Finite Group Databasebeta

← #33057382

Subgroups — #33057382

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#22619971C211yesmaximal, characteristic
2#22619032C211yesmaximal, characteristic
3#22619018C211yesmaximal, characteristic
4#22608841C211yesmaximal, characteristic, complemented
5#22608829C211yesmaximal, characteristic, complemented
6#22608804C211yesmaximal, characteristic, complemented
7#22608804C211yesmaximal, characteristic, complemented
8#22608783C211yesmaximal, characteristic, complemented
9#22608783C211yesmaximal, characteristic, complemented
10#22608751C211yesmaximal, characteristic, complemented
11C8×Dic292C211yesmaximal, characteristic, complemented
12#22608711C211yesmaximal, characteristic
13#22608405C211yesmaximal, characteristic
14#22608327C211yesmaximal, characteristic
15C73×#1454C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17C2×C4×Dic146C2211yescharacteristic
18#17988923C411yescharacteristic
19#17988923C411yescharacteristic
20#17988883C411yescharacteristic
21#17988883C411yescharacteristic
22#17988798C411yescharacteristic
23#17988798C411yescharacteristic
24#17988745C411yescharacteristic
25#17988745C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988717C2211yescharacteristic
28#17988717C2211yescharacteristic
29#17988717C2211yescharacteristic
30#17988716—21no—
31#17988716—21no—
32#17988714—21no—
33C8×Dic146C2211yescharacteristic
34C8×Dic146C2211yescharacteristic
35C8×Dic146C2211yescharacteristic
36C8×Dic146C2211yescharacteristic
37#17988711—21no—
38C4×Dic292C2211yescharacteristic
39C4×Dic292C2211yescharacteristic
40C4×Dic292C2211yescharacteristic
41C4×Dic292C2211yescharacteristic
42#17988645—21no—
43#17988645—21no—
44#17988644C2211yescharacteristic
45#17988641—21no—
46#17988640C2211yescharacteristic
47#17988637—21no—
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988338C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988319C2211yescharacteristic
57#17988319C2211yescharacteristic
58#17988319C2211yescharacteristic
59#17988319C2211yescharacteristic
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic
64#322×C73C2211yescharacteristic
65#322×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C22×Dic146C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×Dic292C2×C411yescharacteristic
70C2×Dic292C2×C411yescharacteristic
71C2×Dic292C2×C411yescharacteristic
72#14556591C2×C411yescharacteristic
73#14556591C2×C411yescharacteristic
74#14556583—21no—
75#14556570—21no—
76#14556570C2×C411yescharacteristic
77#14556570C2×C411yescharacteristic
78C4×Dic146—21no—
79C4×Dic146—21no—
80C4×Dic146—21no—
81C4×Dic146C2×C411yescharacteristic
82C4×Dic146C2×C411yescharacteristic
83C4×Dic146C2311yescharacteristic
84C4×Dic146C2311yescharacteristic
85C4×Dic146C2311yescharacteristic
86C4×Dic146C2311yescharacteristic
87#14556550—21no—
88C2×C4⋊Dic73C2×C411yescharacteristic
89C2×#11924007—21no—
90C2×C4×Dic73—21no—
91#14556525C2×C411yescharacteristic
92#14556525C2×C411yescharacteristic
93#14556525C2×C411yescharacteristic
94#14556525C2×C411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556516C2×C411yescharacteristic
112#14556516C2×C411yescharacteristic
113#14556516C2×C411yescharacteristic
114#14556516C2×C411yescharacteristic
115C22⋊#10596831—21no—
116C22⋊#10596831—21no—
117#14556502—21no—
118#14556501—21no—
119#14556501—21no—
120#14556501—21no—
121#14556501—21no—
122C4×#10596831—21no—
123C8×Dic73—21no—
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73—21no—
129C4⋊C8×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C22⋊C8×C73—21no—
134C22⋊C8×C73C2×C411yescharacteristic
135C22⋊C8×C73C2×C411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137C22⋊C8×C73D411yescharacteristic
