Finite Group Databasebeta

← #33055698

Subgroups — #33055698

Order 18688.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619049C211yesmaximal, characteristic, complemented
2#22619042C211yesmaximal, characteristic, complemented
3C4×#14556611C211yesmaximal, characteristic
4#22608799C212yesmaximal, complemented
5#22608792C212yesmaximal, complemented
6#22608771C212yesmaximal, complemented
7#22608764C212yesmaximal, complemented
8C2×#17988337C211yesmaximal, characteristic, complemented
9#22608319C211yesmaximal, characteristic, complemented
10#22608224C211yesmaximal, characteristic, complemented
11C73×#1477C211yesmaximal, characteristic, complemented
12C2×#14556611C411yescharacteristic
13C4×#11924028C2211yescharacteristic
14#17988714C2212yes—
15Q8×#10596831C2212yes—
16C4×#11924018C411yescharacteristic
17C4×#11924018C2211yescharacteristic
18C4×#11924015C411yescharacteristic
19C4×#11924015C2211yescharacteristic
20C4×#11924016C411yescharacteristic
21C4×#11924016C2211yescharacteristic
22C4×#11924013C411yescharacteristic
23C4×#11924013C2211yescharacteristic
24#17988664C2212yes—
25#17988658—22no—
26D4×#10596831—22no—
27D4×#10596831C2212yes—
28#17988643—21no—
29#17988640—21no—
30#17988640C2211yescharacteristic
31#17988623C411yescharacteristic
32#17988609—21no—
33C2×C4⋊#10596831—21no—
34C2×C4⋊#10596831C2211yescharacteristic
35#17988583C411yescharacteristic
36#17988581C411yescharacteristic
37C2×C4×#10596831C2211yescharacteristic
38#17988337C2212yes—
39#17988337C2212yes—
40#17988319C2212yes—
41#17988316C2212yes—
42#17988309C2212yes—
43#17988308C2212yes—
44C4×#41×C73C2211yescharacteristic
45#431×C73C2211yescharacteristic
46C2×C4⋊C8×C73C2211yescharacteristic
47Q8⋊C8×C73C2212yes—
48D4⋊C8×C73C2212yes—
49C2×#11924028C2×C411yescharacteristic
50#14556611—24no—
51C2×#11924018C2×C411yescharacteristic
52C2×#11924016C2×C411yescharacteristic
53C2×#11924015C2×C411yescharacteristic
54C2×#11924013C2×C411yescharacteristic
55C2×#11924011—22no—
56C22×#10596831—22no—
57C22×#10596831—21no—
58C22×#10596831C2×C411yescharacteristic
59C22×#10596831C2×C411yescharacteristic
60C4×Dic146C2×C411yescharacteristic
61C4×Dic146C2311yescharacteristic
62C4×D292C2×C411yescharacteristic
63C4×D292C2311yescharacteristic
64C4×C22⋊D73—21no—
65C4×C22⋊D73—21no—
66#14556550C2×C411yescharacteristic
67#14556548—21no—
68C42×D73—21no—
69#14556524C2×C411yescharacteristic
70#14556524C2×C411yescharacteristic
71#14556522C2×C411yescharacteristic
72#14556522C2×C411yescharacteristic
73C4⋊#10596831—22no—
74C4⋊#10596831—21no—
75C4⋊#10596831D411yescharacteristic
76C4⋊#10596831D411yescharacteristic
77C4⋊#10596831C2312yes—
78#14556520—22no—
79#14556515C2×C411yescharacteristic
80#14556515C2×C411yescharacteristic
81#14556514C2×C411yescharacteristic
82#14556514C2×C411yescharacteristic
83#14556512C2×C411yescharacteristic
84#14556512C2×C411yescharacteristic
85#14556511C2×C411yescharacteristic
86#14556511C2×C411yescharacteristic
87C22⋊#10596831—22no—
88C22⋊#10596831D412yes—
89#14556503—22no—
90#14556501—22no—
91C4×#10596831—22no—
92C4×#10596831C2×C411yescharacteristic
93C4×#10596831C2×C411yescharacteristic
