Finite Group Databasebeta

← #33056019

Subgroups — #33056019

Order 18688.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620000C211yesmaximal, characteristic
2C8×#11924029C211yesmaximal, characteristic
3#22618860C211yesmaximal, characteristic, complemented
4#22608782C211yesmaximal, characteristic, complemented
5#22608778C211yesmaximal, characteristic, complemented
6#22608770C211yesmaximal, characteristic, complemented
7#22608766C211yesmaximal, characteristic, complemented
8#22608748C211yesmaximal, characteristic, complemented
9#22608745C211yesmaximal, characteristic, complemented
10#22608741C211yesmaximal, characteristic, complemented
11#22608718C211yesmaximal, characteristic, complemented
12#22608369C211yesmaximal, characteristic
13#22608350C211yesmaximal, characteristic, complemented
14#22608219C211yesmaximal, characteristic, complemented
15C73×#1579C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×#11924029C2211yescharacteristic
18#17988930C411yescharacteristic
19#17988926C411yescharacteristic
20#17988870C411yescharacteristic
21#17988866C411yescharacteristic
22#17988795C411yescharacteristic
23#17988791C411yescharacteristic
24#17988752C411yescharacteristic
25#17988748C411yescharacteristic
26#17988718C2211yescharacteristic
27#17988716—21no—
28#17988714C2211yescharacteristic
29Q8×#10596831C2211yescharacteristic
30C8×Dic146—21no—
31C8×Dic146C2211yescharacteristic
32C4×#11924018C2211yescharacteristic
33C4×#11924017C2211yescharacteristic
34C4×#11924015C2211yescharacteristic
35C8×D292—21no—
36C8×D292C2211yescharacteristic
37#17988652—21no—
38#17988652C2211yescharacteristic
39#17988639—21no—
40#17988639C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988612—21no—
43#17988609C2211yescharacteristic
44#17988541—21no—
45C4×#11924011C2211yescharacteristic
46C4×C8×D73—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988309C2211yescharacteristic
60C8×Q8×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924029C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924011—21no—
72C2×#11924011—21no—
73C2×C8×D73—21no—
74C2×C8×D73—21no—
75C2×C8×D73D411yescharacteristic
76C2×C8×D73D411yescharacteristic
77#14556590C2×C411yescharacteristic
78#14556589C2×C411yescharacteristic
79#14556581—21no—
80#14556571C2×C411yescharacteristic
81#14556569—21no—
82#14556567C2×C411yescharacteristic
83Q8×Dic73C2×C411yescharacteristic
84C4×Dic146—21no—
85C4×Dic146C2311yescharacteristic
86C4×D292—21no—
87C4×D292C2311yescharacteristic
88#14556553—21no—
89#14556553C2×C411yescharacteristic
90#14556549—21no—
91#14556549C2×C411yescharacteristic
92#14556548—21no—
93C42×D73—21no—
94C42×D73C2311yescharacteristic
95#14556524C2×C411yescharacteristic
96#14556523C2×C411yescharacteristic
97#14556522C2×C411yescharacteristic
98C4⋊#10596831—21no—
99C4⋊#10596831—21no—
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520C2×C411yescharacteristic
106#14556520C2×C411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556515C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503C2×C411yescharacteristic
117#14556503C2×C411yescharacteristic
118#14556502—21no—
119#14556501—21no—
120#14556501—21no—
121C4×#10596831—21no—
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
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
139C4×C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924029—22no—
145#11924029—22no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×D292—21no—
149C2×D292C22×C411yescharacteristic
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73C22×C411yescharacteristic
154C2×C4×D73C2×D411yescharacteristic
155C2×C4×D73#4111yescharacteristic
156#11924018—22no—
157#11924017—22no—
158#11924015—22no—
159#11924011—42no—
160#11924011—42no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C8×D73—22no—
169C8×D73—41no—
170C8×D73—42no—
