Finite Group Databasebeta

← C29×#9096 #20303996

Subgroups — C29×#9096 #20303996

Order 7424.

514 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#41×C29C211yesmaximal, characteristic
2C4×C29×#137C211yesmaximal, characteristic
3C29×#1477C211yesmaximal, characteristic
4C2×C29×Q8⋊C8C211yesmaximal, characteristic, complemented
5C29×#1461C211yesmaximal, characteristic, complemented
6C29×#1283C211yesmaximal, characteristic, complemented
7C29×#1278C211yesmaximal, characteristic, complemented
8C2×C29×#137C411yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C2×C4×Q8×C29C2211yescharacteristic
11C8×Q8×C29—21no—
12C29×#441—21no—
13C29×#440—21no—
14C4×Q16×C29—21no—
15C4×SD16×C29—21no—
16C8×D4×C29—22no—
17C8×D4×C29—21no—
18C29×#431—21no—
19C29×#431C2211yescharacteristic
20C29×#431C2211yescharacteristic
21C29×#428C411yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C29×#419C411yescharacteristic
24C29×#417C411yescharacteristic
25C4×M16×C29C2211yescharacteristic
26C2×C4×C8×C29—21no—
27C2×C4×C8×C29C2211yescharacteristic
28C29×Q8⋊C8—21no—
29C29×Q8⋊C8—21no—
30C29×Q8⋊C8—21no—
31C29×D4⋊C8—21no—
32C29×#324—22no—
33C2×#41×C29C2×C411yescharacteristic
34C22×Q8×C29C2×C411yescharacteristic
35C29×#137—22no—
36C29×#137C814yescomplemented
37C2×Q16×C29—21no—
38C2×SD16×C29—21no—
39C2×M16×C29C2×C411yescharacteristic
40C2×M16×C29C2×C411yescharacteristic
41C22×C8×C29—22no—
42C22×C8×C29—21no—
43C22×C8×C29—21no—
44C4×Q8×C29—21no—
45C4×Q8×C29—21no—
46C4×Q8×C29—21no—
47C4×Q8×C29—21no—
48C4×Q8×C29D411yescharacteristic
49C4×Q8×C29D411yescharacteristic
50C4×D4×C29—21no—
51C4×D4×C29—21no—
52C4×D4×C29D411yescharacteristic
53C4×D4×C29D411yescharacteristic
54C29×#117—21no—
55C29×#117C2×C411yescharacteristic
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29C2×C411yescharacteristic
58C2×C42×C29—21no—
59C2×C42×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×#107—21no—
62C29×#106—21no—
63C29×C4⋊C8—22no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×#103—21no—
69C29×#103—21no—
70C29×#103—21no—
71C29×#102—21no—
72C29×C22⋊C8—22no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8D412yes—
75C29×#97—21no—
76C4×C8×C29—22no—
77C4×C8×C29—21no—
78C4×C8×C29—21no—
79C4×C8×C29—21no—
80C4×C8×C29—21no—
81C4×C8×C29D411yescharacteristic
82C4×C8×C29D411yescharacteristic
83#41×C29—21no—
84#41×C29—21no—
85#41×C29C2×C812yes—
86#41×C29M1612yes—
87C2×Q8×C29—21no—
88C2×Q8×C29—21no—
89C2×Q8×C29—21no—
90C2×Q8×C29—21no—
91C2×Q8×C29—21no—
92C2×Q8×C29C22⋊C411yescharacteristic
93C2×Q8×C29C2×C812yescomplemented
94C2×D4×C29—21no—
95C2×D4×C29C22⋊C411yescharacteristic
96C22×C4×C29—21no—
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29C22×C411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29#4111yescharacteristic
104Q16×C29—24no—
105SD16×C29—24no—
106M16×C29—21no—
107M16×C29—21no—
108M16×C29—21no—
109M16×C29C2×C812yescomplemented
110C2×C8×C29—21no—
111C2×C8×C29—21no—
112C2×C8×C29—21no—
113C2×C8×C29—22no—
114C2×C8×C29—21no—
115C2×C8×C29—42no—
116C2×C8×C29—44no—
117C2×C8×C29—41no—
118C2×C8×C29—41no—
