Finite Group Databasebeta

← #32980400

Subgroups — #32980400

Order 18688.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612995C211yesmaximal, characteristic
2#22610736C211yesmaximal, characteristic
3#22610687C211yesmaximal, characteristic, complemented
4C2×#17988330C211yesmaximal, characteristic
5#22607772C211yesmaximal, characteristic, complemented
6#22607770C211yesmaximal, characteristic, complemented
7C73×#1948C211yesmaximal, characteristic, complemented
8C2×#14556588C2211yescharacteristic
9C2×C4×D292—21no—
10C2×#14556553—21no—
11C2×#14556524—21no—
12C2×C4⋊#10596831C2211yescharacteristic
13C2×#14556511—22no—
14C2×C4×#10596831C2211yescharacteristic
15#17988489—21no—
16#17988488—21no—
17#17988465—22no—
18C4×C4⋊Dic73C2211yescharacteristic
19#17988349—21no—
20#17988330C414yescomplemented
21C2×#106×C73—21no—
22C2×C4⋊C8×C73C2211yescharacteristic
23#384×C73C2211yescharacteristic
24C4×C4⋊C4×C73C2211yescharacteristic
25#340×C73—21no—
26C22×D292—21no—
27C22×D292—21no—
28C22×D292D412yes—
29C22×C4×D73—22no—
30C22×#10596831—21no—
31C22×#10596831—21no—
32#14556588—21no—
33#14556588—21no—
34#14556588C2×C412yes—
35#14556588Q812yes—
36C4×D292—42no—
37C4×D292—42no—
38#14556553—42no—
39#14556553—42no—
40C2×C4⋊Dic73D411yescharacteristic
41C2×C4⋊Dic73D411yescharacteristic
42C2×#11924005—22no—
43C2×#11924005—22no—
44C2×#11924005—22no—
45C2×C4×Dic73—21no—
46#14556524—42no—
47C4⋊#10596831—21no—
48C4⋊#10596831C2×C412yescomplemented
49#14556511—44no—
50C4×#10596831—21no—
51C4×#10596831—21no—
52#14556498—21no—
53C22×C8×C73—21no—
54C2×C4⋊C4×C73—21no—
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73D411yescharacteristic
58C2×C4⋊C4×C73D411yescharacteristic
59C2×C42×C73—21no—
60C2×C42×C73C2311yescharacteristic
61#106×C73—42no—
62C4⋊C8×C73—21no—
63C4⋊C8×C73C2×C412yescomplemented
64#95×C73—21no—
65C23×D73—22no—
66C2×D292—22no—
67C2×D292—22no—
68C2×D292—22no—
69C2×D292—22no—
70C2×D292—22no—
71C2×D292—41no—
72C2×D292—41no—
73C2×D292—41no—
74C2×D292—41no—
75C2×D292—41no—
76C2×D292—41no—
77C2×D292—41no—
78C2×D292—41no—
79C2×D292—42no—
80C2×D292—42no—
81C2×D292C4⋊C414yes—
82C22×Dic73—21no—
83C22×Dic73—21no—
84C2×C4×D73—44no—
85C2×C4×D73—44no—
86C2×C4×D73—82no—
87C2×#10596831—22no—
88C2×#10596831—22no—
89C2×#10596831—41no—
90C2×#10596831—41no—
91C2×#10596831—41no—
92C2×#10596831—41no—
93C4⋊Dic73—21no—
94C4⋊Dic73—21no—
95C4⋊Dic73—21no—
96C4⋊Dic73SD1612yes—
97#11924005—44no—
98#11924005—44no—
99#11924005—82no—
100C4×Dic73—41no—
101C4×Dic73—41no—
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73—41no—
105C22×C4×C73C2×D411yescharacteristic
106C22×C4×C73C2×D411yescharacteristic
107C22×C4×C73C2×D411yescharacteristic
108C2×C8×C73—22no—
109C2×C8×C73—41no—
110C2×C8×C73—41no—
111C4⋊C4×C73—21no—
112C4⋊C4×C73—21no—
113C4⋊C4×C73—21no—
114C4⋊C4×C73—42no—
115C4⋊C4×C73—41no—
116C4⋊C4×C73—41no—
117C4⋊C4×C73—41no—
118C4⋊C4×C73—41no—
119C4⋊C4×C73D812yes—
120C42×C73—41no—
121C42×C73—41no—
122C42×C73C22×C411yescharacteristic
123C42×C73C2×Q811yescharacteristic
124C42×C73#4111yescharacteristic
125C42×C73#4111yescharacteristic
126C23×C73#12011yescharacteristic
127C22×D73—24no—
128C22×D73—42no—
129C22×D73—42no—
130C22×D73—42no—
131C22×D73—42no—
132C22×D73—42no—
133C22×D73—42no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—22no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73—41no—
142C2×C4×C73—81no—
143C2×C4×C73—81no—
144C2×C4×C73—81no—