171C8×D73—42no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73C22×C411yescharacteristic
190C4×Dic73C2×D411yescharacteristic
191C4×Dic73#4111yescharacteristic
192C2×Q8×C73C22×C411yescharacteristic
193C2×Q8×C73C22×C411yescharacteristic
194Q16×C73—22no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73C22×C411yescharacteristic
205C4⋊C4×C73C22×C411yescharacteristic
206C42×C73—21no—
207C42×C73—21no—
208C42×C73C2411yescharacteristic
209C22×D73—21no—
210C22×D73C4×D411yescharacteristic
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73#13112yes—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73C23×C411yescharacteristic
220C2×C4×C73C22×D411yescharacteristic
221C2×C4×C73C2×#4111yescharacteristic
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73C4×D411yescharacteristic
226C2×Dic73C4×D411yescharacteristic
227C2×Dic73C4×D411yescharacteristic
228D292—24no—
229D292—21no—
230D292#13112yes—
231C4×D73—24no—
232C4×D73—21no—
233C4×D73—21no—
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—22no—
237C4×D73—41no—
238C4×D73—41no—
239C4×D73—42no—
240Dic146—21no—
241Dic146—21no—
242Dic146—42no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—41no—
254#10596831—41no—
255#10596831—41no—
256#10596831#13712yes—
257C22×C73C2×C4×D411yescharacteristic
258C2×D73—21no—
259C2×D73—22no—
260C2×D73—21no—
261C2×D73—21no—
262C2×D73—41no—
263C2×D73—41no—
264C4×C73—22no—
265C4×C73—21no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73C2×#13111yescharacteristic
270C4×C73C2×#13111yescharacteristic
271C4×C73C2×#13711yescharacteristic
272C4×C73#57511yescharacteristic
273Dic73—21no—
274Dic73—21no—
275Dic73—41no—
276Dic73—41no—
277Dic73—41no—
278Dic73#44412yes—
279#17916—731nomaximal, Sylow
280C2×C73#292911yescharacteristic
281C2×C73C4×#13711yescharacteristic
282C2×C73C2×#44411yescharacteristic
283D73—41no—
284D73—42no—
285#3107—731no—
286C8×#41—731no—
287#2960—731no—
288#1584—731no—
289#1584—731no—
290#1582—731no—
291#1582—731no—
292#1579—731no—
293#1579D7311yescharacteristic, complemented
294SD16⋊C8—731no—
295SD16⋊C8—731no—
296#1574—731no—
297#1489—731no—
298#1485—731no—
299#1451—731no—
300C73#1791611yescharacteristic, complemented, Sylow
301#533—731no—
302C4×#41—731no—
303#485—731no—
304#485—731no—
305#475—731no—
306#474—731no—
307#462—731no—
308#461—731no—
309#452—731no—
310#452—731no—
311#446—731no—
312#446—731no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—1461no—
317C8×Q8C2×D7311yescharacteristic
318C8×Q8C2×D7311yescharacteristic
319C4×Q16—731no—
320C4×Q16C2×D7311yescharacteristic
321C4×SD16—731no—
322C4×SD16—731no—
323C8×D4—731no—
324C8×D4—731no—
325C8×D4—1461no—
326C8×D4—1461no—
327#431—731no—
328#431—731no—
329#431—1461no—
330#424—1461no—
331#423—731no—
332#405—1461no—
333C4×M16—731no—
334C2×C4×C8—731no—
335C2×C4×C8—1461no—
336#335—731no—
337#335—731no—
338#334—731no—
339#334C2×D7311yescharacteristic
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8—731no—
344Q8⋊C8C2×D7311yescharacteristic
345Q8⋊C8C2×D7311yescharacteristic
346D4⋊C8—731no—
347D4⋊C8—731no—
348#322—731no—
349#322—731no—
350#322—731no—
351#322C2×D7311yescharacteristic
352C2×#41—731no—
353C2×Q16—731no—
354C2×Q16C4×D7311yescharacteristic
355C2×SD16—731no—
356C2×SD16—731no—
357C2×M16—1461no—
358C2×M16—1461no—
359C22×C8—731no—
360C22×C8—731no—
361C22×C8—1461no—
362C22×C8—1461no—
363C4⋊Q8—731no—
364C4⋊Q8—731no—
365#125—1461no—
366C22⋊Q8—731no—
367C22⋊Q8—731no—
368C22⋊Q8—1461no—
369C4×Q8—731no—
370C4×Q8—731no—
371C4×Q8—1461no—
372C4×Q8C22×D7311yescharacteristic
373C4×Q8C22×D7311yescharacteristic
374C4×D4—731no—
375C4×D4—731no—
376C4×D4—1461no—
377C4×D4—1461no—
378#117—731no—
379#117—1461no—
380#117—1461no—
381C2×C42—731no—
382C2×C42—1461no—
383#107—731no—
384#107C4×D7311yescharacteristic
385#106—731no—