119C2×C8×C29—81no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—41no—
125C4⋊C4×C29—41no—
126C4⋊C4×C29C22⋊C411yescharacteristic
127C4⋊C4×C29C22⋊C411yescharacteristic
128C22⋊C4×C29—21no—
129C22⋊C4×C29—21no—
130C22⋊C4×C29—21no—
131C42×C29—21no—
132C42×C29—21no—
133C42×C29—21no—
134C42×C29—41no—
135C42×C29—41no—
136C42×C29C2×D411yescharacteristic
137C42×C29C2×D411yescharacteristic
138C42×C29C2×D411yescharacteristic
139C42×C29#4111yescharacteristic
140#9096C2911yesmaximal, characteristic, direct product factor, Sylow
141C23×C29—21no—
142C23×C29C4×D411yescharacteristic
143Q8×C29—21no—
144Q8×C29—22no—
145Q8×C29—22no—
146Q8×C29—41no—
147Q8×C29—41no—
148Q8×C29C22⋊C812yes—
149D4×C29—22no—
150D4×C29—22no—
151D4×C29—21no—
152D4×C29C22⋊C812yes—
153C2×C4×C29—21no—
154C2×C4×C29—22no—
155C2×C4×C29—22no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—22no—
161C2×C4×C29—41no—
162C2×C4×C29—42no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—81no—
169C2×C4×C29C2×C22⋊C411yescharacteristic
170C2×C4×C29C4×D411yescharacteristic
171C2×C4×C29#12011yescharacteristic
172C2×C4×C29#12111yescharacteristic
173C2×C4×C29#12111yescharacteristic
174C2×C4×C29#12311yescharacteristic
175C2×C4×C29C22×C811yescharacteristic
176C2×C4×C29C2×M1611yescharacteristic
177C2×C4×C29#13111yescharacteristic
178C2×C4×C29#13111yescharacteristic
179C8×C29—22no—
180C8×C29—22no—
181C8×C29—42no—
182C8×C29—41no—
183C8×C29—41no—
184C8×C29—81no—
185C8×C29—81no—
186C8×#41C2×C2911yescharacteristic
187C4×#137C2×C2911yescharacteristic
188#1477C2×C2911yescharacteristic
189C2×Q8⋊C8C2×C2911yescharacteristic, complemented
190#1461C2×C2911yescharacteristic, complemented
191#1283C2×C2911yescharacteristic, complemented
192#1278C2×C2911yescharacteristic, complemented
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—22no—
196C22×C29—41no—
197C22×C29—41no—
198C22×C29#38611yescharacteristic
199C22×C29C8×D411yescharacteristic
200C22×C29#43511yescharacteristic
201C4×C29—22no—
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—21no—
205C4×C29—42no—
206C4×C29—41no—
207C4×C29—41no—
208C4×C29—81no—
209C4×C29C2×C22⋊C811yescharacteristic
210C4×C29#40811yescharacteristic
211C4×C29C8×D411yescharacteristic
212C4×C29#43511yescharacteristic
213C4×C29#47111yescharacteristic
214C4×C29#47311yescharacteristic
215C2×#137C4×C2911yescharacteristic
216C4×#41C22×C2911yescharacteristic
217C2×C4×Q8C22×C2911yescharacteristic
218C8×Q8—21no—
219#441—21no—
220#440—21no—
221C4×Q16—21no—
222C4×SD16—21no—
223C8×D4—21no—
224C8×D4—22no—
225#431—21no—
226#431C22×C2911yescharacteristic
227#431C22×C2911yescharacteristic
228#428C4×C2911yescharacteristic
229C2×C4⋊C8C22×C2911yescharacteristic
230#419C4×C2911yescharacteristic
231#417C4×C2911yescharacteristic
232C4×M16C22×C2911yescharacteristic
233C2×C4×C8—21no—
234C2×C4×C8C22×C2911yescharacteristic
235Q8⋊C8—21no—
236Q8⋊C8—21no—
237Q8⋊C8—21no—
238D4⋊C8—21no—
239#324—22no—
240C2×C29—21no—
241C2×C29—21no—
242C2×C29—42no—
243C2×C29#186911yescharacteristic
244C2×C29#190611yescharacteristic
245C2×C29#190811yescharacteristic
