Finite Group Databasebeta

← #33093830

Subgroups — #33093830

Order 18688.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619713C211yesmaximal, characteristic
2#22618356C211yesmaximal, characteristic
3#22610876C211yesmaximal, characteristic, complemented
4#22610704C211yesmaximal, characteristic, complemented
5#22610527C211yesmaximal, characteristic, complemented
6#22610527C211yesmaximal, characteristic, complemented
7#22610205C211yesmaximal, characteristic
8#22610205C211yesmaximal, characteristic
9#22609948C211yesmaximal, characteristic
10#22609816C211yesmaximal, characteristic, complemented
11#22609811C211yesmaximal, characteristic, complemented
12#22609803C211yesmaximal, characteristic, complemented
13#22609777C211yesmaximal, characteristic
14#22609770C211yesmaximal, characteristic
15C73×#2961C211yesmaximal, characteristic, complemented
16C2×#14556597C2211yescharacteristic
17C2×#14556597C2211yescharacteristic
18C4×#11924028C2211yescharacteristic
19#17988891C411yescharacteristic, complemented
20#17988891C411yescharacteristic, complemented
21#17988884C411yescharacteristic, complemented
22#17988884C411yescharacteristic, complemented
23#17988879C411yescharacteristic, complemented
24#17988874C411yescharacteristic, complemented
25#17988869C411yescharacteristic, complemented
26#17988864C411yescharacteristic, complemented
27C2×#14556526C2211yescharacteristic
28C2×#14556526C2211yescharacteristic
29#17988623C2211yescharacteristic
30#17988623C2211yescharacteristic
31C2×C4⋊#10596831C2211yescharacteristic
32C2×#14556517C2211yescharacteristic
33C2×#14556517C2211yescharacteristic
34#17988581C2211yescharacteristic
35#17988581C2211yescharacteristic
36#17988544—21no—
37#17988544—21no—
38#17988542C2211yescharacteristic
39#17988542C2211yescharacteristic
40C4×#11924012C2211yescharacteristic
41#17988539—21no—
42C2×#14556501C2211yescharacteristic
43#97×D73—21no—
44C2×C8×Dic73C2211yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46#17988351C2211yescharacteristic
47#17988351C2211yescharacteristic
48#17988348C2211yescharacteristic
49#17988348C2211yescharacteristic
50#17988346C2211yescharacteristic
51#17988346C2211yescharacteristic
52#17988346C2211yescharacteristic
53#17988346C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56#533×C73C2211yescharacteristic
57#446×C73—21no—
58#446×C73—21no—
59#446×C73—21no—
60#446×C73—21no—
61#424×C73C2211yescharacteristic
62#424×C73C2211yescharacteristic
63#423×C73C2211yescharacteristic
64#405×C73C2211yescharacteristic
65#405×C73C2211yescharacteristic
66C2×#97×C73C2211yescharacteristic
67C2×#11924028C2311yescharacteristic
68#14556597—22no—
69#14556597—22no—
70#14556597—22no—
71#14556597Q814yescomplemented
72C2×#11924012C2311yescharacteristic
73C2×#11924012C2311yescharacteristic
74C2×#11924011—21no—
75C2×#11924011—21no—
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80C4×Dic146C2×C411yescharacteristic
81C4×Dic146C2×C411yescharacteristic
82C4×D292C2×C411yescharacteristic
83C4×D292C2×C411yescharacteristic
84C4×C22⋊D73—21no—
85C4×C22⋊D73—21no—
86#14556550C2311yescharacteristic
87#14556548—21no—
88C2×C4⋊Dic73—21no—
89C2×C4×Dic73C2311yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91C42×D73—21no—
92#14556526—22no—
93#14556526—22no—
94#14556524C2×C411yescharacteristic
95#14556524C2×C411yescharacteristic
96#14556524C2×C411yescharacteristic
97#14556524C2×C411yescharacteristic
98#14556522C2×C411yescharacteristic
99#14556522C2×C411yescharacteristic
100#14556522C2×C411yescharacteristic
101#14556522C2×C411yescharacteristic
102C4⋊#10596831C2×C411yescharacteristic
103C4⋊#10596831C2×C411yescharacteristic
104C4⋊#10596831C2×C411yescharacteristic
105C4⋊#10596831C2×C411yescharacteristic
106#14556517—22no—
107#14556517—22no—
108#14556514C2×C411yescharacteristic
