Finite Group Databasebeta

← #33055876

Subgroups — #33055876

Order 18688.

618 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619968C211yesmaximal, characteristic
2#22618862C211yesmaximal, characteristic
3C8×Q8×D73C211yesmaximal, characteristic
4#22608783C211yesmaximal, characteristic, complemented
5#22608781C211yesmaximal, characteristic, complemented
6#22608779C211yesmaximal, characteristic, complemented
7Q16×#10596831C211yesmaximal, characteristic, complemented
8#22608737C211yesmaximal, characteristic, complemented
9#22608735C211yesmaximal, characteristic, complemented
10#22608735C211yesmaximal, characteristic, complemented
11#22608704C211yesmaximal, characteristic
12#22608358C211yesmaximal, characteristic
13#22608332C211yesmaximal, characteristic
14#22608216C211yesmaximal, characteristic
15C73×#1584C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×Q8×D73C2211yescharacteristic
18#17988924C411yescharacteristic
19#17988921C411yescharacteristic
20#17988881C411yescharacteristic
21#17988880C411yescharacteristic
22#17988796C411yescharacteristic
23#17988795C411yescharacteristic
24#17988744C411yescharacteristic
25#17988741C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988715—21no—
28Q8×#10596831C2211yescharacteristic
29Q8×#10596831C2211yescharacteristic
30C8×Dic146—21no—
31C8×Dic146C2211yescharacteristic
32#17988711—21no—
33#17988711—21no—
34#17988711C2211yescharacteristic
35#17988711C2211yescharacteristic
36C4×Dic292C2211yescharacteristic
37C4×#11924018C2211yescharacteristic
38C4×#11924018C2211yescharacteristic
39#17988638C2211yescharacteristic
40#17988638C2211yescharacteristic
41#17988612—21no—
42#17988609C2211yescharacteristic
43C4⋊C8×D73—21no—
44C4⋊C8×D73C2211yescharacteristic
45#17988544—21no—
46C4×C8×D73—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988339C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54Q8⋊#10596831C2211yescharacteristic
55#17988317C2211yescharacteristic
56#17988317C2211yescharacteristic
57#17988308C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×Q8×D73C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924018C2×C411yescharacteristic
71C2×#11924011—21no—
72C2×C8×D73—21no—
73C2×C8×D73D411yescharacteristic
74C2×C8×D73D411yescharacteristic
75#14556590C2×C411yescharacteristic
76#14556589C2×C411yescharacteristic
77#14556581—21no—
78#14556571C2×C411yescharacteristic
79#14556569—21no—
80#14556567C2×C411yescharacteristic
81Q8×Dic73C2×C411yescharacteristic
82C4×Dic146—21no—
83C4×Dic146—21no—
84C4×Dic146C2311yescharacteristic
85C4×Dic146C2311yescharacteristic
86#14556556—21no—
87#14556556C2×C411yescharacteristic
88#14556548—21no—
89C4⋊C4×D73—21no—
90C4⋊C4×D73C2×C411yescharacteristic
91C42×D73—21no—
92C42×D73C2311yescharacteristic
93#14556525C2×C411yescharacteristic
94#14556524C2×C411yescharacteristic
95#14556524C2×C411yescharacteristic
96C4⋊#10596831—21no—
97C4⋊#10596831—21no—
98C4⋊#10596831C2311yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556520C2×C411yescharacteristic
108#14556520C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556515C2×C411yescharacteristic
112#14556515C2×C411yescharacteristic
113#14556514C2×C411yescharacteristic
114#14556514C2×C411yescharacteristic
115#14556503—21no—
116#14556503C2×C411yescharacteristic
117#14556503C2×C411yescharacteristic
118#14556501—21no—
119C4×#10596831—21no—
120C4×#10596831—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
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
148Q8×D73—22no—
149Q8×D73—22no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73C22×C411yescharacteristic
153C2×C4×D73C2×D411yescharacteristic
154C2×C4×D73#4111yescharacteristic
155Dic292—22no—
156#11924018—22no—
157#11924018—22no—
158#11924011—42no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C8×D73—22no—
