Finite Group Databasebeta

← #33057131

Subgroups — #33057131

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619996C211yesmaximal, characteristic
2#22618948C211yesmaximal, characteristic
3#22618880C211yesmaximal, characteristic, complemented
4#22608836C211yesmaximal, characteristic, complemented
5#22608818C211yesmaximal, characteristic, complemented
6#22608806C211yesmaximal, characteristic, complemented
7#22608805C211yesmaximal, characteristic, complemented
8#22608784C211yesmaximal, characteristic, complemented
9#22608771C211yesmaximal, characteristic, complemented
10#22608747C211yesmaximal, characteristic, complemented
11#22608735C211yesmaximal, characteristic, complemented
12#22608717C211yesmaximal, characteristic, complemented
13#22608319C211yesmaximal, characteristic
14#22608226C211yesmaximal, characteristic, complemented
15C73×#1497C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988925C411yescharacteristic
18#17988925C411yescharacteristic
19#17988869C411yescharacteristic
20#17988864C411yescharacteristic
21#17988794C411yescharacteristic
22#17988789C411yescharacteristic
23#17988747C411yescharacteristic
24#17988747C411yescharacteristic
25#17988718—21no—
26#17988718—21no—
27#17988718C2211yescharacteristic
28#17988718C2211yescharacteristic
29Q8×#10596831C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31#17988711C2211yescharacteristic
32#17988711C2211yescharacteristic
33C4×#11924018C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924015C2211yescharacteristic
36C4×#11924015C2211yescharacteristic
37#17988664C2211yescharacteristic
38#17988664C2211yescharacteristic
39#17988662—21no—
40#17988662—21no—
41#17988642—21no—
42#17988640C2211yescharacteristic
43#17988614—21no—
44C2×C4⋊#10596831C2211yescharacteristic
45#17988543—21no—
46C4×#11924012C2211yescharacteristic
47#17988539—21no—
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#533×C73C2211yescharacteristic
61#432×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924015C2×C411yescharacteristic
72C2×#11924012D411yescharacteristic
73C2×#11924012D411yescharacteristic
74C2×#11924011—21no—
75C2×#11924011—21no—
76C22×#10596831—21no—
77C4×Dic146C2×C411yescharacteristic
78C4×Dic146C2311yescharacteristic
79C4×D292C2×C411yescharacteristic
80C4×D292C2311yescharacteristic
81C4×C22⋊D73—21no—
82C4×C22⋊D73—21no—
83#14556550C2×C411yescharacteristic
84#14556548—21no—
85C42×D73—21no—
86#14556524C2×C411yescharacteristic
87#14556524C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90C4⋊#10596831—21no—
91C4⋊#10596831—21no—
92C4⋊#10596831—21no—
93C4⋊#10596831—21no—
94C4⋊#10596831—21no—
95C4⋊#10596831C2×C411yescharacteristic
96C4⋊#10596831C2×C411yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556520—21no—
100#14556520—21no—
101#14556515C2×C411yescharacteristic
102#14556515C2×C411yescharacteristic
103#14556515C2×C411yescharacteristic
104#14556515C2×C411yescharacteristic
105#14556514C2×C411yescharacteristic
106#14556514C2×C411yescharacteristic
107#14556511C2×C411yescharacteristic
108#14556511C2×C411yescharacteristic
109C22⋊#10596831C2×C411yescharacteristic
110C22⋊#10596831C2×C411yescharacteristic
111#14556503—21no—
112#14556503—21no—
113#14556502—21no—
114#14556502—21no—
115#14556502D411yescharacteristic
116#14556502D411yescharacteristic
117C4×#10596831—21no—
118C4×#10596831—21no—
119C4×#10596831C2311yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C8×Dic73—21no—
124C8×Dic73—21no—
125C4⋊Q8×C73C2×C411yescharacteristic
126C4⋊Q8×C73C2×C411yescharacteristic
127#125×C73—21no—
128C22⋊Q8×C73—21no—
129C22⋊Q8×C73C2×C411yescharacteristic
130C22⋊Q8×C73C2×C411yescharacteristic
131C4×Q8×C73—21no—
132C4×Q8×C73C2311yescharacteristic
133C4×Q8×C73C2311yescharacteristic
134#117×C73—21no—
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—41no—
146C2×Dic146C22×C411yescharacteristic
147C2×D292C22×C411yescharacteristic
