Finite Group Databasebeta

← #33057372

Subgroups — #33057372

Order 18688.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619970C211yesmaximal, characteristic
2#22619032C211yesmaximal, characteristic
3#22619020C211yesmaximal, characteristic
4#22608837C211yesmaximal, characteristic, complemented
5#22608825C211yesmaximal, characteristic, complemented
6#22608805C211yesmaximal, characteristic, complemented
7#22608799C211yesmaximal, characteristic, complemented
8#22608784C211yesmaximal, characteristic, complemented
9#22608778C211yesmaximal, characteristic, complemented
10#22608747C211yesmaximal, characteristic, complemented
11#22608735C211yesmaximal, characteristic, complemented
12#22608709C211yesmaximal, characteristic
13#22608405C211yesmaximal, characteristic
14#22608231C211yesmaximal, characteristic
15C73×#1479C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17#17988922C411yescharacteristic
18#17988922C411yescharacteristic
19#17988882C411yescharacteristic
20#17988882C411yescharacteristic
21#17988797C411yescharacteristic
22#17988797C411yescharacteristic
23#17988743C411yescharacteristic
24#17988743C411yescharacteristic
25#17988718—21no—
26#17988718—21no—
27#17988718C2211yescharacteristic
28#17988718C2211yescharacteristic
29#17988717—21no—
30#17988714C2211yescharacteristic
31#17988714C2211yescharacteristic
32Q8×#10596831C2211yescharacteristic
33Q8×#10596831C2211yescharacteristic
34C8×Dic146—21no—
35#17988711C2211yescharacteristic
36#17988711C2211yescharacteristic
37C4×#11924018C2211yescharacteristic
38C4×#11924018C2211yescharacteristic
39C4×#11924018C2211yescharacteristic
40C4×#11924018C2211yescharacteristic
41#17988645—21no—
42#17988645—21no—
43#17988644—21no—
44#17988644C2211yescharacteristic
45#17988640—21no—
46#17988640C2211yescharacteristic
47#17988640C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C2×C4×Q8×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924018C2×C411yescharacteristic
71#14556591C2×C411yescharacteristic
72#14556591C2×C411yescharacteristic
73#14556583—21no—
74#14556570—21no—
75#14556570C2×C411yescharacteristic
76#14556570C2×C411yescharacteristic
77C4×Dic146—21no—
78C4×Dic146C2311yescharacteristic
79C4×Dic146C2311yescharacteristic
80#14556550—21no—
81#14556524C2×C411yescharacteristic
82#14556524C2×C411yescharacteristic
83#14556524C2×C411yescharacteristic
84#14556524C2×C411yescharacteristic
85C4⋊#10596831—21no—
86C4⋊#10596831—21no—
87C4⋊#10596831—21no—
88C4⋊#10596831—21no—
89C4⋊#10596831C2×C411yescharacteristic
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831D411yescharacteristic
92C4⋊#10596831D411yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94C4⋊#10596831C2311yescharacteristic
95#14556520—21no—
96#14556520—21no—
97#14556520—21no—
98#14556520—21no—
99#14556515C2×C411yescharacteristic
100#14556515C2×C411yescharacteristic
101#14556515C2×C411yescharacteristic
102#14556515C2×C411yescharacteristic
103#14556514C2×C411yescharacteristic
104#14556514C2×C411yescharacteristic
105#14556514C2×C411yescharacteristic
106#14556514C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831C2×C411yescharacteristic
109C22⋊#10596831C2×C411yescharacteristic
110C22⋊#10596831D411yescharacteristic
111C22⋊#10596831D411yescharacteristic
112#14556502—21no—
113#14556502—21no—
114#14556502—21no—
115#14556501—21no—
116#14556501—21no—
117C4×#10596831—21no—
118C4×#10596831—21no—
119C4×#10596831C2311yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C8×Dic73—21no—
124C8×Dic73—21no—
125C22×Q8×C73C2×C411yescharacteristic
126C4×Q8×C73—21no—
127C4×Q8×C73—21no—
128C4×Q8×C73C2×C411yescharacteristic
129C4×Q8×C73C2×C411yescharacteristic
130C4×Q8×C73C2311yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132C2×C4⋊C4×C73—21no—
133C2×C4⋊C4×C73C2×C411yescharacteristic
134C2×C42×C73—21no—
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×Dic146C22×C411yescharacteristic
147#11924018—22no—
148#11924018—22no—
149#11924018—41no—
150#11924018—41no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831C22×C411yescharacteristic
154C2×#10596831C22×C411yescharacteristic
