Finite Group Databasebeta

← #33240726

Subgroups — #33240726

Order 18688.

524 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620443C211yesmaximal, characteristic, complemented
2C2×#17988703C211yesmaximal, characteristic
3#22612106C214yesmaximal, complemented
4#22612101C214yesmaximal, complemented
5#22611705C211yesmaximal, characteristic, complemented
6C2×#17988407C211yesmaximal, characteristic, complemented
7#22611668C211yesmaximal, characteristic
8#22611666C211yesmaximal, characteristic
9C73×#2155C211yesmaximal, characteristic, complemented
10C2×#14556613C2211yescharacteristic
11C2×#14556599—21no—
12#17989140—21no—
13C2×#14556531C2211yescharacteristic
14#17988991—21no—
15#17988988—21no—
16#17988987C2212yescomplemented
17#17988984C2212yescomplemented
18#17988703—21no—
19#17988703—21no—
20#17988703C2212yes—
21#17988703C2212yes—
22#17988625C2211yescharacteristic
23#17988623—21no—
24C2×#14556517—21no—
25C2×C8×Dic73C2211yescharacteristic
26#17988411C2214yescomplemented
27#17988407C2212yescomplemented
28#17988407C2212yescomplemented
29#17988398C2214yes—
30#17988396C2214yes—
31C2×M32×C73C2211yescharacteristic
32C2×#108×C73C2211yescharacteristic
33#427×C73C2211yescharacteristic
34#365×C73C2214yescomplemented
35C2×#11924028—21no—
36#14556613—21no—
37#14556613—21no—
38#14556613Q812yescomplemented
39#14556613C2312yes—
40C2×Dic292Q811yescharacteristic, complemented
41C2×#11924017—21no—
42C2×D584Q811yescharacteristic, complemented
43#14556599—22no—
44#14556599—22no—
45#14556599—41no—
46#14556599—41no—
47C2×#11924011—41no—
48C22×#10596831D411yescharacteristic
49C2×C8×D73—41no—
50#14556590—22no—
51#14556582—22no—
52#14556568—42no—
53C4×Dic146—42no—
54#14556550—21no—
55C2×C4×Dic73D411yescharacteristic
56#14556531—21no—
57#14556531C2312yes—
58C2×#11924003—21no—
59#14556525—21no—
60#14556524—22no—
61#14556523C2312yes—
62#14556522—22no—
63#14556517—22no—
64#14556517—22no—
65C8×Dic73D411yescharacteristic
66C8×Dic73D411yescharacteristic
67C8×Dic73C2311yescharacteristic
68C8×Dic73C2311yescharacteristic
69C2×M16×C73—21no—
70C22×C8×C73C2311yescharacteristic
71#117×C73—21no—
72M32×C73—21no—
73M32×C73C2312yes—
74C2×C16×C73—21no—
75#108×C73—21no—
76#108×C73C2312yes—
77#107×C73—21no—
78#106×C73C2312yes—
79#11924028—22no—
80#11924028—22no—
81#11924028—41no—
82#11924028—41no—
83C2×Dic146—21no—
84C2×Dic146—42no—
85C2×D292—21no—
86C2×C22⋊D73—41no—
87C22×Dic73—21no—
88C2×C4×D73—41no—
89Dic292—21no—
90Dic292C2×Q812yes—
91#11924017—22no—
92#11924017—22no—
93D584—21no—
94D584C2×Q812yes—
95#11924011—42no—
96#11924011—42no—
97C2×#10596831SD1611yescharacteristic
98C2×#10596831SD1611yescharacteristic
99C2×#10596831SD1611yescharacteristic
100C2×#10596831SD1611yescharacteristic
101C2×#10596831C2×D411yescharacteristic
102C2×#10596831C2×D411yescharacteristic
103C8×D73—42no—
104C8×D73—42no—
105C4⋊Dic73—22no—
106C4⋊Dic73—42no—
107#11924007—42no—
108#11924007—42no—
109C22⋊Dic73—41no—
110C4×Dic73—21no—
111C4×Dic73—41no—
112C4×Dic73C2×D411yescharacteristic
113C4×Dic73C2×D411yescharacteristic
114#11924003—22no—
115C22×C4×C73C2×D411yescharacteristic
116M16×C73—22no—
