Finite Group Databasebeta

← #33240779

Subgroups — #33240779

Order 18688.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988625C211yesmaximal, characteristic, complemented
2#22612136C212yesmaximal, complemented
3#22612131C211yesmaximal, characteristic, complemented
4#22612126C211yesmaximal, characteristic, complemented
5#22612119C212yesmaximal, complemented
6#22612114C211yesmaximal, characteristic, complemented
7#22612109C211yesmaximal, characteristic, complemented
8#22611713C212yesmaximal, complemented
9#22611638C212yesmaximal, complemented
10C2×C22⋊#11924003C211yesmaximal, characteristic, complemented
11C73×#3050C211yesmaximal, characteristic
12C2×#14556550—21no—
13C22×#11924003C2212yes—
14#17988625—21no—
15#17988625—21no—
16#17988625C2212yes—
17#17988625C2212yes—
18C2×#14556525C2211yescharacteristic
19C2×#14556525C2211yescharacteristic
20C2×#14556523—21no—
21#17988414C2212yescomplemented
22#17988414C2212yescomplemented
23#17988412C2212yescomplemented
24#17988412C2212yescomplemented
25#17988391C2212yescomplemented
26#17988391C2212yescomplemented
27#17988388C2212yescomplemented
28#17988388C2212yescomplemented
29C22⋊#11924003C2211yescharacteristic
30C22⋊#11924003C2211yescharacteristic
31C22⋊#11924003C2212yes—
32C2×#135×C73C2211yescharacteristic
33C23×C8×C73C2211yescharacteristic
34#525×C73—21no—
35#467×C73C2211yescharacteristic
36#467×C73C2211yescharacteristic
37#466×C73C2211yescharacteristic
38#466×C73C2211yescharacteristic
39#465×C73—21no—
40#465×C73—21no—
41#427×C73C2211yescharacteristic
42#416×C73—21no—
43#14556550—22no—
44#14556550—22no—
45#14556550—41no—
46#14556550—41no—
47C2×C4⋊Dic73—21no—
48C2×C4⋊Dic73—21no—
49C2×C22⋊Dic73—41no—
50C2×C4×Dic73—41no—
51C2×#11924003—24no—
52C2×#11924003C2312yes—
53C2×#11924003C2312yes—
54#14556525—21no—
55#14556525—21no—
56#14556525C2312yes—
57#14556525C2312yes—
58#14556523—22no—
59#14556523—22no—
60C2×#41×C73—21no—
61C23×C4×C73D411yescharacteristic
62#135×C73—24no—
63C2×Q16×C73C2311yescharacteristic
64C2×SD16×C73—21no—
65C2×D8×C73C2311yescharacteristic
66C22×C8×C73—24no—
67C22×C8×C73D411yescharacteristic
68C22×C8×C73D411yescharacteristic
69C22×C8×C73D411yescharacteristic
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73#123×C73—41no—
74C22⋊Q8×C73—21no—
75C22⋊Q8×C73—21no—
76#121×C73—21no—
77#121×C73—21no—
78#120×C73—41no—
79C4×D4×C73—41no—
80C4×D4×C73—41no—
81#117×C73—21no—
82#107×C73C2311yescharacteristic
83#107×C73C2311yescharacteristic
84#106×C73—21no—
85#103×C73—21no—
86#103×C73—21no—
87#102×C73—21no—
88#102×C73—21no—
89C22×Dic73—41no—
90C22×Dic73—41no—
91C4⋊Dic73—22no—
92C4⋊Dic73—22no—
93C4⋊Dic73—41no—
94C4⋊Dic73—41no—
95C22⋊Dic73—42no—
96C22⋊Dic73—42no—
97C4×Dic73—42no—
98C4×Dic73—42no—
99#11924003—22no—
100#11924003—22no—
101C24×C73D811yescharacteristic
102#41×C73—42no—
103#41×C73—42no—
104C2×Q8×C73—21no—
105C2×D4×C73—21no—
106C2×D4×C73—41no—
107C2×D4×C73—41no—
108C2×D4×C73—41no—
109C22×C4×C73—22no—
110C22×C4×C73—22no—
111C22×C4×C73—41no—
112C22×C4×C73D811yescharacteristic
113C22×C4×C73D811yescharacteristic
114C22×C4×C73D811yescharacteristic
115C22×C4×C73C2×D411yescharacteristic
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73C2×D411yescharacteristic
118Q16×C73—22no—
119SD16×C73—42no—
120D8×C73—22no—
121C2×C8×C73—22no—
122C2×C8×C73—22no—
123C2×C8×C73—22no—