155C2×#10596831C22×C411yescharacteristic
156C2×#10596831C22×C411yescharacteristic
157C2×#10596831C2×D411yescharacteristic
158C2×#10596831C2×D411yescharacteristic
159C2×#10596831C2×D411yescharacteristic
160C2×#10596831C2×D411yescharacteristic
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73C22×C411yescharacteristic
165C4⋊Dic73C22×C411yescharacteristic
166#11924007—21no—
167#11924007—21no—
168#11924007—21no—
169#11924007—21no—
170C22⋊Dic73—21no—
171C22⋊Dic73—21no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C2×Q8×C73—21no—
175C2×Q8×C73—22no—
176C2×Q8×C73—41no—
177C2×Q8×C73C22×C411yescharacteristic
178C2×Q8×C73C22×C411yescharacteristic
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73#4111yescharacteristic
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73C22×C411yescharacteristic
194C4⋊C4×C73C22×C411yescharacteristic
195C42×C73—21no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73C22×C411yescharacteristic
200C42×C73C2×D411yescharacteristic
201C42×C73#4111yescharacteristic
202C42×C73C2411yescharacteristic
203C23×C73C4×D411yescharacteristic
204Q8×C73—21no—
205Q8×C73—21no—
206Q8×C73—21no—
207Q8×C73—42no—
208Q8×C73#13112yes—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—41no—
218C2×C4×C73—42no—
219C2×C4×C73—42no—
220C2×C4×C73C4×D411yescharacteristic
221C2×C4×C73C4×D411yescharacteristic
222C2×C4×C73C4×D411yescharacteristic
223C2×C4×C73C23×C411yescharacteristic
224C2×C4×C73C22×D411yescharacteristic
225C2×C4×C73C2×#4111yescharacteristic
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230Dic146—21no—
231Dic146—21no—
232Dic146—21no—
233Dic146—21no—
234Dic146—42no—
235C8×C73—41no—
236C8×C73—41no—
237C8×C73—41no—
238C8×C73—41no—
239#10596831—21no—
240#10596831—21no—
241#10596831—21no—
242#10596831—21no—
243#10596831—21no—
244#10596831—21no—
245#10596831—21no—
246#10596831—21no—
247#10596831—41no—
248#10596831—41no—
249C22×C73—21no—
250C22×C73—21no—
251C22×C73—21no—
252C22×C73C2×C4×D411yescharacteristic
253C4×C73—21no—
254C4×C73—22no—
255C4×C73—21no—
256C4×C73—21no—
257C4×C73—21no—
258C4×C73—41no—
259C4×C73—41no—
260C4×C73—41no—
261C4×C73C2×#13111yescharacteristic
262C4×C73#56811yescharacteristic
263C4×C73#57811yescharacteristic
264C4×C73#57811yescharacteristic
265Dic73—41no—
266Dic73—41no—
267Dic73—41no—
268Dic73—41no—
269#18032—731nomaximal, Sylow
270C2×C73—41no—
271C2×C73#293311yescharacteristic
272C2×C73#295011yescharacteristic
273C2×C73#295511yescharacteristic
274#3104—731no—
275#2986—731no—
276#2984—731no—
277#1593—731no—
278#1591—731no—
279#1587—731no—
280#1587—731no—
281#1584—731no—
282#1584—731no—
283#1579—731no—
284C8×Q16—731no—
285#1572—731no—
286#1497—731no—
287#1479D7311yescharacteristic
288#1454—731no—
289C73#1803211yescharacteristic, complemented, Sylow
290#533—731no—
291C2×C4×Q8C2×D7311yescharacteristic
292#484—731no—
293#484—731no—
294#477—731no—
295#477—731no—
296#462—731no—
297#462—731no—
298#451—731no—
299#451—731no—
300#446—731no—
301#446—731no—
302#446—731no—
303#446—731no—
304#446—1461no—
305#446—1461no—
306#446—1461no—
307C8×Q8—731no—
308C8×Q8—731no—
309C8×Q8—731no—
310C8×Q8—731no—
311C8×Q8—1461no—
312C4×Q16—731no—
313C4×Q16—731no—
314C4×Q16—731no—
315C4×Q16—731no—
316#433—1461no—
317#433—1461no—
318#432—731no—
319#432—1461no—
320#431—731no—
321#431—731no—
322#431—1461no—
323#431C2×D7311yescharacteristic
324#431C2×D7311yescharacteristic
325#335—731no—
326#335—731no—
327#334—731no—
328#334—731no—
329Q8⋊C8—731no—
330Q8⋊C8—731no—
331Q8⋊C8—731no—
332Q8⋊C8—731no—
333Q8⋊C8C2×D7311yescharacteristic
334Q8⋊C8C2×D7311yescharacteristic
335Q8⋊C8C2×D7311yescharacteristic
336Q8⋊C8C2×D7311yescharacteristic
337#322—731no—
338#322—731no—
339#322—731no—
340C82—731no—
341C22×Q8C4×D7311yescharacteristic
342C2×Q16—731no—
343C2×Q16—731no—
344C2×Q16—731no—
345C2×Q16—731no—
346C4⋊Q8—731no—
347C4⋊Q8—731no—
348#125—1461no—
349C22⋊Q8—731no—
350C22⋊Q8—731no—
351C22⋊Q8—1461no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—731no—
355C4×Q8—731no—
356C4×Q8—1461no—
357C4×Q8C4×D7311yescharacteristic
358C4×Q8C4×D7311yescharacteristic
