Finite Group Databasebeta

← #33091845

Subgroups — #33091845

Order 18688.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619149C211yesmaximal, characteristic
2C2×#17988707C211yesmaximal, characteristic, complemented
3C2×#17988702C211yesmaximal, characteristic, complemented
4#22618634C211yesmaximal, characteristic, complemented
5#22610258C211yesmaximal, characteristic, complemented
6#22610258C211yesmaximal, characteristic, complemented
7#22610233C211yesmaximal, characteristic, complemented
8#22610206C211yesmaximal, characteristic, complemented
9#22610206C211yesmaximal, characteristic, complemented
10#22610136C211yesmaximal, characteristic, complemented
11#22609875C211yesmaximal, characteristic, complemented
12#22609773C211yesmaximal, characteristic, complemented
13#22609766C211yesmaximal, characteristic, complemented
14#22609712C211yesmaximal, characteristic, complemented
15C2×#568×C73C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556597C2211yescharacteristic, complemented
19#17989098C2211yescharacteristic
20#17988749C411yescharacteristic, complemented
21#17988749C411yescharacteristic, complemented
22#17988743C411yescharacteristic, complemented
23#17988738C411yescharacteristic, complemented
24#17988732C411yescharacteristic, complemented
25#17988732C411yescharacteristic, complemented
26#17988726C411yescharacteristic, complemented
27#17988721C411yescharacteristic, complemented
28#17988707—24no—
29#17988702—24no—
30#17988663—21no—
31#17988663—21no—
32#17988656—21no—
33#17988656—21no—
34C2×#14556526C2211yescharacteristic, complemented
35C2×#14556526C2211yescharacteristic, complemented
36#17988613C2211yescharacteristic, complemented
37C2×#14556518C2211yescharacteristic
38C2×#14556518C2211yescharacteristic
39C2×#14556518C2211yescharacteristic
40C2×#14556518C2211yescharacteristic
41C2×#14556517C2211yescharacteristic, complemented
42C2×#14556517C2211yescharacteristic, complemented
43#17988583C2211yescharacteristic
44#17988583C2211yescharacteristic
45#17988553C2211yescharacteristic, complemented
46#17988551C2211yescharacteristic
47C2×C22⋊#10596831C2211yescharacteristic
48#17988542C2211yescharacteristic, complemented
49C2×#14556501C2211yescharacteristic, complemented
50C2×C8×Dic73C2211yescharacteristic, complemented
51C4×C22⋊Dic73C2211yescharacteristic
52#17988351C2211yescharacteristic, complemented
53#17988351C2211yescharacteristic, complemented
54#17988348C2211yescharacteristic, complemented
55#17988348C2211yescharacteristic, complemented
56#17988341C2211yescharacteristic, complemented
57#17988341C2211yescharacteristic, complemented
58C22×#41×C73C2211yescharacteristic
59#568×C73—24no—
60#568×C73—24no—
61C2×#131×C73—21no—
62C2×#131×C73—21no—
63C2×#131×C73C2211yescharacteristic
64C2×#131×C73C2211yescharacteristic
65C2×#131×C73C2211yescharacteristic
66C2×#131×C73C2211yescharacteristic
67C22×M16×C73—21no—
68C22×M16×C73—21no—
69C22×M16×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C2×#11924028C2311yescharacteristic