124C2×C8×C73—22no—
125C2×C8×C73—22no—
126C2×C8×C73C2×D411yescharacteristic
127C2×C8×C73C2×D411yescharacteristic
128C2×C8×C73C2×D411yescharacteristic
129C2×C8×C73#4114yes—
130C2×C8×C73C2411yescharacteristic
131C4⋊C4×C73—21no—
132C4⋊C4×C73—21no—
133C4⋊C4×C73—41no—
134C4⋊C4×C73—41no—
135C22⋊C4×C73—41no—
136C22⋊C4×C73—41no—
137C22⋊C4×C73—41no—
138C22⋊C4×C73—41no—
139C22⋊C4×C73—41no—
140C42×C73—41no—
141C23×C73—22no—
142C23×C73—22no—
143C23×C73—41no—
144C23×C73—41no—
145C23×C73C2×D811yescharacteristic
146C23×C73C2×D811yescharacteristic
147C23×C73C2×D811yescharacteristic
148Q8×C73—41no—
149Q8×C73—41no—
150D4×C73—41no—
151D4×C73—41no—
152D4×C73—82no—
153D4×C73—82no—
154D4×C73—82no—
155C2×C4×C73—22no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—22no—
161C2×C4×C73—22no—
162C2×C4×C73—41no—
163C2×C4×C73—41no—
164C2×C4×C73—41no—
165C2×C4×C73—82no—
166C2×C4×C73#12312yes—
167C2×C4×C73C2×D811yescharacteristic
168C2×C4×C73C2×D811yescharacteristic
169C2×C4×C73C2×D811yescharacteristic
170C2×C4×C73#13712yes—
171C2×C4×C73C22×D411yescharacteristic
172C2×Dic73—42no—
173C2×Dic73—42no—
174C2×Dic73—82no—
175C2×Dic73—82no—
176C8×C73—21no—
177C8×C73—21no—
178C8×C73#12312yes—
179C8×C73C2×#4112yes—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—21no—
183C22×C73—21no—
184C22×C73—21no—
185C22×C73—21no—
186C22×C73—21no—
187C22×C73—44no—
188C22×C73—81no—
189C22×C73—81no—
190C22×C73—81no—
191C22×C73#48012yes—
192C22×C73#50812yes—
193C22×C73C22×D811yescharacteristic
194C4×C73—21no—
195C4×C73—21no—
196C4×C73—81no—
197C4×C73—81no—
198C4×C73—81no—
199C4×C73#48012yes—
200C4×C73C2×#12311yescharacteristic
201C4×C73C2×#13711yescharacteristic
202Dic73—82no—
203Dic73—82no—
204#33645—731nomaximal, Sylow
205C2×C73—22no—
206C2×C73—22no—
207C2×C73—41no—
208C2×C73—161no—
209C2×C73C2×#48011yescharacteristic
210C2×C73C2×#50811yescharacteristic
211C2×C73#341411yescharacteristic
212#3050D7311yescharacteristic
213C2×#427—731no—
214#2237—732no—
215#2236—731no—
216#2235—731no—
217#2234—732no—
218#2233—731no—
219#2232—731no—
220#2158—732no—
221#2138—732no—
222C2×C22⋊C16—731no—
223C73#3364511yescharacteristic, complemented, Sylow
224C2×#135C2×D7311yescharacteristic
225C23×C8C2×D7311yescharacteristic
226#525—21no—
227C2×#117—1461no—
228C22×C16—732no—
229#467C2×D7311yescharacteristic
230#467C2×D7311yescharacteristic
231#466C2×D7311yescharacteristic
232#466C2×D7311yescharacteristic
233#465—21no—
234#465—21no—
235#427—732no—
236#427—732no—
237#427—1461no—
238#427—1461no—
239#427C2×D7311yescharacteristic
240C2×#107—731no—
241C2×#107—731no—
242C2×#106—1461no—
243#416—21no—
244#367—732no—
245#367—732no—
246#366—732no—
247#366—732no—
248#358—732no—
249#358—732no—
250#357—732no—
251#357—732no—
252C22⋊C16—731no—
253C22⋊C16—731no—
254C22⋊C16—732no—
255C2×#41—21no—
256C23×C4C22⋊D7311yescharacteristic
257#135—24no—
258C2×Q16C22×D7311yescharacteristic
259C2×SD16—21no—
260C2×D8C22×D7311yescharacteristic
261C22×C8—24no—
262C22×C8C22⋊D7311yescharacteristic
263C22×C8C22⋊D7311yescharacteristic
264C22×C8C22⋊D7311yescharacteristic
265C22×C8C22×D7311yescharacteristic
266C22×C8C22×D7311yescharacteristic
267C22×C8C22×D7311yescharacteristic
268#123—41no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271#121—21no—
272#121—21no—
273#120—41no—
274C4×D4—41no—
275C4×D4—41no—
276#117—21no—
