Finite Group Databasebeta

← #33056727

Subgroups — #33056727

Order 18688.

590 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620514C211yesmaximal, characteristic
2#22618862C211yesmaximal, characteristic
3#22618860C211yesmaximal, characteristic
4#22608805C211yesmaximal, characteristic, complemented
5#22608804C211yesmaximal, characteristic, complemented
6#22608803C211yesmaximal, characteristic, complemented
7#22608802C211yesmaximal, characteristic, complemented
8#22608801C211yesmaximal, characteristic, complemented
9#22608800C211yesmaximal, characteristic, complemented
10#22608799C211yesmaximal, characteristic, complemented
11#22608685C211yesmaximal, characteristic
12#22608384C211yesmaximal, characteristic
13#22608384C211yesmaximal, characteristic
14#322×D73C211yesmaximal, characteristic
15C73×#1587C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17#17989141C2211yescharacteristic
18#17988991C411yescharacteristic
19#17988965C411yescharacteristic
20#17988936C411yescharacteristic
21#17988936C411yescharacteristic
22#17988829C411yescharacteristic
23#17988827C411yescharacteristic
24#17988827C411yescharacteristic
25#17988825C411yescharacteristic
26#17988718C2211yescharacteristic
27#17988717C2211yescharacteristic
28#17988716—21no—
29#17988715—21no—
30#17988714C2211yescharacteristic
31Q8×#10596831C2211yescharacteristic
32C8×Dic146—21no—
33C8×Dic146C2211yescharacteristic
34#17988711—21no—
35#17988711C2211yescharacteristic
36C4×Dic292C2211yescharacteristic
37C4×#11924018C2211yescharacteristic
38C4×#11924018C2211yescharacteristic
39#17988612—21no—
40#17988612—21no—
41#17988609C2211yescharacteristic
42#17988609C2211yescharacteristic
43#17988544—21no—
44#17988541—21no—
45C4×C8×D73C2211yescharacteristic
46C4×C8×D73C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988338C2211yescharacteristic
49#17988337C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54Q8⋊#10596831C2211yescharacteristic
55#17988317C2211yescharacteristic
56#17988317C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988308C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×Dic292C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924011—21no—
71C2×#11924011—21no—
72C2×C8×D73—21no—
73C2×C8×D73C2×C411yescharacteristic
74C2×C8×D73C2×C411yescharacteristic
75C2×C8×D73D411yescharacteristic
76C2×C8×D73D411yescharacteristic
77#14556590C2×C411yescharacteristic
78#14556590C2×C411yescharacteristic
79#14556589C2×C411yescharacteristic
80#14556589C2×C411yescharacteristic
81#14556581—21no—
82#14556581—21no—
83#14556571C2×C411yescharacteristic
84#14556571C2×C411yescharacteristic
85#14556569—21no—
86#14556569—21no—
87#14556567C2×C411yescharacteristic
88#14556567C2×C411yescharacteristic
89C4×Dic146—21no—
90C4×Dic146—21no—
91C4×Dic146C2311yescharacteristic
92C4×Dic146C2311yescharacteristic
93#14556548—21no—
94#14556548—21no—
95C42×D73C2311yescharacteristic
96#14556525C2×C411yescharacteristic
97#14556524C2×C411yescharacteristic
98#14556524C2×C411yescharacteristic
99C4⋊#10596831—21no—
100C4⋊#10596831—21no—
101C4⋊#10596831C2311yescharacteristic
102C4⋊#10596831C2311yescharacteristic
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556520—21no—
108#14556520—21no—
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556515C2×C411yescharacteristic
112#14556515C2×C411yescharacteristic
113#14556514C2×C411yescharacteristic
114#14556514C2×C411yescharacteristic
115#14556502—21no—
116#14556501—21no—
117#14556501—21no—
118C4×#10596831—21no—
119C4×#10596831C2311yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C8×Dic73—21no—
123C8×Dic73—21no—
124C8×Dic73—21no—
125C8×Dic73C2×C411yescharacteristic
126C8×Dic73C2×C411yescharacteristic
127C8×Dic73D411yescharacteristic
128C8×Dic73D411yescharacteristic
129C2×Q16×C73C2×C411yescharacteristic
130C4×Q8×C73C2311yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132#107×C73C2×C411yescharacteristic
133C4⋊C8×C73—21no—
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#103×C73C2×C411yescharacteristic
