Finite Group Databasebeta

← #33127256

Subgroups — #33127256

Order 18688.

784 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988895C211yesmaximal, characteristic, complemented
2#22618241C211yesmaximal, characteristic
3C4×#14556570C211yesmaximal, characteristic
4#22611364C211yesmaximal, characteristic
5#22611359C211yesmaximal, characteristic
6#22611135C211yesmaximal, characteristic
7#22611128C211yesmaximal, characteristic
8#22610886C211yesmaximal, characteristic, complemented
9#22610701C211yesmaximal, characteristic, complemented
10#22610674C211yesmaximal, characteristic, complemented
11#22610669C211yesmaximal, characteristic, complemented
12#22610621C211yesmaximal, characteristic, complemented
13#22610621C211yesmaximal, characteristic, complemented
14#22609947C211yesmaximal, characteristic, complemented
15C2×#432×C73C211yesmaximal, characteristic
16C2×#14556583C2211yescharacteristic
17C2×#14556570C2211yescharacteristic
18C2×C4×Dic146C2211yescharacteristic
19#17988895—24no—
20C2×#14556525C2211yescharacteristic
21C2×#14556525C2211yescharacteristic
22C2×#14556523C2211yescharacteristic
23C2×#14556523C2211yescharacteristic
24C2×#14556516C2211yescharacteristic
25C2×#14556516C2211yescharacteristic
26C2×#14556516C2211yescharacteristic
27C2×#14556516C2211yescharacteristic
28#17988493C2211yescharacteristic
29#17988485C2211yescharacteristic
30#17988485C2211yescharacteristic
31#17988485C2211yescharacteristic
32#17988471—21no—
33#17988471—21no—
34#17988471—21no—
35#17988460—21no—
36#17988460—21no—
37#17988460—21no—
38#17988453C2211yescharacteristic
39#17988447C2211yescharacteristic
40#17988447C2211yescharacteristic
41#17988447C2211yescharacteristic
42C4×#11924007—21no—
43C4×C4⋊Dic73C2211yescharacteristic
44C4×C22⋊Dic73—21no—
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53C22×C42×C73C2211yescharacteristic
54#432×C73—24no—
55C2×C4⋊C8×C73C2211yescharacteristic
56C2×C4⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×#97×C73C2211yescharacteristic
60C2×#97×C73C2211yescharacteristic
61C22×Dic146C2311yescharacteristic
62#14556583—22no—
63#14556583—22no—
64#14556570—22no—
65#14556570—22no—
66C4×Dic146—22no—
67C4×Dic146—22no—
68C2×C4⋊Dic73C2311yescharacteristic
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×#11924007—21no—
76C2×#11924007—21no—
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×#11924007—21no—
80C2×#11924007—21no—
81C2×#11924007—21no—
82C2×C22⋊Dic73—21no—
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73—21no—
88#14556525—22no—
89#14556525—22no—
90#14556523—22no—
91#14556523—22no—
92#14556516—22no—
93#14556516—22no—
94#14556516—22no—
95#14556516—22no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107C23×C4×C73D411yescharacteristic
108C23×C4×C73D411yescharacteristic
109C23×C4×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C2×C42×C73—22no—
115C2×C42×C73—22no—
116C2×C42×C73D411yescharacteristic
117C2×C42×C73D411yescharacteristic
118C2×C42×C73C2311yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C4⋊C8×C73—22no—
121C4⋊C8×C73D414yes—
122C22⋊C8×C73—22no—
123C22⋊C8×C73—22no—
124#97×C73—22no—
125#97×C73—22no—
126C2×Dic146—21no—
127C2×Dic146—21no—
128C2×Dic146—21no—
129C2×Dic146—21no—
130C2×Dic146—21no—
131C2×Dic146#4112yes—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C4⋊Dic73—21no—
141C4⋊Dic73—21no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73#4112yes—
154#11924007—24no—
155#11924007—42no—
156#11924007—42no—
157#11924007—42no—
158#11924007—42no—
159#11924007—42no—
160#11924007—42no—
161C22⋊Dic73—24no—
162C22⋊Dic73—42no—
163C22⋊Dic73—42no—
164C22⋊Dic73—42no—
165C4×Dic73—42no—
166C4×Dic73—42no—
167C24×C73C2×D411yescharacteristic
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—41no—
178C22×C4×C73—41no—
179C22×C4×C73—41no—