386#106—731no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—731no—
392C4⋊C8—731no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8—1461no—
398C4⋊C8C22×D7311yescharacteristic
399C4⋊C8C22×D7311yescharacteristic
400#103—731no—
401#103—731no—
402#103—731no—
403#103—731no—
404#103C4×D7311yescharacteristic
405#103C4×D7311yescharacteristic
406#102—731no—
407#102—731no—
408C22⋊C8—731no—
409C22⋊C8—731no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—1461no—
414#97—1461no—
415#97—1461no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—731no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8—1461no—
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428C4×C8C22×D7311yescharacteristic
429#41—1462no—
430#41—1462no—
431C2×Q8—731no—
432C2×Q8—1461no—
433C2×Q8C2×C4×D7311yescharacteristic
434C2×Q8C2×C4×D7311yescharacteristic
435C2×D4—731no—
436C2×D4—1461no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4—1461no—
443Q16—22no—
444Q16—1462no—
445SD16—1462no—
446SD16—1462no—
447M16—2922no—
448M16—2922no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—2922no—
453C2×C8—2921no—
454C2×C8—2922no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—731no—
458C2×C8—731no—
459C2×C8—1462no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8C2×C4×D7311yescharacteristic
464C2×C8C2×C4×D7311yescharacteristic
465C2×C8D4×D7311yescharacteristic
466C2×C8D4×D7311yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—731no—
470C4⋊C4—731no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4C2×C4×D7311yescharacteristic
479C4⋊C4C2×C4×D7311yescharacteristic
480C22⋊C4—1461no—
481C22⋊C4—1461no—
482C22⋊C4—1461no—
483C22⋊C4—1461no—
484C22⋊C4—1461no—
485C42—21no—
486C42—21no—
487C42—731no—
488C42—731no—
489C42—731no—
490C42—1461no—
491C42—1461no—
492C42—1461no—
493C42C23×D7311yescharacteristic
494C23—731no—
495C23—1461no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—2922no—
500Q8—1461no—
501Q8—1461no—
502Q8#1455659712yes—
503D4—732no—
504D4—1464no—
505D4—1461no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—2922no—
511C2×C4—2921no—
512C2×C4—2921no—
513C2×C4—731no—
514C2×C4—731no—
515C2×C4—731no—
516C2×C4—1462no—
517C2×C4—1464no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4C22×C4×D7311yescharacteristic
526C2×C4C2×D4×D7311yescharacteristic
527C2×C4#41×D7311yescharacteristic
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—2921no—
536C8—2921no—
537C8—2921no—
538C8—732no—
539C8—1461no—
540C8—1461no—
541C8—1461no—
542C22—2921no—
543C22—2921no—
544C22—1461no—
545C22—1461no—
546C22—1462no—
547C22—1461no—
548C22C4×D4×D7311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—2921no—
555C4—2921no—
556C4—2921no—
557C4—732no—
558C4—1461no—
559C4—1461no—
560C4#131×D7311yescharacteristic
561C4C2×#1455659711yescharacteristic
562C4#137×D7311yescharacteristic
563C4#1798938611yescharacteristic
564C2—2922no—
565C2—2921no—
566C2#2261862011yescharacteristic
567C2#2261874711yescharacteristic
568C2#444×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1579C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924029C2×C4
cosocleC42×C73C24
hypercenter#1579D73
hypocenterC73#17916
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
3. #22618860C2semidirect
4. #22608782C2semidirect
5. #22608778C2semidirect
6. #22608770C2semidirect
7. #22608766C2semidirect
8. #22608748C2semidirect
9. #22608745C2semidirect
10. #22608741C2semidirect
11. #22608718C2semidirect
13. #22608350C2semidirect
14. #22608219C2semidirect
15. C73×#1579C2semidirect
293. #1579D73semidirect
300. C73#17916semidirect

Maximal subgroups

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

subgroupindex
#226200002
C8×#119240292
#226188602
#226087822
#226087782
#226087702
#226087662
#226087482
#226087452
#226087412
#226087182
#226083692
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