Finite Group Databasebeta

← #33056102

Subgroups — #33056102

Order 18688.

678 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619932C211yesmaximal, characteristic
2#22619009C211yesmaximal, characteristic, complemented
3#22618954C211yesmaximal, characteristic, complemented
4#22608794C212yesmaximal, complemented
5#22608759C212yesmaximal, complemented
6#22608754C212yesmaximal, complemented
7#22608725C212yesmaximal, complemented
8#22608373C211yesmaximal, characteristic, complemented
9#22608347C211yesmaximal, characteristic, complemented
10#22608226C211yesmaximal, characteristic, complemented
11C73×#1572C211yesmaximal, characteristic, complemented
12#17989137C2211yescharacteristic
13C2×C4×D292C2211yescharacteristic
14#17988901C412yes—
15#17988868C412yes—
16#17988783C412yes—
17#17988723C412yes—
18C4×D584C2212yes—
19C4×D584C2212yes—
20#17988664C2212yescomplemented
21#17988660—22no—
22C8×D292—22no—
23#17988652C2212yes—
24#17988652C2212yes—
25#17988652C2212yescomplemented
26#17988640C2211yescharacteristic
27#17988552—22no—
28C22⋊C8×D73—22no—
29C4×#11924012C2211yescharacteristic
30#17988314C2212yes—
31#17988314C2212yes—
32#17988314C2212yescomplemented
33#17988314C2212yescomplemented
34#17988309C2211yescharacteristic, complemented
35#17988309C2211yescharacteristic, complemented
36#17988308C2211yescharacteristic, complemented
37C8×#10596831C2211yescharacteristic, complemented
38#432×C73C2211yescharacteristic
39#431×C73C2211yescharacteristic
40#431×C73C2211yescharacteristic
41#335×C73C2212yescomplemented
42#334×C73C2212yescomplemented
43C2×#11924028—21no—
44C22×D292C2×C411yescharacteristic
45C22×C4×D73—21no—
46C2×D584C2×C412yes—
47C2×D584C2×C412yes—
48C2×#11924012—21no—
49C2×#11924011—22no—
50C2×C8×D73—22no—
51C2×C8×D73—22no—
52C2×C8×D73—22no—
53#14556591C2×C411yescharacteristic
54#14556588C2×C411yescharacteristic
55#14556579—21no—
56#14556565—21no—
57#14556565C2×C412yes—
58C4×D292—21no—
59C4×D292—21no—
60C4×D292—21no—
61C4×D292C2×C412yes—
62C4×D292C2312yes—
63C4×D292C2312yes—
64C2×C4⋊Dic73C2×C411yescharacteristic
65C2×#11924005—21no—
66#14556525C2×C412yes—
67#14556525C2×C412yes—
68C4⋊#10596831D412yes—
69#14556513C2×C412yes—
70#14556513C2×C412yes—
71#14556513C2×C412yes—
72#14556513C2×C412yes—
73C22⋊#10596831D412yes—
74#14556503—22no—
75#14556503—22no—
76#14556503—22no—
77#14556503—22no—
78#14556502—21no—
79C4×#10596831C2311yescharacteristic
80C4×#10596831C2311yescharacteristic
81C4×#10596831C2311yescharacteristic
82C4×#10596831C2311yescharacteristic
83C2×C42×C73C2311yescharacteristic
84C4⋊C8×C73C2×C412yes—
85C4⋊C8×C73C2312yes—
86C4⋊C8×C73C2312yes—
87C22⋊C8×C73—21no—
88C22⋊C8×C73—21no—
89C22⋊C8×C73C2×C412yes—
90#97×C73—21no—
91C4×C8×C73—21no—
92C4×C8×C73C2311yescharacteristic
93C4×C8×C73C2311yescharacteristic
94C23×D73—21no—
95#11924028—82no—
96C2×Dic146—21no—
97C2×D292—21no—
98C2×D292—24no—
99C2×D292—21no—
100C2×D292—21no—
101C2×D292C22×C412yes—
102C2×D292C22×C412yes—
103C2×C22⋊D73—22no—
104C22×Dic73—21no—
105C2×C4×D73—22no—
106C2×C4×D73—22no—
107C2×C4×D73—22no—
108C2×C4×D73—82no—
109D584—24no—
110D584—24no—
111#11924012—42no—
112#11924011—82no—
113C2×#10596831—21no—
114C2×#10596831—21no—
115C2×#10596831C2×D412yes—
116C2×#10596831C2×D412yes—
117C8×D73—82no—
118C8×D73—82no—
119C8×D73—82no—
120C4⋊Dic73—21no—
121C4⋊Dic73—21no—
122C4⋊Dic73C22×C412yes—