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2411yescharacteristic
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73C2×D412yes—
197C2×C8×C73C2×D412yes—
198C42×C73—22no—
199C42×C73—22no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73C2×D412yes—
203C42×C73#4112yes—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73#13712yes—
211C23×C73C22×D411yescharacteristic
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—44no—
226C2×C4×C73—44no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73#12112yes—
232C2×C4×C73#12112yes—
233C2×C4×C73C22×D411yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C2×C4×C73C2×#4111yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C732−1+411yescharacteristic
238C2×C4×C732−1+411yescharacteristic
239C2×Dic73—22no—
240C2×Dic73—22no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263Dic146—22no—
264Dic146—22no—
265Dic146—41no—
266Dic146—41no—
267C8×C73—22no—
268C8×C73—22no—
269C8×C73—41no—
270C8×C73—41no—
271C22×C73—22no—
272C22×C73—22no—
273C22×C73—22no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73C2×#12111yescharacteristic
279C22×C73#52511yescharacteristic
280C22×C73#53611yescharacteristic
281C22×C73C2×#13711yescharacteristic
282C22×C73#57511yescharacteristic
283C22×C73#57511yescharacteristic
284C22×C73#57511yescharacteristic
285C4×C73—22no—
286C4×C73—22no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73#54711yescharacteristic
291C4×C73#54811yescharacteristic
292C4×C73#55211yescharacteristic
293C4×C73#55611yescharacteristic
294Dic73—42no—
295Dic73—42no—
296Dic73—81no—
297Dic73—81no—
298Dic73—81no—
299Dic73—81no—
300Dic73—81no—
301Dic73—81no—
302#24707—731nomaximal, Sylow
303C2×C73—42no—
304C2×C73#241511yescharacteristic
305C2×C73#305411yescharacteristic
306C2×C73#305611yescharacteristic
307C2×C73#311111yescharacteristic
308C2×C73#311711yescharacteristic
309C2×C73#323611yescharacteristic
310C2×C73#324011yescharacteristic
311C2×#479—731no—
312C2×#432D7311yescharacteristic
313#2851—731no—
314C4×C22⋊Q8—731no—
315#2077—731no—
316#2076—731no—
317#2036—731no—
318#2035—731no—
319#1989—731no—
320#1949—731no—
321#1944—731no—
322#1943—731no—
323#1935—731no—
324#1935—731no—
325#1805—731no—
326C73#2470711yescharacteristic, complemented, Sylow
327C2×#125—731no—
328C2×C22⋊Q8—731no—
329C2×C4×Q8—731no—
330C22×C42C2×D7311yescharacteristic
331#479—1464no—
332#432—24no—
333C2×#107—731no—
334C2×#107—731no—
335C2×#106—731no—
336C2×#106—731no—
337C2×C4⋊C8C2×D7311yescharacteristic
338C2×C4⋊C8C2×D7311yescharacteristic
339C2×#103—731no—
340C2×#103—731no—
341C2×#103—731no—
342C2×#103—731no—
343C2×C22⋊C8C2×D7311yescharacteristic
344C2×C22⋊C8C2×D7311yescharacteristic
345C2×#97C2×D7311yescharacteristic
346C2×#97C2×D7311yescharacteristic
347#391—731no—
348#389—731no—
349#389—731no—
350#389—731no—
351#387—1461no—
352#387—1461no—
353#387—1461no—
354#385—1461no—
355#385—1461no—
356#385—1461no—
357#382—731no—
358#380—731no—
359#380—731no—
360#380—731no—
361C4×C4⋊C4—731no—
362C4×C4⋊C4—1461no—
363C4×C22⋊C4—1461no—
364#340—731no—
365#340—731no—
366#340—731no—
367#340—731no—
368#340—731no—
369#340—731no—
370#340—731no—
371#340—731no—
372C22×Q8—731no—
373C23×C4D29211yescharacteristic
374C23×C4D29211yescharacteristic
375C23×C4C22×D7311yescharacteristic
376C22×C8C22×D7311yescharacteristic
377C22×C8C22×D7311yescharacteristic
378C22×C8C22×D7311yescharacteristic
379C22×C8C22×D7311yescharacteristic
380#125—1462no—
381#125—1462no—
382C22⋊Q8—1462no—
383C22⋊Q8—1462no—
384C4×Q8—1462no—
385C4×Q8—1462no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—731no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—731no—
391C2×C4⋊C4—731no—
392C2×C4⋊C4—731no—
393C2×C4⋊C4—1461no—
394C2×C4⋊C4—1461no—
395C2×C4⋊C4—1461no—
396C2×C4⋊C4—1461no—
397C2×C4⋊C4—1461no—
398C2×C4⋊C4—1461no—
399C2×C4⋊C4—1461no—