277#117—2921no—
278#117—2921no—
279#117—1462no—
280#117—1462no—
281C2×C4⋊C4—1461no—
282C2×C4⋊C4—1461no—
283C2×C22⋊C4—2921no—
284C2×C42—2921no—
285C2×C16—732no—
286C2×C16—732no—
287C2×C16—1464no—
288#107—732no—
289#107—732no—
290#107—1461no—
291#107—1461no—
292#107C22×D7311yescharacteristic
293#107C22×D7311yescharacteristic
294#106—21no—
295#106—1462no—
296#106—1462no—
297#103—21no—
298#103—21no—
299#102—21no—
300#102—21no—
301C24#1192401311yescharacteristic
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—2921no—
313C22×C4—2921no—
314C22×C4#1192401311yescharacteristic
315C22×C4#1192401311yescharacteristic
316C22×C4#1192401311yescharacteristic
317C22×C4C2×C22⋊D7311yescharacteristic
318C22×C4C2×C22⋊D7311yescharacteristic
319C22×C4C2×C22⋊D7311yescharacteristic
320Q16—22no—
321SD16—42no—
322D8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8C2×C22⋊D7311yescharacteristic
329C2×C8C2×C22⋊D7311yescharacteristic
330C2×C8C2×C22⋊D7311yescharacteristic
331C2×C8#1192402714yes—
332C2×C8C23×D7311yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—2921no—
338C4⋊C4—2921no—
339C4⋊C4—1462no—
340C4⋊C4—1462no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—2922no—
347C22⋊C4—2922no—
348C42—41no—
349C42—2922no—
350C42—2922no—
351C16—1462no—
352C16—1462no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23C2×#1192401311yescharacteristic
358C23C2×#1192401311yescharacteristic
359C23C2×#1192401311yescharacteristic
360Q8—41no—
361Q8—41no—
362D4—41no—
363D4—41no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—82no—
378C2×C4—2922no—
379C2×C4—2922no—
380C2×C4—5842no—
381C2×C4—5842no—
382C2×C4#1455657212yes—
383C2×C4C2×#1192401311yescharacteristic
384C2×C4C2×#1192401311yescharacteristic
385C2×C4C2×#1192401311yescharacteristic
386C2×C4#1455662112yes—
387C2×C4C22×C22⋊D7311yescharacteristic
388C8—21no—
389C8—21no—
390C8#1455657212yes—
391C8C2×#1192402712yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22#1798889812yes—
404C22#1798901712yes—
405C22C22×#1192401311yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—5842no—
412C4—5842no—
413C4#1798889812yes—
414C4C2×#1455657211yescharacteristic
415C4C2×#1455662111yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—161no—
420C2C2×#1798889811yescharacteristic
421C2C2×#1798901711yescharacteristic
422C2#2262306511yescharacteristic
subgroupG/H
centerC2×C4C2×#11924013
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
Fitting, prime radicalC73×#3050C2
socleC22×C73C22×D8
hypercenter#3050D73
hypocenterC73#33645
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#17988625C2semidirect
2. #22612136C2semidirect
3. #22612131C2semidirect
4. #22612126C2semidirect
5. #22612119C2semidirect
6. #22612114C2semidirect
7. #22612109C2semidirect
8. #22611713C2semidirect
9. #22611638C2semidirect
10. C2×C22⋊#11924003C2semidirect
21. #17988414C22semidirect
22. #17988414C22semidirect
23. #17988412C22semidirect
24. #17988412C22semidirect
25. #17988391C22semidirect
26. #17988391C22semidirect
27. #17988388C22semidirect
28. #17988388C22semidirect
223. C73#33645semidirect

Maximal subgroups

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

subgroupindex
C2×#179886252
#226121362
#226121312
#226121262
#226121192
#226121142
#226121092
#226117132
#226116382
C2×C22⋊#119240032
C73×#30502
#3364573