72#14556611—22no—
73#14556611—22no—
74#14556611—22no—
75#14556611—22no—
76C2×#11924018C2×C411yescharacteristic
77C2×#11924018C2×C411yescharacteristic
78C2×#11924016C2×C411yescharacteristic
79C2×#11924016C2×C411yescharacteristic
80C2×#11924015C2×C411yescharacteristic
81C2×#11924015C2×C411yescharacteristic
82C2×#11924013C2×C411yescharacteristic
83C2×#11924013C2×C411yescharacteristic
84#14556597—22no—
85#14556597—22no—
86C2×#11924012C2311yescharacteristic
87C2×#11924012C2311yescharacteristic
88C2×#11924011—21no—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91C2×C8×D73—21no—
92#14556574—21no—
93#14556570C2×C411yescharacteristic
94#14556570C2×C411yescharacteristic
95#14556565C2×C411yescharacteristic
96#14556565C2×C411yescharacteristic
97#14556560—21no—
98C4×C22⋊D73—21no—
99C4×C22⋊D73—21no—
100#14556550C2311yescharacteristic
101C2×C22⋊Dic73—21no—
102C2×C4×Dic73C2311yescharacteristic
103C2×C4×Dic73C2311yescharacteristic
104#14556526—22no—
105#14556526—22no—
106#14556520—21no—
107#14556520—21no—
108#14556518—22no—
109#14556518—22no—
110#14556518—22no—
111#14556518—22no—
112#14556517—22no—
113#14556517—22no—
114#14556515C2×C411yescharacteristic
115#14556515C2×C411yescharacteristic
116#14556515C2×C411yescharacteristic
117#14556515C2×C411yescharacteristic
118#14556512C2×C411yescharacteristic
119#14556512C2×C411yescharacteristic
120#14556512C2×C411yescharacteristic
121#14556512C2×C411yescharacteristic
122C22⋊#10596831—21no—
123C22⋊#10596831—21no—
124C22⋊#10596831C2×C411yescharacteristic
125C22⋊#10596831C2×C411yescharacteristic
126C22⋊#10596831C2×C411yescharacteristic
127C22⋊#10596831C2×C411yescharacteristic
128#14556503—21no—
129#14556503—21no—
130#14556501—21no—
131#14556501—22no—
132C8×Dic73—21no—
133C8×Dic73—22no—
134#14556498—21no—
135C2×#41×C73—22no—
136C2×#41×C73—22no—
137C2×#41×C73—22no—
138C2×#41×C73—22no—
139C2×#41×C73—21no—
140C2×#41×C73—21no—
141C2×#41×C73C2×C411yescharacteristic
142C2×#41×C73C2×C411yescharacteristic
143C2×#41×C73C2311yescharacteristic
144C2×#41×C73C2311yescharacteristic
145C22×Q8×C73C2×C411yescharacteristic
146C22×D4×C73—21no—
147C22×D4×C73C2×C411yescharacteristic
148C23×C4×C73—21no—
149C23×C4×C73C2311yescharacteristic
150#131×C73—28no—
151#131×C73—28no—
152#131×C73—22no—
153#131×C73—22no—
154#131×C73—22no—
155#131×C73—22no—
156#131×C73—22no—
157#131×C73—22no—
158#131×C73D414yescomplemented
159#131×C73D414yescomplemented
160C2×M16×C73—28no—
161C2×M16×C73—28no—
162C2×M16×C73—21no—
163C2×M16×C73—22no—
164C2×M16×C73—22no—
165C2×M16×C73—21no—
166C2×M16×C73—21no—
167C2×M16×C73—21no—
168C2×M16×C73—21no—
169C2×M16×C73—22no—
170C2×M16×C73—22no—
171C2×M16×C73D411yescharacteristic
172C2×M16×C73D411yescharacteristic
173C2×M16×C73D411yescharacteristic
174C2×M16×C73D411yescharacteristic
175C2×M16×C73C2311yescharacteristic
176C2×M16×C73C2311yescharacteristic
177C22×C8×C73—21no—
178C22×C8×C73—21no—
179C22×C8×C73—21no—
180C22×C8×C73—21no—