94C4×#10596831C2311yescharacteristic
95C4×#10596831C2311yescharacteristic
96C4×#10596831C2312yes—
97C2×#41×C73C2×C411yescharacteristic
98C22×C8×C73—21no—
99C4×Q8×C73C2×C411yescharacteristic
100C4×Q8×C73C2311yescharacteristic
101C4×D4×C73—21no—
102C4×D4×C73—21no—
103C4×D4×C73C2×C411yescharacteristic
104C4×D4×C73C2311yescharacteristic
105#117×C73—21no—
106#117×C73C2×C411yescharacteristic
107C2×C42×C73—21no—
108C2×C42×C73C2311yescharacteristic
109C4⋊C8×C73—21no—
110C4⋊C8×C73—21no—
111C4⋊C8×C73C2312yes—
112C22⋊C8×C73—21no—
113C4×C8×C73C2312yes—
114#11924028—22no—
115#11924028—22no—
116C2×Dic146C22×C411yescharacteristic
117C2×D292C22×C411yescharacteristic
118C2×C22⋊D73—21no—
119C2×C4×D73—21no—
120C2×C4×D73—21no—
121C2×C4×D73—21no—
122#11924018—22no—
123#11924016—22no—
124#11924015—22no—
125#11924013—22no—
126#11924011—82no—
127C2×#10596831—22no—
128C2×#10596831—22no—
129C2×#10596831—22no—
130C2×#10596831—82no—
131C2×#10596831—81no—
132C2×#10596831C22×C411yescharacteristic
133C2×#10596831C22×C411yescharacteristic
134C2×#10596831C22×C411yescharacteristic
135C2×#10596831C22×C411yescharacteristic
136C2×#10596831C2×D412yes—
137C2×#10596831C2×D412yes—
138C4⋊Dic73C22×C411yescharacteristic
139C4⋊Dic73C22×C411yescharacteristic
140#11924007—21no—
141#11924007—21no—
142C22⋊Dic73—21no—
143#11924005—21no—
144#11924005—21no—
145C4×Dic73—21no—
146C4×Dic73—21no—
147C4×Dic73—21no—
148#41×C73—22no—
149#41×C73M1614yescomplemented
150C2×Q8×C73C22×C411yescharacteristic
151C2×D4×C73—21no—
152C2×D4×C73C22×C411yescharacteristic
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73C22×C411yescharacteristic
157C22×C4×C73C2×D411yescharacteristic
158C22×C4×C73#4111yescharacteristic
159C2×C8×C73—22no—
160C2×C8×C73—22no—
161C2×C8×C73—81no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73C22×C411yescharacteristic
165C4⋊C4×C73C22×C411yescharacteristic
166C22⋊C4×C73—21no—
167C22⋊C4×C73—21no—
168C22⋊C4×C73—21no—
169C42×C73—21no—
170C42×C73—21no—
171C42×C73—21no—
172C42×C73C22×C411yescharacteristic
173C42×C73C2×D411yescharacteristic
174C42×C73#4111yescharacteristic
175C42×C73C2411yescharacteristic
176C23×C73—21no—
177C23×C73C4×D411yescharacteristic
178C22×D73—21no—
179Q8×C73—21no—
180Q8×C73C2×M1612yes—
181D4×C73—24no—
182D4×C73—21no—
183D4×C73C2×M1612yes—
184C2×C4×C73—21no—
185C2×C4×C73—21no—
186C2×C4×C73—21no—
187C2×C4×C73—24no—
188C2×C4×C73—21no—
189C2×C4×C73—21no—
190C2×C4×C73—41no—
191C2×C4×C73—41no—
192C2×C4×C73—41no—
193C2×C4×C73—81no—
194C2×C4×C73C4×D411yescharacteristic
195C2×C4×C73C4×D411yescharacteristic
196C2×C4×C73C4×D411yescharacteristic
197C2×C4×C73C2×M1612yes—
198C2×C4×C73#13112yes—
199C2×C4×C73C23×C411yescharacteristic
200C2×C4×C73C22×D411yescharacteristic
201C2×C4×C73C2×#4111yescharacteristic
202C22⋊D73—42no—
203C2×Dic73—21no—
204C2×Dic73—21no—
205C2×Dic73—21no—
206D292—21no—
207D292—21no—
208C4×D73—41no—
209C4×D73—41no—
210C4×D73—42no—
211C4×D73—81no—
212Dic146—21no—
213Dic146—21no—
214C8×C73—42no—
215C8×C73—42no—
216#10596831—21no—
217#10596831—21no—
218#10596831—21no—
219#10596831—21no—
220#10596831—22no—
221#10596831—22no—
222#10596831—42no—