117M16×C73—41no—
118C2×C8×C73—41no—
119C2×C8×C73C2×D411yescharacteristic
120C2×C8×C73C2×Q811yescharacteristic
121C2×C8×C73C2×Q811yescharacteristic
122C2×C8×C73#4111yescharacteristic
123C2×C8×C73#4111yescharacteristic
124C2×C8×C73C2411yescharacteristic
125C4⋊C4×C73—22no—
126C22⋊C4×C73—41no—
127C42×C73—41no—
128C16×C73—22no—
129C23×C73AGL(1,ℤ/8)11yescharacteristic
130C22×D73—41no—
131C2×C4×C73—42no—
132C2×C4×C73C22⋊Q811yescharacteristic
133C2×C4×C73C22⋊Q811yescharacteristic
134C2×C4×C73C2×SD1611yescharacteristic
135C2×C4×C73C2×SD1611yescharacteristic
136C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C73C22×D411yescharacteristic
138C22⋊D73—42no—
139C22⋊D73—42no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—42no—
143C2×Dic73—41no—
144C2×Dic73—42no—
145D292—22no—
146D292—41no—
147C4×D73—42no—
148C4×D73—42no—
149Dic146—22no—
150Dic146—41no—
151Dic146—84no—
152C8×C73—42no—
153C8×C73C22⋊Q811yescharacteristic
154C8×C73C22⋊Q811yescharacteristic
155C8×C73C22×Q811yescharacteristic
156C8×C73C2×#4111yescharacteristic
157#10596831C2×SD1611yescharacteristic
158#10596831C2×SD1611yescharacteristic
159#10596831C2×SD1611yescharacteristic
160#10596831C2×SD1611yescharacteristic
161C22×C73—41no—
162C22×C73#47611yescharacteristic
163C22×C73#47611yescharacteristic
164C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
165C2×D73—42no—
166C2×D73—82no—
167C4×C73—82no—
168C4×C73#47611yescharacteristic
169C4×C73#47611yescharacteristic
170C4×C73C2×C22⋊Q811yescharacteristic
171C4×C73C22×SD1611yescharacteristic
172Dic73—22no—
173Dic73—41no—
174Dic73—42no—
175Dic73—82no—
176#33637—731nomaximal, Sylow
177C2×C73—21no—
178C2×C73—21no—
179C2×C73—21no—
180C2×C73C2×#47611yescharacteristic
181D73—82no—
182#3160—731no—
183C2×#443—731no—
184#2231—734no—
185#2230—734no—
186#2155—731no—
187#2155D7311yescharacteristic, complemented
188C2×#364—731no—
189#2145—731no—
190#2145—731no—
191C73#3363711yescharacteristic, complemented, Sylow
192C2×#135—731no—
193C2×#131—1461no—
194#533—1461no—
195C2×M32—731no—
196C2×M32C2×D7311yescharacteristic
197#500—1461no—
198#499—732no—
199#499—1461no—
200#498—732no—
201#443—732no—
202#443—732no—
203#443—1461no—
204#443—1461no—
205C2×#108C2×D7311yescharacteristic
206#427—731no—
207#427—1461no—
208#427C2×D7311yescharacteristic
209C2×#104—1461no—
210C2×C4×C8—731no—
211#365—734no—
212#365C2×D7314yescomplemented
213#364—732no—
214#364—732no—
215#360—734no—
216#360—734no—
217C2×#41—1461no—
218#135—732no—
219#135—732no—
220#135—1461no—
221#135—1461no—
222C2×Q16—731no—
223C2×SD16—1461no—
224C2×D8—731no—
225#131—2921no—
226#131—2921no—
227#131—1462no—
228#131—1462no—
229C2×M16—21no—
230C2×M16—2921no—
231C22×C8—2921no—
232C22×C8—731no—
233C22×C8C22×D7311yescharacteristic
234C4⋊Q8—1462no—
235#125—1462no—
236C22⋊Q8—2922no—
237C4×Q8—2922no—
238#117—21no—
239#117—1461no—
240C2×C42—731no—
241M32—21no—
242M32—732no—
243M32—1461no—
244M32C22×D7312yes—
245C2×C16—21no—
246C2×C16—1461no—
247#108—21no—
248#108C22×D7312yes—
249#107—21no—
250#107—1462no—
251#107—1461no—
252#106—732no—
253#106—1462no—
254#106C22×D7312yes—
255#104—1462no—
256#104—1462no—
257C4×C8—731no—