181C22×C8×C73—21no—
182C22×C8×C73C2311yescharacteristic
183C22×C8×C73C2311yescharacteristic
184#11924028—21no—
185#11924028—21no—
186#11924028—21no—
187#11924028—21no—
188C2×Dic146C22×C411yescharacteristic
189C2×D292C22×C411yescharacteristic
190C2×C22⋊D73—21no—
191C2×C22⋊D73—21no—
192C2×C22⋊D73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C2×C4×D73—21no—
196#11924018—22no—
197#11924018—22no—
198#11924016—22no—
199#11924016—22no—
200#11924015—22no—
201#11924015—22no—
202#11924013—22no—
203#11924013—22no—
204#11924012—21no—
205#11924012—21no—
206#11924012—21no—
207#11924012—21no—
208#11924011—42no—
209C2×#10596831—21no—
210C2×#10596831—21no—
211C2×#10596831—21no—
212C2×#10596831—21no—
213C2×#10596831—21no—
214C2×#10596831—21no—
215C2×#10596831C22×C411yescharacteristic
216C2×#10596831C22×C411yescharacteristic
217C2×#10596831C22×C411yescharacteristic
218C2×#10596831C22×C411yescharacteristic
219C8×D73—42no—
220C4⋊Dic73C22×C411yescharacteristic
221C4⋊Dic73C22×C411yescharacteristic
222#11924007—21no—
223#11924007—21no—
224C22⋊Dic73—21no—
225C22⋊Dic73—21no—
226C22⋊Dic73—21no—
227C22⋊Dic73—42no—
228#11924005—21no—
229#11924005—21no—
230C4×Dic73—21no—
231C4×Dic73—21no—
232C4×Dic73—21no—
233C4×Dic73—21no—
234C4×Dic73—21no—
235C24×C73—21no—
236C24×C73#4111yescharacteristic
237#41×C73—24no—
238#41×C73—24no—
239#41×C73—24no—
240#41×C73—24no—
241#41×C73—22no—
242#41×C73—22no—
243#41×C73—22no—
244#41×C73—22no—
245#41×C73—21no—
246#41×C73—21no—
247#41×C73—21no—
248#41×C73—21no—
249#41×C73C2×D412yes—
250#41×C73C2×D412yes—
251#41×C73#4112yes—
252#41×C73#4112yes—
253C2×Q8×C73—22no—
254C2×Q8×C73—22no—
255C2×Q8×C73—21no—
256C2×Q8×C73C22×C411yescharacteristic
257C2×Q8×C73C22×C411yescharacteristic
258C2×D4×C73—24no—
259C2×D4×C73—24no—
260C2×D4×C73—21no—
261C2×D4×C73—21no—
262C2×D4×C73—21no—
263C2×D4×C73—21no—
264C2×D4×C73—22no—
265C2×D4×C73—22no—
266C2×D4×C73—21no—
267C2×D4×C73C22×C411yescharacteristic
268C2×D4×C73C22×C411yescharacteristic
269C22×C4×C73—24no—
270C22×C4×C73—24no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73C22×C411yescharacteristic
281C22×C4×C73C22×C411yescharacteristic
282C22×C4×C73C2×D411yescharacteristic
283C22×C4×C73C2×D411yescharacteristic
284C22×C4×C73#4111yescharacteristic
285C22×C4×C73C2411yescharacteristic
286M16×C73—24no—
287M16×C73—24no—
288M16×C73—24no—
289M16×C73—21no—
290M16×C73—21no—
291M16×C73—22no—
292M16×C73—22no—
293M16×C73—24no—
294M16×C73—24no—
295M16×C73—22no—
296M16×C73—22no—
297M16×C73C2×D412yes—
298M16×C73C2×D412yes—
299C2×C8×C73—24no—
300C2×C8×C73—24no—
301C2×C8×C73—24no—
302C2×C8×C73—21no—
303C2×C8×C73—21no—
304C2×C8×C73—21no—
305C2×C8×C73—21no—
306C2×C8×C73—24no—
307C2×C8×C73—24no—
308C2×C8×C73C2×D411yescharacteristic
309C2×C8×C73C2×D411yescharacteristic
310C2×C8×C73C2×D411yescharacteristic
311C2×C8×C73C2×D411yescharacteristic
312C2×C8×C73C2×D412yes—
313C2×C8×C73C2×D412yes—
314C23×C73—24no—
315C23×C73—21no—
316C23×C73—21no—
317C23×C73—21no—
318C23×C73—21no—