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146C22×C411yescharacteristic
147C2×Dic146C22×C411yescharacteristic
148C2×C4×D73C22×C411yescharacteristic
149C2×C4×D73C2×D411yescharacteristic
150C2×C4×D73#4111yescharacteristic
151Dic292—41no—
152#11924018—41no—
153#11924018—41no—
154#11924011—42no—
155#11924011—42no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C2×D411yescharacteristic
162C2×#10596831C2×D411yescharacteristic
163C8×D73—24no—
164C8×D73—22no—
165C8×D73—22no—
166C8×D73—41no—
167C8×D73—41no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73C22×C411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73C22×C411yescharacteristic
189C4×Dic73C2×D411yescharacteristic
190C4×Dic73#4111yescharacteristic
191C2×Q8×C73C22×C411yescharacteristic
192C2×Q8×C73C22×C411yescharacteristic
193Q16×C73—41no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73C22×C411yescharacteristic
204C4⋊C4×C73C22×C411yescharacteristic
205C42×C73—21no—
206C42×C73—21no—
207C42×C73C2411yescharacteristic
208C22×D73C4×D411yescharacteristic
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73C23×C411yescharacteristic
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73C4×D411yescharacteristic
225C2×Dic73C4×D411yescharacteristic
226C2×Dic73C4×D411yescharacteristic
227C4×D73—21no—
228C4×D73—21no—
229C4×D73—22no—
230C4×D73#13712yes—
231C4×D73#13712yes—
232Dic146—21no—
233Dic146—21no—
234Dic146—21no—
235Dic146—21no—
236Dic146—42no—
237Dic146—42no—
238C8×C73—22no—
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—41no—
244C8×C73—41no—
245#10596831—22no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—41no—
251#10596831—41no—
252C22×C73C2×C4×D411yescharacteristic
253C2×D73—21no—
254C2×D73—21no—
255C2×D73#44112yes—
256C4×C73—21no—
257C4×C73—41no—
258C4×C73—41no—
259C4×C73—41no—
260C4×C73—41no—
261C4×C73#56811yescharacteristic
262C4×C73#56811yescharacteristic
263C4×C73C2×#13711yescharacteristic
264C4×C73C2×#13711yescharacteristic
265Dic73—21no—
266Dic73—41no—
267Dic73—41no—
268Dic73—41no—
269Dic73—41no—
270Dic73#44112yes—
271Dic73#44312yes—
272#17980—731nomaximal, Sylow
273C2×C73#293211yescharacteristic
274C2×C73C2×#44111yescharacteristic
275C2×C73C2×#44311yescharacteristic
276D73—22no—
277#3170—731no—
278#2960—731no—
279#2960—731no—
280#1587—731no—
281#1587—731no—
282#1587—731no—
283#1587—731no—
284#1587—731no—
285#1587—731no—
286#1587—731no—
287#1587D7311yescharacteristic, complemented
288#1566—731no—
289#1493—731no—
290#1493—731no—
291C2×#322—731no—
292C73#1798011yescharacteristic, complemented, Sylow
293#533—731no—
294#533—731no—
295#500—731no—
296#494—731no—
297#487—731no—
298#487—731no—
299#467—731no—
300#467—731no—
301#467—731no—
302#467—731no—
303#446—731no—
304#446—731no—
305#446—731no—
306#446—1461no—
307#446—1461no—
308#446C2×D7311yescharacteristic
309C8×Q8—731no—
310C8×Q8—731no—
311C8×Q8—731no—
312C8×Q8—1461no—
313C8×Q8—1461no—
314C8×Q8C2×D7311yescharacteristic
315C4×Q16—731no—
316C4×Q16—731no—
317C4×Q16—731no—
318C4×Q16C2×D7311yescharacteristic
319#424—1461no—
320#424—1461no—
321#423—731no—
322#423—731no—
323#405—1461no—
324#405—1461no—
325C2×C4×C8—731no—
326C2×C4×C8—731no—
327C2×C4×C8—731no—
328#334—731no—
329#334—731no—
330#334—731no—
331#334C2×D7311yescharacteristic
332Q8⋊C8—731no—
333Q8⋊C8—731no—
334Q8⋊C8—731no—
335Q8⋊C8—731no—
336Q8⋊C8—731no—
337Q8⋊C8—731no—
338Q8⋊C8C2×D7311yescharacteristic
339Q8⋊C8C2×D7311yescharacteristic
340#322—731no—
341#322—731no—
342#322—731no—
343#322C2×D7311yescharacteristic
344C2×Q16—731no—
345C2×Q16—731no—
346C2×Q16—731no—
347C2×Q16C4×D7311yescharacteristic
348C2×M16—1461no—
349C2×M16—1461no—
350C22×C8—731no—
351C22×C8—731no—
352C22×C8—731no—
353C22×C8—731no—
354C22×C8—1461no—
355C4⋊Q8—731no—
356C4⋊Q8—731no—
357C4⋊Q8—731no—
358C4⋊Q8—731no—
359#125—1461no—
360#125—1461no—
361C22⋊Q8—731no—
362C22⋊Q8—731no—
363C22⋊Q8—731no—
364C22⋊Q8—731no—
365C22⋊Q8—1461no—
366C22⋊Q8—1461no—
367C4×Q8—731no—
368C4×Q8—731no—
369C4×Q8—1461no—
370C4×Q8—1461no—