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—22no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—41no—
148C2×Dic146C22×C411yescharacteristic
149C2×Dic146C22×C411yescharacteristic
150C2×Dic146C22×C411yescharacteristic
151C2×Dic146C22×C411yescharacteristic
152C22×Dic73—21no—
153C22×Dic73—21no—
154Dic292—22no—
155Dic292—22no—
156Dic292—41no—
157Dic292—41no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73C22×C411yescharacteristic
167C4⋊Dic73C22×C411yescharacteristic
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170#11924007—21no—
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178C22⋊Dic73—21no—
179C22⋊Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73#4111yescharacteristic
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73C22×C411yescharacteristic
192C2×C8×C73C22×C411yescharacteristic
193C2×C8×C73C22×C411yescharacteristic
194C2×C8×C73C22×C411yescharacteristic
195C2×C8×C73C2×D411yescharacteristic
196C2×C8×C73C2×D411yescharacteristic
197C2×C8×C73C2×D411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C42×C73C22×C411yescharacteristic
200C42×C73C2×D411yescharacteristic
201C42×C73#4111yescharacteristic
202C42×C73C2411yescharacteristic
203C23×C73C4×D411yescharacteristic
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—41no—
209C2×C4×C73C4×D411yescharacteristic
210C2×C4×C73C4×D411yescharacteristic
211C2×C4×C73C4×D411yescharacteristic
212C2×C4×C73C23×C411yescharacteristic
213C2×C4×C73C22×D411yescharacteristic
214C2×C4×C73C2×#4111yescharacteristic
215C2×Dic73—21no—
216C2×Dic73—21no—
217C2×Dic73—21no—
218C2×Dic73—21no—
219C2×Dic73—21no—
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—42no—
224C2×Dic73—42no—
225Dic146—21no—
226Dic146—21no—
227Dic146—21no—
228Dic146—21no—
229Dic146—21no—
230Dic146—21no—
231Dic146—21no—
232Dic146—42no—
233Dic146—42no—
234Dic146#13112yes—
235C8×C73—21no—
236C8×C73—21no—
237C8×C73—21no—
238C8×C73—21no—
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—41no—
244C8×C73—41no—
245#10596831—41no—
246#10596831—41no—
247#10596831—41no—
248#10596831—41no—
249C22×C73—21no—
250C22×C73—21no—
251C22×C73—21no—
252C22×C73C2×C4×D411yescharacteristic
253C4×C73—21no—
254C4×C73—21no—
255C4×C73—21no—
256C4×C73—21no—
257C4×C73C2×#13111yescharacteristic
258C4×C73#56811yescharacteristic
259C4×C73#57811yescharacteristic
260C4×C73#57811yescharacteristic
261Dic73—22no—
262Dic73—41no—
263Dic73—41no—
264Dic73—41no—
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#1479—731no—
288#1454D7311yescharacteristic
289C73#1803211yescharacteristic, complemented, Sylow
290#533—731no—
291C2×C4×Q8—731no—
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—1461no—
322#431C2×D7311yescharacteristic
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⋊C8—731no—
334Q8⋊C8—731no—
335Q8⋊C8—731no—
336Q8⋊C8—731no—
337#322C2×D7311yescharacteristic
338#322C2×D7311yescharacteristic
339#322C2×D7311yescharacteristic
340C82C2×D7311yescharacteristic
341C22×Q8—731no—
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—731no—
353C4×Q8—731no—
354C4×Q8—731no—
355C4×Q8—731no—
356C4×Q8—731no—
357C4×Q8—731no—
358C4×Q8—1461no—
359C4×Q8—1461no—
360C4×Q8—1461no—
361#117—1461no—
362C2×C4⋊C4—731no—
363C2×C4⋊C4—1461no—
364C2×C42—1461no—
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—1461no—
376C4⋊C8—1461no—
377C4⋊C8—1461no—
378C4⋊C8—1461no—
379C4⋊C8—1461no—
380C4⋊C8—1461no—
381C4⋊C8—1461no—
382C4⋊C8—1461no—
383C4⋊C8C4×D7311yescharacteristic
384C4⋊C8C4×D7311yescharacteristic
385C4⋊C8D29211yescharacteristic
386C4⋊C8D29211yescharacteristic
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—1461no—