258C4×C8—731no—
259C4×C8—731no—
260C4×C8—731no—
261#41—2921no—
262#41—2921no—
263#41—1462no—
264#41—1462no—
265C2×Q8—2922no—
266C2×Q8—1461no—
267C2×D4—2921no—
268C2×D4—1461no—
269C22×C4—2921no—
270C22×C4—1461no—
271C22×C4D4×D7311yescharacteristic
272Q16—732no—
273Q16—1461no—
274SD16—1462no—
275SD16—1462no—
276D8—732no—
277D8—1461no—
278M16—22no—
279M16—41no—
280M16—2922no—
281M16—2922no—
282C2×C8—41no—
283C2×C8—2922no—
284C2×C8—2922no—
285C2×C8—731no—
286C2×C8—731no—
287C2×C8—731no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8—731no—
291C2×C8D4×D7311yescharacteristic
292C2×C8Q8×D7311yescharacteristic
293C2×C8Q8×D7311yescharacteristic
294C2×C8#1192402811yescharacteristic
295C2×C8#1192402811yescharacteristic
296C2×C8C23×D7311yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—2922no—
299C4⋊C4—2922no—
300C4⋊C4—2922no—
301C4⋊C4—1462no—
302C22⋊C4—41no—
303C22⋊C4—2921no—
304C42—41no—
305C42—2921no—
306C42—731no—
307C42—731no—
308C42—1461no—
309C16—22no—
310C16—1462no—
311C23—2921no—
312C23#1455661811yescharacteristic
313Q8—2921no—
314Q8—5844no—
315Q8—1462no—
316D4—2922no—
317D4—2922no—
318D4—2921no—
319D4—1462no—
320C2×C4—42no—
321C2×C4—2921no—
322C2×C4—2922no—
323C2×C4—2922no—
324C2×C4—2922no—
325C2×C4—2922no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4#1455656911yescharacteristic
329C2×C4#1455656911yescharacteristic
330C2×C4SD16×D7311yescharacteristic
331C2×C4SD16×D7311yescharacteristic
332C2×C4#1455661811yescharacteristic
333C2×C4C2×D4×D7311yescharacteristic
334C8—42no—
335C8—731no—
336C8—731no—
337C8—731no—
338C8—731no—
339C8#1455656911yescharacteristic
340C8#1455656911yescharacteristic
341C8C2×Q8×D7311yescharacteristic
342C8C2×#1192402811yescharacteristic
343C22—41no—
344C22—2922no—
345C22—5842no—
346C22#1798887611yescharacteristic
347C22#1798887611yescharacteristic
348C22C2×#1455661811yescharacteristic
349C4—82no—
350C4—2921no—
351C4—2922no—
352C4—5842no—
353C4—1462no—
354C4#1798887611yescharacteristic
355C4#1798887611yescharacteristic
356C4C2×#1455656911yescharacteristic
357C4C2×SD16×D7311yescharacteristic
358C2—21no—
359C2—21no—
360C2—21no—
361C2—5842no—
362C2C2×#1798887611yescharacteristic
subgroupG/H
centerC4#17988876
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#2155C2
socleC2×C73C2×#476
prime radicalC2×#14556613C22
hypercenter#2155D73
hypocenterC73#33637
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2155

Complements

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

NH ≅ G/Ntype
1. #22620443C2semidirect
3. #22612106C2semidirect
4. #22612101C2semidirect
5. #22611705C2semidirect
6. C2×#17988407C2semidirect
9. C73×#2155C2semidirect
16. #17988987C22semidirect
17. #17988984C22semidirect
26. #17988411C22semidirect
27. #17988407C22semidirect
28. #17988407C22semidirect
34. #365×C73C22semidirect
38. #14556613Q8semidirect
40. C2×Dic292Q8semidirect
42. C2×D584Q8semidirect
187. #2155D73semidirect
191. C73#33637semidirect
212. #365C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226204432
C2×#179887032
#226121062
#226121012
#226117052
C2×#179884072
#226116682
#226116662
C73×#21552
#3363773