371C4×Q8C22×D7311yescharacteristic
372C4×Q8C22×D7311yescharacteristic
373#117—1461no—
374#117—1461no—
375C2×C42—731no—
376#107—731no—
377#107—731no—
378#107—731no—
379#107C4×D7311yescharacteristic
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—731no—
383C4⋊C8—731no—
384C4⋊C8—1461no—
385C4⋊C8—1461no—
386C4⋊C8—1461no—
387C4⋊C8—1461no—
388C4⋊C8—1461no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8C22×D7311yescharacteristic
393C4⋊C8C22×D7311yescharacteristic
394#103—731no—
395#103—731no—
396#103—731no—
397#103—731no—
398#103—731no—
399#103—731no—
400#103C4×D7311yescharacteristic
401#103C4×D7311yescharacteristic
402#97—21no—
403#97—1461no—
404#97—1461no—
405#97—1461no—
406C4×C8—21no—
407C4×C8—731no—
408C4×C8—731no—
409C4×C8—731no—
410C4×C8—731no—
411C4×C8—731no—
412C4×C8—731no—
413C4×C8—731no—
414C4×C8—1461no—
415C4×C8—1461no—
416C4×C8—1461no—
417C4×C8—1461no—
418C4×C8C22×D7311yescharacteristic
419C4×C8C22×D7311yescharacteristic
420C4×C8C22×D7311yescharacteristic
421C2×Q8—731no—
422C2×Q8—731no—
423C2×Q8—1461no—
424C2×Q8—1461no—
425C2×Q8C2×C4×D7311yescharacteristic
426C2×Q8C2×C4×D7311yescharacteristic
427C22×C4—731no—
428C22×C4—731no—
429C22×C4—731no—
430Q16—41no—
431Q16—2921no—
432Q16—2921no—
433Q16—2921no—
434M16—2922no—
435M16—2922no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—2921no—
440C2×C8—2921no—
441C2×C8—731no—
442C2×C8—731no—
443C2×C8—731no—
444C2×C8—731no—
445C2×C8—1462no—
446C2×C8—1462no—
447C2×C8—1464no—
448C2×C8—1461no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8C2×C4×D7311yescharacteristic
452C2×C8C2×C4×D7311yescharacteristic
453C2×C8D4×D7311yescharacteristic
454C2×C8D4×D7311yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—731no—
458C4⋊C4—731no—
459C4⋊C4—1461no—
460C4⋊C4—1461no—
461C4⋊C4—1461no—
462C4⋊C4—1461no—
463C4⋊C4—1461no—
464C4⋊C4—1461no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4C2×C4×D7311yescharacteristic
472C4⋊C4C2×C4×D7311yescharacteristic
473C22⋊C4—1461no—
474C22⋊C4—1461no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C42—21no—
478C42—21no—
479C42—731no—
480C42—731no—
481C42—731no—
482C42—1461no—
483C42—1461no—
484C42C23×D7311yescharacteristic
485C23—731no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—2922no—
491Q8—2922no—
492Q8—1461no—
493Q8—1461no—
494Q8—1461no—
495Q8—1461no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—731no—
501C2×C4—731no—
502C2×C4—732no—
503C2×C4—732no—
504C2×C4—731no—
505C2×C4—1462no—
506C2×C4—1461no—
507C2×C4—1461no—
508C2×C4—1461no—
509C2×C4—1461no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4C22×C4×D7311yescharacteristic
513C2×C4C2×D4×D7311yescharacteristic
514C2×C4#41×D7311yescharacteristic
515C8—22no—
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—2921no—
523C8—2921no—
524C8—1462no—
525C8—1461no—
526C8—1461no—
527C8—1461no—
528C8—1461no—
529C22—732no—
530C22—1461no—
531C22—1461no—
532C22C4×D4×D7311yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—2921no—
539C4—2921no—
540C4—2921no—
541C4—2921no—
542C4—732no—
543C4—732no—
544C4—1461no—
545C4#1798935211yescharacteristic
546C4#1798935311yescharacteristic
547C4#137×D7311yescharacteristic
548C4#137×D7311yescharacteristic
549C2—1462no—
550C2#2261864511yescharacteristic
551C2#441×D7311yescharacteristic
552C2#443×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1587C2
socleC22×C73C2×C4×D4
prime radicalC22×D73C4×D4
cosocleC42×C73C24
hypercenter#1587D73
hypocenterC73#17980
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #22608805C2semidirect
5. #22608804C2semidirect
6. #22608803C2semidirect
7. #22608802C2semidirect
8. #22608801C2semidirect
9. #22608800C2semidirect
10. #22608799C2semidirect
15. C73×#1587C2semidirect
287. #1587D73semidirect
292. C73#17980semidirect

Maximal subgroups

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

subgroupindex
#226205142
#226188622
#226188602
#226088052
#226088042
#226088032
#226088022
#226088012
#226088002
#226087992
#226086852
#226083842
#322×D732
C73×#15872
#1798073