123C4⋊Dic73C22×C412yes—
124#11924005—22no—
125#11924005—22no—
126#11924005—22no—
127#11924005—22no—
128C22×C4×C73C22×C411yescharacteristic
129C22×C4×C73C2×D411yescharacteristic
130C22×C4×C73#4111yescharacteristic
131C2×C8×C73—22no—
132C2×C8×C73—22no—
133C2×C8×C73C22×C412yes—
134C2×C8×C73C22×C412yes—
135C42×C73C22×C411yescharacteristic
136C42×C73C2×D411yescharacteristic
137C42×C73#4111yescharacteristic
138C42×C73C2411yescharacteristic
139C23×C73C4×D411yescharacteristic
140C22×D73—22no—
141C22×D73—24no—
142C22×D73—22no—
143C22×D73—81no—
144C22×D73—81no—
145C2×C4×C73—22no—
146C2×C4×C73—22no—
147C2×C4×C73—41no—
148C2×C4×C73C4×D411yescharacteristic
149C2×C4×C73C4×D411yescharacteristic
150C2×C4×C73C4×D411yescharacteristic
151C2×C4×C73C23×C411yescharacteristic
152C2×C4×C73C22×D411yescharacteristic
153C2×C4×C73C2×#4111yescharacteristic
154C22⋊D73—82no—
155C2×Dic73—22no—
156C2×Dic73—22no—
157C2×Dic73—81no—
158D292—24no—
159D292—22no—
160D292—22no—
161D292—22no—
162D292—81no—
163D292—81no—
164D292#13114yes—
165C4×D73—42no—
166C4×D73—42no—
167C4×D73—42no—
168C4×D73—42no—
169C4×D73—82no—
170Dic146—81no—
171C8×C73—22no—
172C8×C73—22no—
173C8×C73—42no—
174C8×C73—42no—
175#10596831—22no—
176#10596831—22no—
177#10596831—22no—
178#10596831—41no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73C2×C4×D411yescharacteristic
183C2×D73—24no—
184C2×D73—42no—
185C2×D73—42no—
186C2×D73—42no—
187C2×D73—42no—
188C2×D73—42no—
189C2×D73—84no—
190C4×C73—21no—
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73C2×#13112yes—
195C4×C73#57612yes—
196Dic73—42no—
197Dic73—42no—
198#17922—731nomaximal, Sylow
199C2×C73—41no—
200C2×C73#292911yescharacteristic
201C2×C73#294811yescharacteristic
202C2×C73#295611yescharacteristic
203D73—44no—
204D73—82no—
205#3100—731no—
206#2981—731no—
207#2972—731no—
208#1586—732no—
209#1581—732no—
210#1580—732no—
211C8×D8—732no—
212#1572D7311yescharacteristic, complemented
213#1490—731no—
214#1484—731no—
215#1453—731no—
216C73#1792211yescharacteristic, complemented, Sylow
217#532—731no—
218C2×C4×D4—731no—
219#480—732no—
220#474—732no—
221#459—732no—
222#447—732no—
223C4×D8—732no—
224C4×D8—732no—
225#436—732no—
226#435—1462no—
227C8×D4—732no—
228C8×D4—732no—
229C8×D4—732no—
230C8×D4—1462no—
231#432C2×D7311yescharacteristic
232#431—731no—
233#431C2×D7311yescharacteristic
234#431C2×D7311yescharacteristic
235#408—1462no—
236C2×C22⋊C8—1462no—
237C4×M16—731no—
238#335C2×D7312yescomplemented
239#334C2×D7312yescomplemented
240D4⋊C8—732no—
241D4⋊C8—732no—
242D4⋊C8—732no—
243D4⋊C8—732no—
244#322—731no—
245#322—731no—
246#322—731no—
247C82—731no—
248C2×#41—1461no—
249C22×D4—731no—
250C23×C4—1461no—
251C2×D8—732no—
252C2×D8—732no—
253C2×M16—1462no—
254C2×M16—1461no—
255C22×C8—1462no—
256C22×C8—1462no—
257C22×C8—1462no—
258C4⋊Q8—731no—
259#127—731no—
260#124—1461no—
261#121—732no—
262#121—1461no—
263C4×D4—732no—
264C4×D4—732no—
265C4×D4—732no—
266C4×D4—1461no—
267C4×D4—1461no—
268C4×D4—1461no—
269C2×C4⋊C4—731no—
270C2×C22⋊C4—1461no—
271C2×C42C22×D7311yescharacteristic
272#107—732no—
273#107—732no—
274C4⋊C8—732no—
275C4⋊C8C4×D7312yes—
276C4⋊C8C22×D7312yes—
277C4⋊C8C22×D7312yes—
278#102—732no—
279#102—732no—
280#102—732no—
281#102—732no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—732no—
285C22⋊C8—1462no—
286C22⋊C8—1462no—