167C8×D73—42no—
168C8×D73Q1614yescomplemented
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
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#11924005—21no—
182#11924005—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73C22×C411yescharacteristic
188C4×Dic73C2×D411yescharacteristic
189C4×Dic73#4111yescharacteristic
190C2×Q8×C73C22×C411yescharacteristic
191C2×Q8×C73C22×C411yescharacteristic
192Q16×C73—22no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73C22×C411yescharacteristic
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73C22×C411yescharacteristic
203C4⋊C4×C73C22×C411yescharacteristic
204C42×C73—21no—
205C42×C73—21no—
206C42×C73C2411yescharacteristic
207C22×D73C4×D411yescharacteristic
208Q8×C73—21no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73#13112yes—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73C23×C411yescharacteristic
217C2×C4×C73C22×D411yescharacteristic
218C2×C4×C73C2×#4111yescharacteristic
219C2×Dic73—21no—
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73C4×D411yescharacteristic
224C2×Dic73C4×D411yescharacteristic
225C2×Dic73C4×D411yescharacteristic
226C4×D73—24no—
227C4×D73—21no—
228C4×D73—21no—
229C4×D73—41no—
230C4×D73—42no—
231C4×D73C2×Q1612yes—
232C4×D73#13512yes—
233Dic146—24no—
234Dic146—21no—
235Dic146—21no—
236Dic146—21no—
237Dic146—42no—
238Dic146#13112yes—
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—41no—
243C8×C73—41no—
244C8×C73—41no—
245C8×C73C2×Q1612yes—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—41no—
250#10596831—41no—
251#10596831—41no—
252#10596831C2×Q1612yes—
253C22×C73C2×C4×D411yescharacteristic
254C2×D73—21no—
255C2×D73—21no—
256C2×D73C4×Q1612yes—
257C4×C73—22no—
258C4×C73—21no—
259C4×C73—41no—
260C4×C73—41no—
261C4×C73—41no—
262C4×C73C2×#13111yescharacteristic
263C4×C73C2×#13111yescharacteristic
264C4×C73C22×Q1611yescharacteristic
265C4×C73C2×#13511yescharacteristic
266Dic73—21no—
267Dic73—22no—
268Dic73—21no—
269Dic73—41no—
270Dic73—41no—
271Dic73—41no—
272Dic73C4×Q1612yes—
273#17903—731nomaximal, Sylow
274C2×C73#292911yescharacteristic
275C2×C73C2×C4×Q1611yescharacteristic
276C2×C73#295511yescharacteristic
277D73—22no—
278#3104—731no—
279#2960—731no—
280C2×C8×Q8—731no—
281#1584—731no—
282#1584—731no—
283#1584—731no—
284#1584D7311yescharacteristic, complemented
285C8×Q16—731no—
286C8×Q16—731no—
287C8×Q16—731no—
288C8×Q16—731no—
289#1571—731no—
290#1487—731no—
291#1481—731no—
292#1450—731no—
293C73#1790311yescharacteristic, complemented, Sylow
294#533—731no—
295C2×C4×Q8—731no—
296#484—731no—
297#484—731no—
298#477—731no—
299#477—731no—
300#462—731no—
301#462—731no—
302#451—731no—
303#451—731no—
304#446—731no—
305#446—1461no—
306#446C2×D7311yescharacteristic
307C8×Q8—731no—
308C8×Q8—731no—
309C8×Q8—731no—
310C8×Q8—731no—
311C8×Q8—731no—
312C8×Q8—1461no—
313C8×Q8—1461no—
314C8×Q8—1461no—
315C8×Q8C2×D7311yescharacteristic
316C4×Q16—731no—
317C4×Q16—731no—
318C4×Q16—731no—
319C4×Q16C2×D7311yescharacteristic
320#431—731no—
321#431—731no—
322#424—1461no—
323#423—731no—
324C2×C4⋊C8—731no—
325C2×C4⋊C8—1461no—
326#405—1461no—
327C2×C4×C8—731no—
328C2×C4×C8—1461no—
329#335—731no—
330#335—731no—
331#335—731no—
332#335C2×D7311yescharacteristic
333Q8⋊C8—731no—
334Q8⋊C8—731no—
335Q8⋊C8—731no—
336Q8⋊C8—731no—
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8C2×D7311yescharacteristic
340Q8⋊C8C2×D7311yescharacteristic
341#322—731no—
342#322C2×D7311yescharacteristic
343C82—731no—
344C82—731no—
345C22×Q8—731no—
346C2×Q16—731no—
347C2×Q16—731no—
348C2×Q16—731no—
349C2×Q16C4×D7311yescharacteristic
350C2×M16—1461no—
351C22×C8—731no—
352C22×C8—731no—
353C22×C8—1461no—
354C4⋊Q8—731no—
355C4⋊Q8—731no—
356#125—1461no—
357C22⋊Q8—731no—
358C22⋊Q8—731no—
359C22⋊Q8—1461no—
360C4×Q8—731no—
361C4×Q8—731no—
362C4×Q8—731no—