148C2×C22⋊D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152#11924018—22no—
153#11924018—22no—
154#11924015—41no—
155#11924015—41no—
156#11924012—22no—
157#11924012—41no—
158#11924011—42no—
159#11924011—42no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—42no—
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C2×#10596831C2×D411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173#11924007—21no—
174#11924007—21no—
175C22⋊Dic73—21no—
176#11924005—21no—
177#11924005—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C2×Q8×C73—21no—
182C2×Q8×C73C22×C411yescharacteristic
183C2×Q8×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73#4111yescharacteristic
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73C22×C411yescharacteristic
199C4⋊C4×C73C22×C411yescharacteristic
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73C22×C411yescharacteristic
205C42×C73C2×D411yescharacteristic
206C42×C73#4111yescharacteristic
207C42×C73C2411yescharacteristic
208C23×C73C4×D411yescharacteristic
209C22×D73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—81no—
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—41no—
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C23×C411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C22⋊D73—42no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234D292—21no—
235D292—21no—
236C4×D73—42no—
237C4×D73—41no—
238C4×D73—41no—
239C4×D73—81no—
240Dic146—21no—
241Dic146#13112yes—
242C8×C73—41no—
243C8×C73—41no—
244C8×C73—41no—
245C8×C73—41no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—41no—
254#10596831—41no—
255#10596831#13712yes—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73C2×C4×D411yescharacteristic
260C2×D73—41no—
261C2×D73—41no—
262C2×D73—41no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73—21no—
266C4×C73—21no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73C2×#13111yescharacteristic
272C4×C73#56811yescharacteristic
273C4×C73C2×#13711yescharacteristic
274C4×C73#57511yescharacteristic
275Dic73—22no—
276Dic73—41no—
277Dic73—41no—
278#18013—731nomaximal, Sylow
279C2×C73—41no—
280C2×C73#293311yescharacteristic
281C2×C73C4×#13711yescharacteristic
282C2×C73#295711yescharacteristic
283D73—81no—
284#3107—731no—
285#2971—731no—
286#2962—731no—
287#1592—731no—
288#1590—731no—
289#1588—731no—
290#1587—731no—
291#1584—731no—
292#1583—731no—
293#1579—731no—
294C8×Q16—731no—
295#1573—731no—
296#1497D7311yescharacteristic, complemented
297#1477—731no—
298#1453—731no—
299C73#1801311yescharacteristic, complemented, Sylow
300#533C2×D7311yescharacteristic
301C4×#41—731no—
302#485—731no—
303#485—731no—
304#475—731no—
305#474—731no—
306#462—731no—
307#461—731no—
308#452—731no—
309#452—731no—
310#446—731no—
311#446—731no—
312#446—1461no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C8×Q8—731no—
318C4×Q16—731no—
319C4×Q16—731no—
320C4×SD16—731no—
321C4×SD16—731no—
322#436—731no—
323#436—731no—
324#436—1461no—
325#436—1461no—
326#432—1461no—
327#432C2×D7311yescharacteristic
328#431—731no—
329#431C2×D7311yescharacteristic
330#424—1461no—
331C2×C4⋊C8—731no—
332#405—1461no—
333C4×M16—731no—
334C4×M16—1461no—
335#335—731no—
336#335—731no—
337#334—731no—
338#334—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8C2×D7311yescharacteristic
342Q8⋊C8C2×D7311yescharacteristic
343Q8⋊C8C2×D7311yescharacteristic
344Q8⋊C8C2×D7311yescharacteristic
345D4⋊C8—731no—
346D4⋊C8—731no—
347#322—731no—
348#322—731no—
349#322—731no—
350C82—731no—
351C2×#41—731no—
352C2×Q16—731no—
353C2×Q16—731no—
354C2×SD16—731no—
355C2×SD16—731no—
356C2×M16—731no—
357C2×M16—731no—
358C2×M16—1461no—
359C2×M16—1461no—
360C22×C8—1461no—
361C4⋊Q8C4×D7311yescharacteristic
362C4⋊Q8C4×D7311yescharacteristic
363#125—21no—
364C22⋊Q8—21no—
365C22⋊Q8C4×D7311yescharacteristic
366C22⋊Q8C4×D7311yescharacteristic
367C4×Q8—21no—
368C4×Q8—731no—
369C4×Q8—731no—
370C4×Q8C22×D7311yescharacteristic
371C4×Q8C22×D7311yescharacteristic