109#14556514C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556514C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113#14556511C2×C411yescharacteristic
114#14556511C2×C411yescharacteristic
115#14556511C2×C411yescharacteristic
116#14556502—21no—
117#14556501—21no—
118#14556501—21no—
119#14556501—22no—
120C4×#10596831—21no—
121C8×Dic73—21no—
122C8×Dic73—21no—
123C8×Dic73—22no—
124#14556498—21no—
125C2×M16×C73C2311yescharacteristic
126C2×M16×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C4⋊Q8×C73C2×C411yescharacteristic
130C4⋊Q8×C73C2×C411yescharacteristic
131#125×C73C2×C411yescharacteristic
132#125×C73C2×C411yescharacteristic
133C22⋊Q8×C73—21no—
134C22⋊Q8×C73—21no—
135C4×Q8×C73—21no—
136C4×Q8×C73—21no—
137#117×C73C2311yescharacteristic
138#117×C73C2311yescharacteristic
139C2×C42×C73C2311yescharacteristic
140C4⋊C8×C73—21no—
141C4⋊C8×C73—21no—
142C4⋊C8×C73—21no—
143C4⋊C8×C73—21no—
144C4⋊C8×C73—21no—
145C4⋊C8×C73—21no—
146#97×C73—21no—
147#97×C73—21no—
148#97×C73D411yescharacteristic
149#97×C73D411yescharacteristic
150#97×C73D411yescharacteristic
151#97×C73D411yescharacteristic
152C4×C8×C73—21no—
153C4×C8×C73—21no—
154#11924028—21no—
155#11924028—21no—
156#11924028C2×Q812yes—
157#11924028#4112yes—
158C2×Dic146C22×C411yescharacteristic
159C2×D292C22×C411yescharacteristic
160C2×C22⋊D73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166#11924012—21no—
167#11924012—21no—
168#11924012C2×Q812yes—
169#11924012#4112yes—
170#11924011—24no—
171#11924011—24no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831C22×C411yescharacteristic
179C2×#10596831C22×C411yescharacteristic
180C2×#10596831C22×C411yescharacteristic
181C2×#10596831C22×C411yescharacteristic
182C8×D73—24no—
183C8×D73—24no—
184C4⋊Dic73—42no—
185C4⋊Dic73C22×C411yescharacteristic
186C4⋊Dic73C22×C411yescharacteristic
187#11924007—21no—
188#11924007—21no—
189C22⋊Dic73—21no—
190#11924005—21no—
191#11924005—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C2×Q8×C73—21no—
200C2×Q8×C73—21no—
201C22×C4×C73#4111yescharacteristic
202C22×C4×C73#4111yescharacteristic
203C22×C4×C73C2411yescharacteristic
204M16×C73—21no—
205M16×C73—21no—
206M16×C73—21no—
207M16×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73C2×D411yescharacteristic
213C2×C8×C73C2×D411yescharacteristic
214C2×C8×C73C2×D411yescharacteristic
215C2×C8×C73C2×D411yescharacteristic
216C2×C8×C73C2×Q812yes—
217C2×C8×C73#4112yes—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73C22×C411yescharacteristic
225C4⋊C4×C73C22×C411yescharacteristic
226C4⋊C4×C73C22×C411yescharacteristic
227C4⋊C4×C73C22×C411yescharacteristic
228C22⋊C4×C73—21no—
229C22⋊C4×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73C22×C411yescharacteristic
233C42×C73C22×C411yescharacteristic
234C42×C73C2×D411yescharacteristic
235C42×C73C2×D411yescharacteristic
236C23×C73C2×#4111yescharacteristic
237C22×D73—21no—
238Q8×C73—81no—
239Q8×C73—81no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73C4×D411yescharacteristic
247C2×C4×C73C4×D411yescharacteristic
248C2×C4×C73C4×D411yescharacteristic
249C2×C4×C73C4×D411yescharacteristic
250C2×C4×C73C23×C411yescharacteristic
251C2×C4×C73C22×D411yescharacteristic
252C2×C4×C73C22×Q811yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C22⋊D73—22no—
257C22⋊D73—22no—
258C2×Dic73—21no—
259C2×Dic73—22no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267D292—21no—
268D292C4×Q812yes—
269C4×D73—22no—
270C4×D73—22no—
271C4×D73—81no—
272C4×D73—81no—
273Dic146—21no—
274Dic146C4×Q812yes—
275C8×C73—21no—
276C8×C73—21no—
277C8×C73—41no—
278C8×C73—41no—
279C8×C73C22⋊Q812yes—
280C8×C73C22⋊Q812yes—
281#10596831—21no—
282#10596831—21no—
283#10596831—21no—
284#10596831—21no—
285#10596831—22no—
286#10596831—22no—