145C2×C4×C73C2×C4⋊C411yescharacteristic
146C2×C4×C73C4×D411yescharacteristic
147C2×C4×C73C4×D411yescharacteristic
148C2×C4×C73C22⋊Q811yescharacteristic
149C2×C4×C73C22⋊Q811yescharacteristic
150C2×C4×C73#12311yescharacteristic
151C2×C4×C73C2×D811yescharacteristic
152C2×C4×C73C2×SD1611yescharacteristic
153C2×C4×C73#13511yescharacteristic
154C2×C4×C73#13511yescharacteristic
155C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C73#13711yescharacteristic
159C2×Dic73—22no—
160C2×Dic73—41no—
161C2×Dic73—41no—
162C2×Dic73—41no—
163C2×Dic73—41no—
164C2×Dic73—41no—
165D292—44no—
166D292—42no—
167D292—42no—
168D292—42no—
169D292—42no—
170D292—42no—
171D292—42no—
172D292—42no—
173D292—42no—
174D292—82no—
175C4×D73—88no—
176C8×C73—42no—
177#10596831—42no—
178#10596831—42no—
179C22×C73#38511yescharacteristic
180C22×C73#44711yescharacteristic
181C22×C73#44911yescharacteristic
182C22×C73#45011yescharacteristic
183C22×C73#45211yescharacteristic
184C22×C73#45311yescharacteristic
185C22×C73#45511yescharacteristic
186C2×D73—44no—
187C2×D73—44no—
188C2×D73—44no—
189C2×D73—82no—
190C2×D73—82no—
191C2×D73—82no—
192C2×D73—82no—
193C4×C73—21no—
194C4×C73—21no—
195C4×C73—42no—
196C4×C73—81no—
197C4×C73—161no—
198C4×C73C4×D811yescharacteristic
199C4×C73C4×SD1611yescharacteristic
200C4×C73#44011yescharacteristic
201C4×C73#44211yescharacteristic
202C4×C73#47411yescharacteristic
203C4×C73#47611yescharacteristic
204C4×C73#47811yescharacteristic
205C4×C73#47811yescharacteristic
206Dic73—42no—
207Dic73—81no—
208#8921—731nomaximal, Sylow
209C2×C73#162111yescharacteristic
210C2×C73#163111yescharacteristic
211C2×C73#163911yescharacteristic
212C2×C73#164011yescharacteristic
213C2×C73#185611yescharacteristic
214C2×C73#186211yescharacteristic
215C2×C73#186411yescharacteristic
216D73—84no—
217#2366—731no—
218#1957—731no—
219#1948D7311yescharacteristic, complemented
220#1947—731no—
221C2×#331—731no—
222#1279—731no—
223#1279—731no—
224C73#892111yescharacteristic, complemented, Sylow
225C2×#127—731no—
226C2×C4×D4—1461no—
227C2×C4×D4—1461no—
228C2×#107—1461no—
229C2×#106—21no—
230C2×C4⋊C8—731no—
231C2×C4⋊C8C2×D7311yescharacteristic
232C2×#102—1462no—
233C2×C4×C8—731no—
234#390—1461no—
235#390—1461no—
236#386—1462no—
237#384C2×D7311yescharacteristic
238C4×C4⋊C4—731no—
239C4×C4⋊C4C2×D7311yescharacteristic
240#340—21no—
241#340—1461no—
242#331—734no—
243C22×D4—732no—
244C22×D4—1461no—
245C22×D4—1461no—
246C23×C4—1462no—
247C22×C8—21no—
248C22×C8—1461no—
249C22×C8—1461no—
250#127—732no—
251#127—732no—
252#127—1461no—
253#127—1461no—
254C4×D4—2922no—
255C4×D4—2922no—
256C4×D4—2922no—
257C4×D4—2922no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—731no—
262C2×C4⋊C4—731no—
263C2×C4⋊C4C22⋊D7311yescharacteristic
264C2×C4⋊C4C22⋊D7311yescharacteristic
265C2×C22⋊C4—1462no—
266C2×C22⋊C4—1462no—
267C2×C22⋊C4—1462no—
268C2×C42—21no—
269C2×C42—1461no—
270C2×C42C22×D7311yescharacteristic
271#107—2922no—
272#106—42no—
273C4⋊C8—21no—
274C4⋊C8—732no—
275C4⋊C8—1461no—
276C4⋊C8C4×D7312yescomplemented
277#102—2924no—
278C4×C8—1461no—
279C4×C8—1461no—
280#95—21no—
281#95—1461no—
282C24—1462no—
283C2×D4—2922no—
284C2×D4—2922no—
285C2×D4—2921no—
286C2×D4—2921no—
287C2×D4—2921no—
288C2×D4—2921no—
289C2×D4—2921no—
290C2×D4—2921no—
291C2×D4—2921no—
292C2×D4—2921no—
293C2×D4—734no—
294C2×D4—1462no—
295C2×D4—1462no—
296C2×D4—1462no—
297C2×D4—1462no—
298C2×D4—1462no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—2924no—