319C23×C73—41no—
320C23×C73—41no—
321C23×C73—81no—
322C23×C73—81no—
323C23×C73C4×D411yescharacteristic
324C23×C73C4×D411yescharacteristic
325C23×C73C2×#4111yescharacteristic
326C22×D73—21no—
327Q8×C73—24no—
328Q8×C73—21no—
329Q8×C73—21no—
330Q8×C73C4×D412yes—
331Q8×C73C4×D412yes—
332D4×C73—24no—
333D4×C73—24no—
334D4×C73—24no—
335D4×C73—22no—
336D4×C73—22no—
337D4×C73—22no—
338D4×C73—22no—
339D4×C73—21no—
340D4×C73—21no—
341D4×C73C4×D412yes—
342D4×C73C4×D412yes—
343C2×C4×C73—24no—
344C2×C4×C73—24no—
345C2×C4×C73—24no—
346C2×C4×C73—21no—
347C2×C4×C73—21no—
348C2×C4×C73—21no—
349C2×C4×C73—21no—
350C2×C4×C73—21no—
351C2×C4×C73—21no—
352C2×C4×C73—21no—
353C2×C4×C73—21no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—21no—
357C2×C4×C73—21no—
358C2×C4×C73—21no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—21no—
362C2×C4×C73C4×D411yescharacteristic
363C2×C4×C73C4×D411yescharacteristic
364C2×C4×C73C23×C411yescharacteristic
365C2×C4×C73C22×D411yescharacteristic
366C2×C4×C73C22×D411yescharacteristic
367C2×C4×C73C22×D411yescharacteristic
368C2×C4×C73C2×#4111yescharacteristic
369C2×C4×C73C2×#4111yescharacteristic
370C22⋊D73—41no—
371C22⋊D73—41no—
372C22⋊D73—81no—
373C22⋊D73—81no—
374C2×Dic73—22no—
375C2×Dic73—21no—
376C2×Dic73—21no—
377C2×Dic73—21no—
378C2×Dic73—41no—
379C2×Dic73—41no—
380C2×Dic73—41no—
381C2×Dic73—41no—
382C2×Dic73—41no—
383D292—21no—
384D292—21no—
385C4×D73—41no—
386C4×D73—41no—
387Dic146—21no—
388Dic146—21no—
389C8×C73—22no—
390C8×C73—22no—
391C8×C73—21no—
392C8×C73—21no—
393C8×C73#12012yes—
394C8×C73#12012yes—
395#10596831—21no—
396#10596831—21no—
397#10596831—21no—
398#10596831—21no—
399#10596831—41no—
400#10596831—41no—
401C22×C73—21no—
402C22×C73—21no—
403C22×C73—21no—
404C22×C73—21no—
405C22×C73—21no—
406C22×C73—21no—
407C22×C73—21no—
408C22×C73—21no—
409C22×C73—22no—
410C22×C73—22no—
411C22×C73—41no—
412C22×C73—41no—
413C22×C73—41no—
414C22×C73—41no—
415C22×C73—81no—
416C22×C73—81no—
417C22×C73—84no—
418C22×C73C2×C4×D411yescharacteristic
419C22×C73#52511yescharacteristic
420C22×C73#52511yescharacteristic
421C2×D73—41no—
422C2×D73—41no—
423C2×D73—41no—
424C4×C73—21no—
425C4×C73—22no—
426C4×C73—22no—
427C4×C73—21no—
428C4×C73C2×C4×D411yescharacteristic
429C4×C73C2×C4×D411yescharacteristic
430C4×C73C2×#12011yescharacteristic
431C4×C73#52511yescharacteristic
432Dic73—42no—
433Dic73—41no—
434Dic73—41no—
435Dic73—41no—
436Dic73—81no—
437#21468—731nomaximal, Sylow
438C2×C73—21no—
439C2×C73—21no—
440C2×C73—41no—
441C2×C73—41no—
442C2×C73—42no—
443C2×C73—42no—
444C2×C73C4×#12011yescharacteristic
445C2×C73#295611yescharacteristic
446C2×C73#295711yescharacteristic
447D73—81no—
448C2×#568D7311yescharacteristic, complemented
449#3002—731no—
450C2×#444—731no—
451C2×#443—731no—
452#2930—731no—
453#1876—731no—
454#1876—731no—
455#1871—731no—
456#1866—731no—
457#1866—731no—
458#1855—731no—
459#1789—731no—
460#1765—731no—
461#1764—731no—
462#1753—731no—