287C22×C73—21no—
288C22×C73—21no—
289C22×C73C2×C4×D411yescharacteristic
290C22×C73#52911yescharacteristic
291C22×C73#53311yescharacteristic
292C2×D73—22no—
293C2×D73—41no—
294C2×D73—41no—
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—21no—
299C4×C73—41no—
300C4×C73—41no—
301C4×C73—41no—
302C4×C73—41no—
303C4×C73C2×C4×Q811yescharacteristic
304C4×C73C4×#4111yescharacteristic
305C4×C73C2×C22⋊Q811yescharacteristic
306C4×C73#52511yescharacteristic
307Dic73—22no—
308Dic73—42no—
309Dic73—41no—
310Dic73—41no—
311Dic73—81no—
312#21629—731nomaximal, Sylow
313C2×C73—21no—
314C2×C73—21no—
315C2×C73C4×C22⋊Q811yescharacteristic
316C2×C73#295611yescharacteristic
317C2×C73#295711yescharacteristic
318D73—42no—
319#3076—731no—
320#2961D7311yescharacteristic, complemented
321#2875—731no—
322#1986—731no—
323#1950—731no—
324#1922—731no—
325#1922—731no—
326#1866—731no—
327#1866—731no—
328#1806—731no—
329#1773—731no—
330#1772—731no—
331#1771—731no—
332#1765—731no—
333#1764—731no—
334C73#2162911yescharacteristic, complemented, Sylow
335C2×#131—731no—
336C2×#131—731no—
337#533C2×D7311yescharacteristic
338C4×#41—731no—
339#479—731no—
340#479—731no—
341#478—731no—
342#478—731no—
343#477—731no—
344#476—731no—
345#475—731no—
346#474—731no—
347#446—21no—
348#446—21no—
349#446—21no—
350#446—21no—
351C2×#108—731no—
352C2×#108—731no—
353#427—731no—
354#427—731no—
355#424C2×D7311yescharacteristic
356#424C2×D7311yescharacteristic
357#423C2×D7311yescharacteristic
358C2×C4⋊C8—731no—
359C2×#104—731no—
360C2×#104—731no—
361#416—731no—
362#416—731no—
363#405—731no—
364#405—731no—
365#405—1461no—
366#405—1461no—
367#405C2×D7311yescharacteristic
368#405C2×D7311yescharacteristic
369C4×M16—731no—
370C4×M16—1461no—
371C2×#97—731no—
372C2×#97—1461no—
373C2×#97C2×D7311yescharacteristic
374C2×C4×C8—731no—
375C4×C4⋊C4—731no—
376#341—731no—
377#341—731no—
378#339—731no—
379#339—731no—
380#339—731no—
381#339—731no—
382#339—731no—
383#339—731no—
384#336—731no—
385#336—731no—
386C2×#41—731no—
387#131—734no—
388#131—1462no—
389#131—1462no—
390#131—1462no—
391C2×M16—731no—
392C2×M16—731no—
393C2×M16—1461no—
394C2×M16—1461no—
395C2×M16C22×D7311yescharacteristic
396C2×M16C22×D7311yescharacteristic
397C22×C8—731no—
398C22×C8—731no—
399C22×C8—1461no—
400C22×C8—1461no—
401C22×C8C22×D7311yescharacteristic
402C22×C8C22×D7311yescharacteristic
403C4⋊Q8C4×D7311yescharacteristic
404C4⋊Q8C4×D7311yescharacteristic
405#125C4×D7311yescharacteristic
406#125C4×D7311yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—731no—
412C4×Q8—731no—
413C4×D4—731no—
414C4×D4—731no—
415C4×D4—1461no—
416C4×D4—1461no—
417#117—731no—
418#117—1461no—
419#117C22×D7311yescharacteristic
420#117C22×D7311yescharacteristic
421C2×C4⋊C4—1461no—
422C2×C42—731no—
423C2×C42—731no—
424C2×C42—1461no—
425C2×C42C22×D7311yescharacteristic
426#108—1462no—
427#108—1462no—
428#107—731no—
429#107—731no—
430#107—731no—
431#107—731no—
432#106—731no—
433#106—731no—
434#106—731no—
435#106—731no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—731no—
443C4⋊C8—731no—
444C4⋊C8—731no—
445C4⋊C8—731no—
446#104—1462no—
447#104—1462no—
448#103—731no—
449#103—731no—
450#103—731no—
451#103—731no—
452#102—731no—
453#102—731no—
454#102—731no—
455#102—731no—
456#97—21no—
457#97—21no—
458#97—1461no—
459#97—1461no—
460#97—1462no—
461#97—1461no—
462#97C22⋊D7311yescharacteristic
463#97C22⋊D7311yescharacteristic
464#97C22⋊D7311yescharacteristic
465#97C22⋊D7311yescharacteristic
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—1461no—
469C4×C8—1461no—
470C4×C8—1462no—
471C4×C8—1461no—
472#95—1461no—
473#41—732no—
474#41—732no—
475#41—1461no—
476#41—1461no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—731no—
480C2×D4—731no—
481C2×D4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4#1192402811yescharacteristic