303C22×C4—2924no—
304C22×C4—5842no—
305C22×C4—1461no—
306C22×C4—1461no—
307C22×C4D4×D7311yescharacteristic
308C22×C4D4×D7311yescharacteristic
309C22×C4C2×C22⋊D7311yescharacteristic
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—2921no—
314C2×C8—2921no—
315C2×C8—2921no—
316C2×C8—2921no—
317C2×C8—1462no—
318C2×C8—1462no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—42no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—732no—
328C4⋊C4—1461no—
329C4⋊C4—1461no—
330C4⋊C4—1461no—
331C4⋊C4#1192401312yes—
332C22⋊C4—2924no—
333C22⋊C4—2924no—
334C22⋊C4—5842no—
335C42—41no—
336C42—41no—
337C42—2921no—
338C42—2921no—
339C42C2×C4×D7311yescharacteristic
340C42Q8×D7311yescharacteristic
341C42#1192402811yescharacteristic
342C42#1192402911yescharacteristic
343C23—2922no—
344C23—2922no—
345C23—2922no—
346C23—2922no—
347C23—2922no—
348C23—2922no—
349C23—1464no—
350C23#1455655911yescharacteristic
351D4—2924no—
352D4—2922no—
353D4—2922no—
354D4—2922no—
355D4—2922no—
356D4—2922no—
357D4—2922no—
358D4—2922no—
359D4—2922no—
360D4—5842no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—2921no—
373C2×C4—2921no—
374C2×C4—2921no—
375C2×C4—2921no—
376C2×C4—2921no—
377C2×C4—5848no—
378C2×C4—1462no—
379C2×C4C4⋊C4×D7311yescharacteristic
380C2×C4C4×C22⋊D7311yescharacteristic
381C2×C4#1455655311yescharacteristic
382C2×C4#1455656711yescharacteristic
383C2×C4#1455656911yescharacteristic
384C2×C4#1455657611yescharacteristic
385C2×C4C2×#1192401311yescharacteristic
386C2×C4SD16×D7311yescharacteristic
387C2×C4#1455661111yescharacteristic
388C2×C4#1455661211yescharacteristic
389C2×C4#1455661611yescharacteristic
390C2×C4#1455661811yescharacteristic
391C2×C4#1455661811yescharacteristic
392C2×C4#1455662211yescharacteristic
393C8—42no—
394C8—2922no—
395C8—2922no—
396C22—2924no—
397C22—2924no—
398C22—2924no—
399C22—5842no—
400C22—5842no—
401C22—5842no—
402C22—5842no—
403C22#1798845811yescharacteristic
404C22#1798872011yescharacteristic
405C22#1798873111yescharacteristic
406C22#1798873611yescharacteristic
407C22#1798874711yescharacteristic
408C22#1798875311yescharacteristic
409C22#1798876311yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—161no—
415C4—2922no—
416C4—5841no—
417C4C4×#1192401311yescharacteristic
418C4#1798867411yescharacteristic
419C4#1798868511yescharacteristic
420C4#1798869811yescharacteristic
421C4#1798886411yescharacteristic
422C4#1798887611yescharacteristic
423C4#1798888411yescharacteristic
424C4#1798888611yescharacteristic
425C2—5844no—
426C2#2260899411yescharacteristic
427C2#2260905711yescharacteristic
428C2#2260910811yescharacteristic
429C2#2260911611yescharacteristic
430C2#2261013911yescharacteristic
431C2#2261017711yescharacteristic
432C2#2261018911yescharacteristic
subgroupG/H
centerC23#14556559
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1948C2
socleC23×C73#120
prime radicalC2×#14556588C22
cosocleC2×C42×C73C23
hypercenter#1948D73
hypocenterC73#8921
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #22610687C2semidirect
5. #22607772C2semidirect
6. #22607770C2semidirect
7. C73×#1948C2semidirect
20. #17988330C4semidirect
48. C4⋊#10596831C2×C4semidirect
63. C4⋊C8×C73C2×C4semidirect
219. #1948D73semidirect
224. C73#8921semidirect
276. C4⋊C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
#226129952
#226107362
#226106872
C2×#179883302
#226077722
#226077702
C73×#19482
#892173