400C2×C22⋊C4—1461no—
401C2×C22⋊C4—1461no—
402C2×C22⋊C4—1461no—
403C2×C22⋊C4—1461no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—1461no—
407C2×C42—1461no—
408C2×C42D29211yescharacteristic
409C2×C42D29211yescharacteristic
410C2×C42C22×D7311yescharacteristic
411C2×C42C22×D7311yescharacteristic
412#107—1462no—
413#107—1462no—
414#106—1462no—
415#106—1462no—
416C4⋊C8—22no—
417C4⋊C8C22⋊D7314yes—
418#103—1462no—
419#103—1462no—
420#103—1462no—
421#103—1462no—
422C22⋊C8—22no—
423C22⋊C8—22no—
424#97—22no—
425#97—22no—
426#95—1461no—
427#95—1461no—
428#95—1461no—
429#95—1461no—
430#95—1461no—
431#95—1461no—
432#95—1461no—
433#95—1461no—
434#95—1461no—
435#95—1461no—
436#95—1461no—
437C24C2×D29211yescharacteristic
438C2×Q8—732no—
439C2×Q8—1461no—
440C2×Q8—1461no—
441C2×Q8—1461no—
442C2×Q8—1461no—
443C2×Q8—1461no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4C2×D29211yescharacteristic
465C22×C4C2×D29211yescharacteristic
466C22×C4C2×D29211yescharacteristic
467C22×C4C2×D29211yescharacteristic
468C22×C4C2×D29211yescharacteristic
469C22×C4C23×D7311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8C2×C22⋊D7312yes—
481C2×C8C2×C22⋊D7312yes—
482C4⋊C4—2922no—
483C4⋊C4—2922no—
484C4⋊C4—2922no—
485C4⋊C4—2922no—
486C4⋊C4—2922no—
487C4⋊C4—2922no—
488C4⋊C4—732no—
489C4⋊C4—1464no—
490C4⋊C4—1461no—
491C4⋊C4—1461no—
492C4⋊C4—1461no—
493C4⋊C4—1461no—
494C4⋊C4—1461no—
495C4⋊C4—1461no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4—1461no—
503C22⋊C4—2922no—
504C22⋊C4—2922no—
505C22⋊C4—2922no—
506C22⋊C4—1464no—
507C42—22no—
508C42—22no—
509C42—21no—
510C42—21no—
511C42—2922no—
512C42—2922no—
513C42C2×C22⋊D7312yes—
514C42#1192402812yes—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23#1455662412yes—
522C23C22×D29211yescharacteristic
523Q8—2921no—
524Q8—2921no—
525Q8—1462no—
526Q8—1462no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2921no—
555C2×C4—2921no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—2921no—
568C2×C4—1462no—
569C2×C4—1462no—
570C2×C4#1455656512yes—
571C2×C4#1455656512yes—
572C2×C4C22×C22⋊D7311yescharacteristic
573C2×C4#41×D7311yescharacteristic
574C2×C4#41×D7311yescharacteristic
575C2×C4C2×#1192402811yescharacteristic
576C2×C4#1455663811yescharacteristic
577C2×C4#1455663811yescharacteristic
578C8—22no—
579C8—22no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C2×#1455656511yescharacteristic
590C22#1798909911yescharacteristic
591C22#1798916311yescharacteristic
592C22C2×#1455662411yescharacteristic
593C22#1798938711yescharacteristic
594C22#1798938711yescharacteristic
595C22#1798938711yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—2922no—
602C4—2922no—
603C4—5841no—
604C4—5841no—
605C4—5841no—
606C4—5841no—
607C4—5841no—
608C4—5841no—
609C4#1798923611yescharacteristic
610C4#1798924411yescharacteristic
611C4#1798927611yescharacteristic
612C4#1798930511yescharacteristic
613C2—42no—
614C2#2261335411yescharacteristic
615C2#2261954011yescharacteristic
616C2#2261956111yescharacteristic
617C2#2262004211yescharacteristic
618C2#2262010411yescharacteristic
619C2#2262113911yescharacteristic
620C2#2262117311yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#432×C73C2
socleC23×C73C22×D4
prime radicalC24×C73C2×D4
hypercenterC2×#432D73
hypocenterC73#24707
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#17988895C2semidirect
8. #22610886C2semidirect
9. #22610701C2semidirect
10. #22610674C2semidirect
11. #22610669C2semidirect
12. #22610621C2semidirect
13. #22610621C2semidirect
14. #22609947C2semidirect
326. C73#24707semidirect

Maximal subgroups

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

subgroupindex
C2×#179888952
#226182412
C4×#145565702
#226113642
#226113592
#226111352
#226111282
#226108862
#226107012
#226106742
#226106692
#226106212
#226099472
C2×#432×C732
#2470773