232
#191330062
#191330012
#191329972
#191329892
#191329802
C2×#145826292
C43×#29902
#1752443