359C4×Q8C22×D7311yescharacteristic
360C4×Q8C22×D7311yescharacteristic
361#117—1461no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C4×D7311yescharacteristic
364C2×C42—21no—
365C2×C42C22×D7311yescharacteristic
366#107—731no—
367#107—731no—
368#107—731no—
369#107—731no—
370C4⋊C8—21no—
371C4⋊C8—731no—
372C4⋊C8—731no—
373C4⋊C8—731no—
374C4⋊C8—731no—
375C4⋊C8—731no—
376C4⋊C8—731no—
377C4⋊C8—1461no—
378C4⋊C8—1461no—
379C4⋊C8—1461no—
380C4⋊C8—1461no—
381C4⋊C8—1461no—
382C4⋊C8—1461no—
383C4⋊C8—1461no—
384C4⋊C8—1461no—
385C4⋊C8C22×D7311yescharacteristic
386C4⋊C8C22×D7311yescharacteristic
387#103—731no—
388#103—731no—
389#103—731no—
390#103—731no—
391#103—731no—
392#103—731no—
393#103—731no—
394#103—731no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—731no—
398C22⋊C8—731no—
399C22⋊C8—731no—
400C22⋊C8—731no—
401C22⋊C8—1461no—
402#97—1461no—
403#97—1461no—
404#97—1461no—
405#97—1461no—
406#97—1461no—
407C4×C8—21no—
408C4×C8—731no—
409C4×C8—731no—
410C4×C8—731no—
411C4×C8—731no—
412C4×C8—1461no—
413C4×C8—1461no—
414C4×C8—1461no—
415C4×C8—1461no—
416C4×C8C22×D7311yescharacteristic
417C4×C8C22×D7311yescharacteristic
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×Q8—731no—
422C2×Q8—731no—
423C2×Q8—1461no—
424C2×Q8C2×C4×D7311yescharacteristic
425C2×Q8C2×C4×D7311yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4C2×C4×D7311yescharacteristic
429C22×C4D4×D7311yescharacteristic
430C22×C4#1192402711yescharacteristic
431Q16—2921no—
432Q16—2921no—
433Q16—1462no—
434Q16—1462no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—731no—
440C2×C8—731no—
441C2×C8—731no—
442C2×C8—731no—
443C2×C8—731no—
444C2×C8—731no—
445C2×C8—731no—
446C2×C8—731no—
447C2×C8—1461no—
448C2×C8—1461no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—731no—
455C4⋊C4—731no—
456C4⋊C4—1461no—
457C4⋊C4—1461no—
458C4⋊C4—1461no—
459C4⋊C4—1461no—
460C4⋊C4—1461no—
461C4⋊C4—1461no—
462C4⋊C4—1461no—
463C4⋊C4C2×C4×D7311yescharacteristic
464C4⋊C4C2×C4×D7311yescharacteristic
465C22⋊C4—1461no—
466C22⋊C4—1461no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—1461no—
472C42—1461no—
473C42C2×C4×D7311yescharacteristic
474C42D4×D7311yescharacteristic
475C42#1192402711yescharacteristic
476C42C23×D7311yescharacteristic
477C23#1455655111yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—42no—
482Q8—2922no—
483Q8—1461no—
484Q8—1461no—
485Q8—1461no—
486Q8—1461no—
487Q8#1455659712yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—1461no—
500C2×C4—1461no—
501C2×C4—1461no—
502C2×C4—1461no—
503C2×C4#1455655111yescharacteristic
504C2×C4#1455655111yescharacteristic
505C2×C4#1455655111yescharacteristic
506C2×C4C22×C4×D7311yescharacteristic
507C2×C4C2×D4×D7311yescharacteristic
508C2×C4C2×#1192402711yescharacteristic
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—2921no—
514C8—2921no—
515C8—1461no—
516C8—1461no—
517C8—1461no—
518C8—1461no—
519C8—1461no—
520C8—1461no—
521C8—1461no—
522C8—1461no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×#1455655111yescharacteristic
527C4—21no—
528C4—22no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—2921no—
536C4—2921no—
537C4—2921no—
538C4—2921no—
539C4C2×#1455659711yescharacteristic
540C4#1798935311yescharacteristic
541C4#1798940311yescharacteristic
542C4#1798940311yescharacteristic
543C2—41no—
544C2#2261865211yescharacteristic
545C2#2261879511yescharacteristic
546C2#2261883011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1479C2
socleC22×C73C2×C4×D4
prime radicalC23×C73C4×D4
cosocleC42×C73C24
hypercenter#1479D73
hypocenterC73#18032
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #22608837C2semidirect
5. #22608825C2semidirect
6. #22608805C2semidirect
7. #22608799C2semidirect
8. #22608784C2semidirect
9. #22608778C2semidirect
10. #22608747C2semidirect
11. #22608735C2semidirect
289. C73#18032semidirect

Maximal subgroups

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

subgroupindex
#226199702
#226190322
#226190202
#226088372
#226088252
#226088052
#226087992
#226087842
#226087782
#226087472
#226087352
#226087092
#226084052
#226082312
C73×#14792
#1803273