463C73#2146811yescharacteristic, complemented, Sylow
464C22×#41C2×D7311yescharacteristic
465C2×#135—731no—
466C2×#135—731no—
467#568—24no—
468#568—24no—
469C2×#131—21no—
470C2×#131—21no—
471C2×#131—731no—
472C2×#131C2×D7311yescharacteristic
473C2×#131C2×D7311yescharacteristic
474C2×#131C2×D7311yescharacteristic
475C2×#131C2×D7311yescharacteristic
476C22×M16—21no—
477C22×M16—21no—
478C22×M16C2×D7311yescharacteristic
479C22×M16C2×D7311yescharacteristic
480#525—731no—
481#452—731no—
482#452—731no—
483#451—731no—
484#450—731no—
485#449—731no—
486#449—731no—
487#448—731no—
488#447—731no—
489#444—1464no—
490#443—1464no—
491#436—1461no—
492#436—1461no—
493#435—1461no—
494#435—1461no—
495C2×#108—731no—
496C2×#108—731no—
497#424—731no—
498C2×#104—731no—
499C2×#104—731no—
500C2×#104—731no—
501C2×#104—731no—
502C2×#104—731no—
503C2×#104—731no—
504#416—731no—
505#416—731no—
506#408—731no—
507#407—731no—
508C2×C22⋊C8—731no—
509#405—731no—
510C2×#97—731no—
511C2×C4×C8—731no—
512C4×C22⋊C4—731no—
513#341—731no—
514#341—731no—
515#339—731no—
516#339—731no—
517#336—731no—
518#336—731no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41—731no—
526C2×#41C4×D7311yescharacteristic
527C2×#41C4×D7311yescharacteristic
528C2×#41C22×D7311yescharacteristic
529C2×#41C22×D7311yescharacteristic
530C22×Q8C4×D7311yescharacteristic
531C22×D4—21no—
532C22×D4C4×D7311yescharacteristic
533C23×C4—21no—
534C23×C4C22×D7311yescharacteristic
535#135—1462no—
536#135—1462no—
537#135—1462no—
538#135—1462no—
539C2×Q16—731no—
540C2×Q16—731no—
541C2×SD16—731no—
542C2×SD16—731no—
543C2×SD16—731no—
544C2×SD16—731no—
545C2×D8—731no—
546C2×D8—731no—
547#131—28no—
548#131—28no—
549#131—22no—
550#131—22no—
551#131—22no—
552#131—22no—
553#131—22no—
554#131—22no—
555#131—1462no—
556#131—1462no—
557#131C22⋊D7314yescomplemented
558#131C22⋊D7314yescomplemented
559C2×M16—28no—
560C2×M16—28no—
561C2×M16—21no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—21no—
565C2×M16—21no—
566C2×M16—21no—
567C2×M16—21no—
568C2×M16—22no—
569C2×M16—22no—
570C2×M16—731no—
571C2×M16—731no—
572C2×M16—1461no—
573C2×M16C22⋊D7311yescharacteristic
574C2×M16C22⋊D7311yescharacteristic
575C2×M16C22⋊D7311yescharacteristic
576C2×M16C22⋊D7311yescharacteristic
577C2×M16C22×D7311yescharacteristic
578C2×M16C22×D7311yescharacteristic
579C22×C8—21no—
580C22×C8—21no—
581C22×C8—21no—
582C22×C8—21no—
583C22×C8—21no—
584C22×C8—731no—
585C22×C8—731no—
586C22×C8—1461no—
587C22×C8C22×D7311yescharacteristic
588C22×C8C22×D7311yescharacteristic
589#123—1461no—
590C22⋊Q8—731no—
591C22⋊Q8—731no—
592#121—731no—
593#121—731no—
594#120—1461no—
595C4×D4—1461no—
596C4×D4—1461no—
597#117—731no—
598C2×C22⋊C4—1461no—
599C2×C42—731no—
600C2×C42—731no—
601#108—1462no—
602#108—1462no—
603C4⋊C8—1461no—
604C4⋊C8—1461no—
605#104—1462no—
606#104—1462no—
607#104—1462no—
608#104—1462no—
609#104—1462no—
610#104—1462no—
611#103—731no—
612#103—731no—
613#103—731no—
614#103—731no—
615#102—731no—
616#102—731no—
617#102—731no—