287C22⋊C8—1462no—
288C22⋊C8—1462no—
289C22⋊C8C4×D7312yes—
290#97—21no—
291#97—1461no—
292C4×C8—21no—
293C4×C8—731no—
294C4×C8—731no—
295C4×C8—731no—
296C4×C8—731no—
297C4×C8C22×D7311yescharacteristic
298C4×C8C22×D7311yescharacteristic
299C24—1461no—
300#41—5842no—
301C2×Q8—1461no—
302C2×D4—732no—
303C2×D4—732no—
304C2×D4—1464no—
305C2×D4—1462no—
306C2×D4—1461no—
307C2×D4—1461no—
308C2×D4—1461no—
309C22×C4—5842no—
310C22×C4—1462no—
311C22×C4—1462no—
312C22×C4—1461no—
313C22×C4—1462no—
314C22×C4C2×C4×D7311yescharacteristic
315C22×C4D4×D7311yescharacteristic
316C22×C4#1192402911yescharacteristic
317D8—1464no—
318D8—1464no—
319M16—2922no—
320M16—5842no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—5842no—
324C2×C8—5842no—
325C2×C8—5842no—
326C2×C8—732no—
327C2×C8—732no—
328C2×C8—1461no—
329C2×C8—1461no—
330C2×C8C2×C4×D7312yes—
331C2×C8C2×C4×D7312yes—
332C4⋊C4—732no—
333C4⋊C4—732no—
334C4⋊C4—1461no—
335C4⋊C4—1461no—
336C22⋊C4—1462no—
337C22⋊C4—1462no—
338C22⋊C4—1462no—
339C22⋊C4—1462no—
340C42C2×C4×D7311yescharacteristic
341C42D4×D7311yescharacteristic
342C42#1192402911yescharacteristic
343C42C23×D7311yescharacteristic
344C23—5841no—
345C23—5841no—
346C23—1464no—
347C23—1462no—
348C23—1462no—
349C23#1455655311yescharacteristic
350Q8—5841no—
351D4—5841no—
352D4—5841no—
353D4—5842no—
354D4—734no—
355D4—1464no—
356D4—1462no—
357D4—1462no—
358D4—1462no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—2922no—
363C2×C4—2922no—
364C2×C4—2922no—
365C2×C4—2922no—
366C2×C4—5842no—
367C2×C4—5841no—
368C2×C4—1462no—
369C2×C4—1462no—
370C2×C4#1455655311yescharacteristic
371C2×C4#1455655311yescharacteristic
372C2×C4#1455655311yescharacteristic
373C2×C4C22×C4×D7311yescharacteristic
374C2×C4C2×D4×D7311yescharacteristic
375C2×C4C2×#1192402911yescharacteristic
376C8—22no—
377C8—22no—
378C8—42no—
379C8—42no—
380C8—2921no—
381C8—1462no—
382C8—1462no—
383C8—1462no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—2922no—
388C22—2922no—
389C22—2922no—
390C22—2922no—
391C22—2922no—
392C22—5844no—
393C22—1464no—
394C22C2×#1455655311yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—2922no—
400C4—2922no—
401C4#131×D7312yes—
402C4#1798938912yes—
403C2—41no—
404C2—2924no—
405C2—5842no—
406C2#2261862411yescharacteristic
407C2#2261878211yescharacteristic
408C2#2261884011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1572C2
socleC22×C73C2×C4×D4
prime radical#22619932C2
cosocleC42×C73C24
hypercenter#1572D73
hypocenterC73#17922
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #22619009C2semidirect
3. #22618954C2semidirect
4. #22608794C2semidirect
5. #22608759C2semidirect
6. #22608754C2semidirect
7. #22608725C2semidirect
8. #22608373C2semidirect
9. #22608347C2semidirect
10. #22608226C2semidirect
11. C73×#1572C2semidirect
20. #17988664C22semidirect
25. #17988652C22semidirect
32. #17988314C22semidirect
33. #17988314C22semidirect
34. #17988309C22semidirect
35. #17988309C22semidirect
36. #17988308C22semidirect
37. C8×#10596831C22semidirect
41. #335×C73C22semidirect
42. #334×C73C22semidirect
212. #1572D73semidirect
216. C73#17922semidirect
238. #335C2×D73semidirect
239. #334C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199322
#226190092
#226189542
#226087942
#226087592
#226087542
#226087252
#226083732
#226083472
#226082262
C73×#15722
#1792273