397C22⋊C8—1461no—
398C22⋊C8C4×D7311yescharacteristic
399C22⋊C8C4×D7311yescharacteristic
400C22⋊C8D29211yescharacteristic
401C22⋊C8D29211yescharacteristic
402#97—1461no—
403#97—1461no—
404#97—1461no—
405#97—1461no—
406#97—1461no—
407C4×C8—1461no—
408C4×C8—1461no—
409C4×C8—1461no—
410C4×C8—1461no—
411C4×C8—1461no—
412C4×C8C22×D7311yescharacteristic
413C4×C8C22×D7311yescharacteristic
414C4×C8C22×D7311yescharacteristic
415C4×C8C22×D7311yescharacteristic
416C4×C8C22×D7311yescharacteristic
417C4×C8C22×D7311yescharacteristic
418C2×Q8—2921no—
419C2×Q8—731no—
420C2×Q8—731no—
421C2×Q8—731no—
422C2×Q8—731no—
423C2×Q8—1462no—
424C2×Q8—1461no—
425C2×Q8—1461no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4C2×C4×D7311yescharacteristic
429C22×C4C2×D29211yescharacteristic
430C22×C4#1192402811yescharacteristic
431Q16—2921no—
432Q16—2921no—
433Q16—1462no—
434Q16—1462no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—1461no—
438C2×C8—1461no—
439C2×C8—1461no—
440C2×C8—1461no—
441C2×C8C2×C4×D7311yescharacteristic
442C2×C8C2×C4×D7311yescharacteristic
443C2×C8C2×C4×D7311yescharacteristic
444C2×C8C2×C4×D7311yescharacteristic
445C2×C8C2×D29211yescharacteristic
446C2×C8C2×D29211yescharacteristic
447C2×C8C2×D29211yescharacteristic
448C2×C8C2×D29211yescharacteristic
449C4⋊C4—731no—
450C4⋊C4—731no—
451C4⋊C4—731no—
452C4⋊C4—731no—
453C4⋊C4—1461no—
454C4⋊C4—1461no—
455C4⋊C4—1461no—
456C4⋊C4—1461no—
457C4⋊C4—1461no—
458C4⋊C4—1461no—
459C4⋊C4—1461no—
460C4⋊C4—1461no—
461C4⋊C4—1461no—
462C4⋊C4—1461no—
463C4⋊C4—1461no—
464C4⋊C4—1461no—
465C22⋊C4—1461no—
466C22⋊C4—1461no—
467C42—1461no—
468C42—1461no—
469C42—1461no—
470C42—1461no—
471C42—1461no—
472C42—1461no—
473C42C2×C4×D7311yescharacteristic
474C42C2×D29211yescharacteristic
475C42#1192402811yescharacteristic
476C42C23×D7311yescharacteristic
477C23C4×D29211yescharacteristic
478Q8—2922no—
479Q8—2922no—
480Q8—732no—
481Q8—1461no—
482Q8—1461no—
483Q8—1461no—
484Q8—1461no—
485Q8—1461no—
486Q8—1461no—
487Q8—1461no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—2922no—
494C2×C4—2922no—
495C2×C4—1461no—
496C2×C4—1461no—
497C2×C4—1461no—
498C2×C4—1461no—
499C2×C4—1461no—
500C2×C4—1461no—
501C2×C4—1461no—
502C2×C4—1461no—
503C2×C4C4×D29211yescharacteristic
504C2×C4C4×D29211yescharacteristic
505C2×C4C4×D29211yescharacteristic
506C2×C4C22×C4×D7311yescharacteristic
507C2×C4C22×D29211yescharacteristic
508C2×C4C2×#1192402811yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—2921no—
520C8—2921no—
521C8—2921no—
522C8—2921no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×C4×D29211yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—2921no—
532C4—2921no—
533C4—2921no—
534C4—2921no—
535C4—2921no—
536C4—2921no—
537C4—2921no—
538C4—1462no—
539C4#131×D7311yescharacteristic
540C4#1798935211yescharacteristic
541C4#1798940411yescharacteristic
542C4#1798940411yescharacteristic
543C2—41no—
544C2#2261865911yescharacteristic
545C2#2261880011yescharacteristic
546C2#2261883511yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1454C2
socleC22×C73C2×C4×D4
prime radicalC23×C73C4×D4
cosocleC42×C73C24
hypercenter#1454D73
hypocenterC73#18032
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
4. #22608841C2semidirect
5. #22608829C2semidirect
6. #22608804C2semidirect
7. #22608804C2semidirect
8. #22608783C2semidirect
9. #22608783C2semidirect
10. #22608751C2semidirect
11. C8×Dic292C2semidirect
289. C73#18032semidirect

Maximal subgroups

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

subgroupindex
#226199712
#226190322
#226190182
#226088412
#226088292
#226088042
#226087832
#226087512
C8×Dic2922
#226087112
#226084052
#226083272
C73×#14542
#1803273