618#102—731no—
619C22⋊C8—731no—
620C22⋊C8—731no—
621C22⋊C8—731no—
622C22⋊C8—731no—
623C22⋊C8—1461no—
624C22⋊C8—1461no—
625C22⋊C8—1461no—
626C22⋊C8—1461no—
627#97—1462no—
628#97—1461no—
629C4×C8—1462no—
630C4×C8—1461no—
631#95—1461no—
632C24—21no—
633C24#1192402811yescharacteristic
634#41—24no—
635#41—24no—
636#41—24no—
637#41—24no—
638#41—22no—
639#41—22no—
640#41—22no—
641#41—22no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—1461no—
647#41—1461no—
648#41—1461no—
649#41—1461no—
650#41C2×C22⋊D7312yes—
651#41C2×C22⋊D7312yes—
652#41#1192402812yes—
653#41#1192402812yes—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—731no—
658C2×Q8C2×C4×D7311yescharacteristic
659C2×Q8C2×C4×D7311yescharacteristic
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—731no—
670C2×D4—1461no—
671C2×D4—1461no—
672C2×D4—1461no—
673C2×D4C2×C4×D7311yescharacteristic
674C2×D4C2×C4×D7311yescharacteristic
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—1461no—
687C22×C4—1461no—
688C22×C4—1461no—
689C22×C4C2×C4×D7311yescharacteristic
690C22×C4C2×C4×D7311yescharacteristic
691C22×C4C2×C22⋊D7311yescharacteristic
692C22×C4C2×C22⋊D7311yescharacteristic
693C22×C4#1192402811yescharacteristic
694C22×C4C23×D7311yescharacteristic
695Q16—1462no—
696Q16—1462no—
697SD16—1462no—
698SD16—1462no—
699SD16—1462no—
700SD16—1462no—
701D8—1462no—
702D8—1462no—
703M16—24no—
704M16—24no—
705M16—24no—
706M16—21no—
707M16—21no—
708M16—22no—
709M16—22no—
710M16—24no—
711M16—24no—
712M16—22no—
713M16—22no—
714M16—2922no—
715M16—1461no—
716M16—1461no—
717M16—1461no—
718M16—1461no—
719M16C2×C22⋊D7312yes—
720M16C2×C22⋊D7312yes—
721C2×C8—24no—
722C2×C8—24no—
723C2×C8—24no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—24no—
729C2×C8—24no—
730C2×C8—2922no—
731C2×C8—731no—
732C2×C8—731no—
733C2×C8—731no—
734C2×C8—731no—
735C2×C8—1461no—
736C2×C8—1461no—
737C2×C8—1461no—
738C2×C8—1461no—
739C2×C8—1461no—
740C2×C8—1461no—
741C2×C8C2×C22⋊D7311yescharacteristic
742C2×C8C2×C22⋊D7311yescharacteristic
743C2×C8C2×C22⋊D7312yes—
744C2×C8C2×C22⋊D7312yes—
745C2×C8C2×C22⋊D7311yescharacteristic
746C2×C8C2×C22⋊D7311yescharacteristic
747C4⋊C4—731no—
748C4⋊C4—731no—
749C4⋊C4—1461no—
750C4⋊C4—1461no—
751C22⋊C4—2922no—
752C22⋊C4—1461no—
753C22⋊C4—1461no—
754C22⋊C4—1461no—
755C22⋊C4—1461no—
756C22⋊C4—1461no—
757C42—1461no—
758C42—1461no—
759C42—1461no—
760C42—1461no—
761C42—1461no—
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—41no—
768C23—41no—
769C23—81no—
770C23—81no—
771C23—1461no—
772C23C4×C22⋊D7311yescharacteristic
773C23C4×C22⋊D7311yescharacteristic
774C23C2×#1192402811yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—1461no—
779Q8—1461no—
780Q8C4×C22⋊D7312yes—
781Q8C4×C22⋊D7312yes—
782D4—24no—
783D4—24no—
784D4—24no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—2921no—
792D4—2921no—
793D4—5841no—
794D4—5841no—
795D4—1461no—
796D4—1461no—
797D4C4×C22⋊D7312yes—
798D4C4×C22⋊D7312yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—2921no—