223C22×C73—21no—
224C22×C73—21no—
225C22×C73—22no—
226C22×C73—41no—
227C22×C73—41no—
228C22×C73#43512yes—
229C22×C73C2×C4×D411yescharacteristic
230C2×D73—41no—
231C2×D73—41no—
232C2×D73—41no—
233C4×C73—22no—
234C4×C73—21no—
235C4×C73—21no—
236C4×C73—21no—
237C4×C73—41no—
238C4×C73—41no—
239C4×C73#43512yes—
240C4×C73C22×M1611yescharacteristic
241C4×C73C2×#13111yescharacteristic
242C4×C73#57711yescharacteristic
243C4×C73#57711yescharacteristic
244Dic73—41no—
245Dic73—41no—
246Dic73—41no—
247#17882—731nomaximal, Sylow
248C2×C73—22no—
249C2×C73—42no—
250C2×C73C2×#43511yescharacteristic
251C2×C73#295211yescharacteristic
252C2×C73#295711yescharacteristic
253D73—81no—
254#2989—731no—
255#2988—731no—
256C4×#135—731no—
257#1587—732no—
258#1586—732no—
259#1583—732no—
260#1582—732no—
261C2×#334—731no—
262#1477—731no—
263#1477D7311yescharacteristic, complemented
264#1452—731no—
265C73#1788211yescharacteristic, complemented, Sylow
266C2×#135—731no—
267C4×#41—731no—
268C4×#41C2×D7311yescharacteristic
269#446—732no—
270C8×Q8—732no—
271C4×Q16—731no—
272C4×Q16—731no—
273C4×SD16—731no—
274C4×SD16—731no—
275C4×SD16—731no—
276C4×SD16—731no—
277C4×D8—731no—
278C4×D8—731no—
279#436—732no—
280#435—1462no—
281C8×D4—732no—
282C8×D4—1462no—
283#432—1461no—
284#431—731no—
285#431—1461no—
286#431C2×D7311yescharacteristic
287#427—731no—
288#423—1461no—
289C2×C4⋊C8—731no—
290C2×C4⋊C8—1461no—
291C2×C4⋊C8C2×D7311yescharacteristic
292#416—731no—
293#416—731no—
294C2×C4×C8—731no—
295#334—732no—
296#334—732no—
297Q8⋊C8—732no—
298Q8⋊C8C2×D7312yes—
299D4⋊C8—732no—
300D4⋊C8C2×D7312yes—
301#322—732no—
302#322—732no—
303C2×#41—731no—
304C2×#41C4×D7311yescharacteristic
305#135—1464no—
306C2×Q16—731no—
307C2×SD16—731no—
308C2×SD16—731no—
309C2×D8—731no—
310C2×M16—1462no—
311C22×C8—21no—
312C22×C8—731no—
313C22×C8—731no—
314C22×C8—1462no—
315C22×C8—1461no—
316C4×Q8—731no—
317C4×Q8—731no—
318C4×Q8C4×D7311yescharacteristic
319C4×Q8C22×D7311yescharacteristic
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—731no—
323C4×D4—731no—
324C4×D4—1461no—
325C4×D4—1461no—
326C4×D4C4×D7311yescharacteristic
327C4×D4C22×D7311yescharacteristic
328#117—21no—
329#117—731no—
330#117—1461no—
331#117C4×D7311yescharacteristic
332C2×C42—21no—
333C2×C42—1461no—
334C2×C42C22×D7311yescharacteristic
335#107—731no—
336#107—731no—
337#106—731no—
338#106—731no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8—731no—
342C4⋊C8—731no—
343C4⋊C8—732no—
344C4⋊C8—1462no—
345C4⋊C8—1462no—
346C4⋊C8—1461no—
347C4⋊C8C22×D7312yes—
348#103—731no—
349#103—731no—
350#103—731no—
351#103—731no—
352#102—731no—
353#102—731no—
354#102—731no—
355#102—731no—
356C22⋊C8—21no—
357C22⋊C8—732no—
358C22⋊C8—1462no—
359C22⋊C8—1462no—
360#97—1462no—
361C4×C8—731no—
362C4×C8—731no—
363C4×C8—731no—
364C4×C8—731no—
365C4×C8—732no—
366C4×C8—1462no—
367C4×C8C22×D7312yes—
368#41—22no—
369#41—1462no—
370#41—1462no—
371#41#1192401114yescomplemented
372C2×Q8—731no—
373C2×Q8C2×C4×D7311yescharacteristic
374C2×D4—21no—
375C2×D4—731no—
376C2×D4—1461no—
377C2×D4C2×C4×D7311yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—1461no—