363C4×Q8—731no—
364C4×Q8—1461no—
365C4×Q8—1461no—
366C4×Q8—1461no—
367C4×Q8C22×D7311yescharacteristic
368C4×Q8C22×D7311yescharacteristic
369#117—1461no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—1461no—
372C2×C42—731no—
373C2×C42—1461no—
374#107—731no—
375#107—731no—
376#107—731no—
377#107C4×D7311yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—731no—
381C4⋊C8—731no—
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⋊C8—1461no—
393C4⋊C8C22×D7311yescharacteristic
394C4⋊C8C22×D7311yescharacteristic
395#103—731no—
396#103—731no—
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103C4×D7311yescharacteristic
402#103C4×D7311yescharacteristic
403C22⋊C8—731no—
404C22⋊C8—731no—
405C22⋊C8—1461no—
406#97—21no—
407#97—1461no—
408C4×C8—21no—
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×C8—1461no—
419C4×C8C22×D7311yescharacteristic
420C4×C8C22×D7311yescharacteristic
421C4×C8C22×D7311yescharacteristic
422C2×Q8—731no—
423C2×Q8—731no—
424C2×Q8—1461no—
425C2×Q8—1461no—
426C2×Q8—1462no—
427C2×Q8—1462no—
428C2×Q8C2×C4×D7311yescharacteristic
429C2×Q8C2×C4×D7311yescharacteristic
430C22×C4—731no—
431C22×C4—731no—
432C22×C4—731no—
433C22×C4—1461no—
434C22×C4—1461no—
435Q16—22no—
436Q16—1462no—
437Q16—1462no—
438Q16—1462no—
439M16—2922no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—2922no—
444C2×C8—731no—
445C2×C8—734no—
446C2×C8—731no—
447C2×C8—731no—
448C2×C8—731no—
449C2×C8—1462no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8C2×C4×D7311yescharacteristic
454C2×C8C2×C4×D7311yescharacteristic
455C2×C8D4×D7311yescharacteristic
456C2×C8D4×D7311yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—731no—
460C4⋊C4—731no—
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—
475C42—21no—
476C42—21no—
477C42—731no—
478C42—731no—
479C42—731no—
480C42—1461no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42C23×D7311yescharacteristic
485C23—731no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—2922no—
490Q8—732no—
491Q8—1464no—
492Q8—1461no—
493Q8—1461no—
494Q8—1461no—
495Q8#1455659912yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—2921no—
501C2×C4—2922no—
502C2×C4—731no—
503C2×C4—732no—
504C2×C4—732no—
505C2×C4—731no—
506C2×C4—731no—
507C2×C4—1464no—
508C2×C4—1461no—
509C2×C4—1461no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4C22×C4×D7311yescharacteristic
515C2×C4C2×D4×D7311yescharacteristic
516C2×C4#41×D7311yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—2921no—
524C8—2921no—
525C8—2921no—
526C8—732no—
527C8—1461no—
528C8—1461no—
529C8—1461no—
530C8Q16×D7312yes—
531C22—732no—
532C22—1461no—
533C22—1461no—
534C22C4×D4×D7311yescharacteristic
535C4—21no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—2921no—
541C4—2921no—
542C4—2921no—
543C4—732no—
544C4—1461no—
545C4—1461no—
546C4—1462no—
547C4#131×D7311yescharacteristic
548C4C2×#1455659911yescharacteristic
549C4C2×Q16×D7311yescharacteristic
550C4#135×D7311yescharacteristic
551C2—1462no—
552C2#2261862211yescharacteristic
553C2C4×Q16×D7311yescharacteristic
554C2#2261883111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1584C2
socleC22×C73C2×C4×D4
prime radicalC22×D73C4×D4
cosocleC42×C73C24
hypercenter#1584D73
hypocenterC73#17903
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #22608783C2semidirect
5. #22608781C2semidirect
6. #22608779C2semidirect
7. Q16×#10596831C2semidirect
8. #22608737C2semidirect
9. #22608735C2semidirect
10. #22608735C2semidirect
15. C73×#1584C2semidirect
168. C8×D73Q16semidirect
284. #1584D73semidirect
293. C73#17903semidirect

Maximal subgroups

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

subgroupindex
#226199682
#226188622
C8×Q8×D732
#226087832
#226087812
#226087792
Q16×#105968312
#226087372
#226087352
#226087042
#226083582
#226083322
#226082162
C73×#15842
#1790373