372C4×D4—731no—
373C4×D4—731no—
374C4×D4—1461no—
375C4×D4—1461no—
376#117—21no—
377#117—731no—
378#117—1461no—
379C2×C42—1461no—
380C2×C42C22×D7311yescharacteristic
381#107—731no—
382#107—731no—
383#106—731no—
384#106—731no—
385C4⋊C8—21no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8C22×D7311yescharacteristic
398C4⋊C8C22×D7311yescharacteristic
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#103—731no—
404#103—731no—
405#102—731no—
406#102—731no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—731no—
410C22⋊C8—731no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—21no—
414#97—731no—
415#97—731no—
416#97—1461no—
417#97—1461no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8—1461no—
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428#41—2921no—
429#41—1462no—
430C2×Q8—21no—
431C2×Q8—731no—
432C2×Q8C2×C4×D7311yescharacteristic
433C2×Q8C2×C4×D7311yescharacteristic
434C2×D4—731no—
435C2×D4—1461no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4C2×C4×D7311yescharacteristic
440C22×C4D4×D7311yescharacteristic
441C22×C4#1192402711yescharacteristic
442Q16—1462no—
443Q16—1462no—
444SD16—2921no—
445SD16—2921no—
446M16—2922no—
447M16—2922no—
448M16—2921no—
449M16—1462no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—2922no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—731no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—731no—
462C2×C8—731no—
463C2×C8—1461no—
464C2×C8—1461no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—731no—
473C4⋊C4—731no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4C2×C4×D7311yescharacteristic
477C4⋊C4C2×C4×D7311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—1461no—
481C22⋊C4—1461no—
482C22⋊C4—1461no—
483C42—21no—
484C42—21no—
485C42—1461no—
486C42—1461no—
487C42—1461no—
488C42C2×C4×D7311yescharacteristic
489C42D4×D7311yescharacteristic
490C42#1192402711yescharacteristic
491C42C23×D7311yescharacteristic
492C23—1461no—
493C23#1455655111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—732no—
500Q8—1461no—
501D4—2922no—
502D4—1461no—
503D4—1461no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—2922no—
514C2×C4—2921no—
515C2×C4—2921no—
516C2×C4—5841no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4#1455655111yescharacteristic
521C2×C4#1455655111yescharacteristic
522C2×C4#1455655111yescharacteristic
523C2×C4C22×C4×D7311yescharacteristic
524C2×C4C2×D4×D7311yescharacteristic
525C2×C4C2×#1192402711yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—2921no—
531C8—2921no—
532C8—732no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C8—1461no—
537C8—1461no—
538C8—1461no—
539C8—1461no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—2921no—
544C22—2921no—
545C22—2921no—
546C22C2×#1455655111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—2921no—
556C4—2921no—
557C4—1462no—
558C4#131×D7311yescharacteristic
559C4#1798935211yescharacteristic
560C4#137×D7311yescharacteristic
561C4#1798938611yescharacteristic
562C2—41no—
563C2—5841no—
564C2#2261866111yescharacteristic
565C2#2261874611yescharacteristic
566C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1497C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C2×C4
cosocleC42×C73C24
hypercenter#1497D73
hypocenterC73#18013
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
3. #22618880C2semidirect
4. #22608836C2semidirect
5. #22608818C2semidirect
6. #22608806C2semidirect
7. #22608805C2semidirect
8. #22608784C2semidirect
9. #22608771C2semidirect
10. #22608747C2semidirect
11. #22608735C2semidirect
12. #22608717C2semidirect
14. #22608226C2semidirect
15. C73×#1497C2semidirect
296. #1497D73semidirect
299. C73#18013semidirect

Maximal subgroups

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

subgroupindex
#226199962
#226189482
#226188802
#226088362
#226088182
#226088062
#226088052
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