819C2×C4—2921no—
820C2×C4—2921no—
821C2×C4—2921no—
822C2×C4—2921no—
823C2×C4—2921no—
824C2×C4—2921no—
825C2×C4—1462no—
826C2×C4—1461no—
827C2×C4—1461no—
828C2×C4—1461no—
829C2×C4C4×C22⋊D7311yescharacteristic
830C2×C4C4×C22⋊D7311yescharacteristic
831C2×C4C22×C4×D7311yescharacteristic
832C2×C4C22×C22⋊D7311yescharacteristic
833C2×C4C22×C22⋊D7311yescharacteristic
834C2×C4C22×C22⋊D7311yescharacteristic
835C2×C4C2×#1192402811yescharacteristic
836C2×C4C2×#1192402811yescharacteristic
837C8—22no—
838C8—22no—
839C8—21no—
840C8—21no—
841C8—2921no—
842C8—2921no—
843C8—1461no—
844C8—1461no—
845C8—1461no—
846C8—1461no—
847C8#1455656012yes—
848C8#1455656012yes—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—22no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—81no—
864C22—81no—
865C22—84no—
866C22—2921no—
867C22—2921no—
868C22—2921no—
869C22C2×C4×C22⋊D7311yescharacteristic
870C22#1798909811yescharacteristic
871C22#1798909811yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—2922no—
877C4—2921no—
878C4—2921no—
879C4—2921no—
880C4—5841no—
881C4C2×C4×C22⋊D7311yescharacteristic
882C4C2×C4×C22⋊D7311yescharacteristic
883C4C2×#1455656011yescharacteristic
884C4#1798909811yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—5841no—
892C2C4×#1455656011yescharacteristic
893C2#2261883811yescharacteristic
894C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#568×C73C2
socleC22×C73C2×C4×D4
prime radical#22619149C2
cosocleC22×C4×C73C24
hypercenterC2×#568D73
hypocenterC73#21468
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#17988707C2semidirect
3. C2×#17988702C2semidirect
4. #22618634C2semidirect
5. #22610258C2semidirect
6. #22610258C2semidirect
7. #22610233C2semidirect
8. #22610206C2semidirect
9. #22610206C2semidirect
10. #22610136C2semidirect
11. #22609875C2semidirect
12. #22609773C2semidirect
13. #22609766C2semidirect
14. #22609712C2semidirect
15. C2×#568×C73C2semidirect
18. C2×#14556597C22semidirect
20. #17988749C4semidirect
21. #17988749C4semidirect
22. #17988743C4semidirect
23. #17988738C4semidirect
24. #17988732C4semidirect
25. #17988732C4semidirect
26. #17988726C4semidirect
27. #17988721C4semidirect
34. C2×#14556526C22semidirect
35. C2×#14556526C22semidirect
36. #17988613C22semidirect
41. C2×#14556517C22semidirect
42. C2×#14556517C22semidirect
45. #17988553C22semidirect
48. #17988542C22semidirect
49. C2×#14556501C22semidirect
50. C2×C8×Dic73C22semidirect
52. #17988351C22semidirect
53. #17988351C22semidirect
54. #17988348C22semidirect
55. #17988348C22semidirect
56. #17988341C22semidirect
57. #17988341C22semidirect
158. #131×C73D4semidirect
159. #131×C73D4semidirect
448. C2×#568D73semidirect
463. C73#21468semidirect
557. #131C22⋊D73semidirect
558. #131C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226191492
C2×#179887072
C2×#179887022
#226186342
#226102582
#226102332
#226102062
#226101362
#226098752
#226097732
#226097662
#226097122
C2×#568×C732
#2146873