382C22×C4—1461no—
383C22×C4—1461no—
384C22×C4C2×C4×D7311yescharacteristic
385C22×C4D4×D7311yescharacteristic
386C22×C4#1192402711yescharacteristic
387Q16—1462no—
388SD16—1462no—
389SD16—1462no—
390D8—1462no—
391M16—5842no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—81no—
395C2×C8—5841no—
396C2×C8—5842no—
397C2×C8—731no—
398C2×C8—731no—
399C2×C8—731no—
400C2×C8—731no—
401C2×C8—732no—
402C2×C8—732no—
403C2×C8—1462no—
404C2×C8—1462no—
405C2×C8—1462no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—731no—
409C4⋊C4—731no—
410C4⋊C4—1461no—
411C4⋊C4—1461no—
412C4⋊C4C2×C4×D7311yescharacteristic
413C4⋊C4C2×C4×D7311yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—1461no—
418C22⋊C4—1461no—
419C22⋊C4—1461no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42—1461no—
424C42—1461no—
425C42—1461no—
426C42C2×C4×D7311yescharacteristic
427C42D4×D7311yescharacteristic
428C42#1192402711yescharacteristic
429C42C23×D7311yescharacteristic
430C23—21no—
431C23—1461no—
432C23#1455655111yescharacteristic
433Q8—21no—
434Q8—1461no—
435Q8—1461no—
436Q8C2×#1192401112yes—
437D4—24no—
438D4—21no—
439D4—2922no—
440D4—1461no—
441D4—1461no—
442D4C2×#1192401112yes—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—2921no—
454C2×C4—2921no—
455C2×C4—2922no—
456C2×C4—5841no—
457C2×C4—1461no—
458C2×C4—1461no—
459C2×C4—1461no—
460C2×C4#1455655111yescharacteristic
461C2×C4#1455655111yescharacteristic
462C2×C4#1455655111yescharacteristic
463C2×C4C2×#1192401112yes—
464C2×C4#1455659912yes—
465C2×C4C22×C4×D7311yescharacteristic
466C2×C4C2×D4×D7311yescharacteristic
467C2×C4C2×#1192402711yescharacteristic
468C8—42no—
469C8—42no—
470C8—2922no—
471C8—1462no—
472C8—1462no—
473C8—1461no—
474C8—1461no—
475C8—1461no—
476C8—1461no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—41no—
481C22—41no—
482C22—2921no—
483C22—2921no—
484C22—2921no—
485C22#1798865512yes—
486C22C2×#1455655111yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—22no—
491C4—41no—
492C4—41no—
493C4—2921no—
494C4—2921no—
495C4—2921no—
496C4#1798865512yes—
497C4C22×#1192401111yescharacteristic
498C4C2×#1455659911yescharacteristic
499C4#1798939611yescharacteristic
500C4#1798939711yescharacteristic
501C2—22no—
502C2—42no—
503C2—5841no—
504C2C2×#1798865511yescharacteristic
505C2#2261881011yescharacteristic
506C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1477C2
socleC22×C73C2×C4×D4
prime radicalC2×#14556611C4
cosocleC42×C73C24
hypercenter#1477D73
hypocenterC73#17882
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
1. #22619049C2semidirect
2. #22619042C2semidirect
4. #22608799C2semidirect
5. #22608792C2semidirect
6. #22608771C2semidirect
7. #22608764C2semidirect
8. C2×#17988337C2semidirect
9. #22608319C2semidirect
10. #22608224C2semidirect
11. C73×#1477C2semidirect
149. #41×C73M16semidirect
263. #1477D73semidirect
265. C73#17882semidirect
371. #41#11924011semidirect

Maximal subgroups

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

subgroupindex
#226190492
#226190422
C4×#145566112
#226087992
#226087922
#226087712
#226087642
C2×#179883372
#226083192
#226082242
C73×#14772
#1788273