488C22×C4#1192402811yescharacteristic
489C22×C4C23×D7311yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—732no—
495M16—732no—
496M16—1464no—
497M16—1461no—
498M16—1461no—
499M16—1464no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—731no—
505C2×C8—731no—
506C2×C8—731no—
507C2×C8—731no—
508C2×C8—1464no—
509C2×C8—1461no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1464no—
516C2×C8C2×C22⋊D7311yescharacteristic
517C2×C8C2×C22⋊D7311yescharacteristic
518C2×C8C2×C22⋊D7311yescharacteristic
519C2×C8C2×C22⋊D7311yescharacteristic
520C2×C8Q8×D7312yes—
521C2×C8#1192402912yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—2922no—
529C4⋊C4—731no—
530C4⋊C4—731no—
531C4⋊C4—1461no—
532C4⋊C4—1461no—
533C4⋊C4C2×C4×D7311yescharacteristic
534C4⋊C4C2×C4×D7311yescharacteristic
535C4⋊C4C2×C4×D7311yescharacteristic
536C4⋊C4C2×C4×D7311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—1461no—
540C22⋊C4—1461no—
541C22⋊C4—1461no—
542C42—21no—
543C42—21no—
544C42—1461no—
545C42—1461no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C42—1461no—
550C42—1461no—
551C42C2×C4×D7311yescharacteristic
552C42C2×C4×D7311yescharacteristic
553C42C2×C22⋊D7311yescharacteristic
554C42C2×C22⋊D7311yescharacteristic
555C23—1461no—
556C23C2×#1192402811yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—732no—
560Q8—1461no—
561D4—732no—
562D4—1462no—
563D4—1462no—
564D4—1461no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—2921no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—2921no—
575C2×C4—2921no—
576C2×C4—5841no—
577C2×C4—5841no—
578C2×C4—1462no—
579C2×C4—1461no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4—1462no—
583C2×C4—1462no—
584C2×C4C4×C22⋊D7311yescharacteristic
585C2×C4C4×C22⋊D7311yescharacteristic
586C2×C4C4×C22⋊D7311yescharacteristic
587C2×C4C4×C22⋊D7311yescharacteristic
588C2×C4C22×C4×D7311yescharacteristic
589C2×C4C22×C22⋊D7311yescharacteristic
590C2×C4C2×Q8×D7311yescharacteristic
591C2×C4#41×D7311yescharacteristic
592C2×C4#41×D7311yescharacteristic
593C2×C4C2×#1192402911yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—1461no—
599C8—1461no—
600C8—1461no—
601C8—1461no—
602C8—1462no—
603C8—1462no—
604C8#1455656712yes—
605C8#1455656712yes—
606C22—21no—
607C22—21no—
608C22—2921no—
609C22—2921no—
610C22—1462no—
611C22C2×C4×C22⋊D7311yescharacteristic
612C22#1798912411yescharacteristic
613C22#1798914111yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—2922no—
623C4—2921no—
624C4—2921no—
625C4—5841no—
626C4—1462no—
627C4C4×Q8×D7311yescharacteristic
628C4C4×#1192402911yescharacteristic
629C4C2×#1455656711yescharacteristic
630C4#1798909411yescharacteristic
631C2—21no—
632C2—21no—
633C2—2922no—
634C2C4×#1455656711yescharacteristic
635C2#2261883811yescharacteristic
636C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2961C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C23
cosocleC22×C4×C73C24
hypercenter#2961D73
hypocenterC73#21629
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #22610876C2semidirect
4. #22610704C2semidirect
5. #22610527C2semidirect
6. #22610527C2semidirect
10. #22609816C2semidirect
11. #22609811C2semidirect
12. #22609803C2semidirect
15. C73×#2961C2semidirect
19. #17988891C4semidirect
20. #17988891C4semidirect
21. #17988884C4semidirect
22. #17988884C4semidirect
23. #17988879C4semidirect
24. #17988874C4semidirect
25. #17988869C4semidirect
26. #17988864C4semidirect
71. #14556597Q8semidirect
320. #2961D73semidirect
334. C73#21629semidirect

Maximal subgroups

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

subgroupindex
#226197132
#226183562
#226108762
#226107042
#226105272
#226102052
#226099482
#226098162
#226098112
#226098032
#226097772
#226097702
C73×#29612
#2162973