246C2×#41C2×C4×C2911yescharacteristic
247C22×Q8C2×C4×C2911yescharacteristic
248#137—22no—
249#137C8×C2914yescomplemented
250C2×Q16—21no—
251C2×SD16—21no—
252C2×M16C2×C4×C2911yescharacteristic
253C2×M16C2×C4×C2911yescharacteristic
254C22×C8—22no—
255C22×C8—21no—
256C22×C8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8D4×C2911yescharacteristic
262C4×Q8D4×C2911yescharacteristic
263C4×D4—21no—
264C4×D4—21no—
265C4×D4D4×C2911yescharacteristic
266C4×D4D4×C2911yescharacteristic
267#117—21no—
268#117C2×C4×C2911yescharacteristic
269C2×C4⋊C4—21no—
270C2×C4⋊C4C2×C4×C2911yescharacteristic
271C2×C42—21no—
272C2×C42—21no—
273C2×C42C23×C2911yescharacteristic
274#107—21no—
275#106—21no—
276C4⋊C8—22no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281#103—21no—
282#103—21no—
283#103—21no—
284#102—21no—
285C22⋊C8—22no—
286C22⋊C8—21no—
287C22⋊C8D4×C2912yes—
288#97—21no—
289C4×C8—22no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8D4×C2911yescharacteristic
295C4×C8D4×C2911yescharacteristic
296C29#909611yescharacteristic, direct product factor, Sylow
297#41—21no—
298#41—21no—
299#41C2×C8×C2912yes—
300#41M16×C2912yes—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8C22⋊C4×C2911yescharacteristic
307C2×Q8C2×C8×C2912yescomplemented
308C2×D4—21no—
309C2×D4C22⋊C4×C2911yescharacteristic
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4C22×C4×C2911yescharacteristic
316C22×C4C2×D4×C2911yescharacteristic
317C22×C4#41×C2911yescharacteristic
318Q16—24no—
319SD16—24no—
320M16—21no—
321M16—21no—
322M16—21no—
323M16C2×C8×C2912yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—42no—
330C2×C8—44no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—81no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4C22⋊C4×C2911yescharacteristic
341C4⋊C4C22⋊C4×C2911yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—41no—
349C42—41no—
350C42C2×D4×C2911yescharacteristic
351C42C2×D4×C2911yescharacteristic
352C42C2×D4×C2911yescharacteristic
353C42#41×C2911yescharacteristic
354C23—21no—
355C23C4×D4×C2911yescharacteristic
356Q8—21no—
357Q8—22no—
358Q8—22no—
359Q8—41no—
360Q8—41no—
361Q8C29×C22⋊C812yes—
362D4—22no—
363D4—22no—
364D4—21no—
365D4C29×C22⋊C812yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4C2×C22⋊C4×C2911yescharacteristic
383C2×C4C4×D4×C2911yescharacteristic
384C2×C4C29×#12011yescharacteristic
385C2×C4C29×#12111yescharacteristic
386C2×C4C29×#12111yescharacteristic
387C2×C4C29×#12311yescharacteristic
388C2×C4C22×C8×C2911yescharacteristic
389C2×C4C2×M16×C2911yescharacteristic
390C2×C4C29×#13111yescharacteristic
391C2×C4C29×#13111yescharacteristic
392C8—22no—
393C8—22no—
394C8—42no—
395C8—41no—
396C8—41no—
397C8—81no—
398C8—81no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22C29×#38611yescharacteristic
405C22C8×D4×C2911yescharacteristic
406C22C29×#43511yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—22no—
411C4—41no—
412C4—41no—
413C4—42no—
414C4—81no—
415C4C2×C29×C22⋊C811yescharacteristic
416C4C29×#40811yescharacteristic
417C4C8×D4×C2911yescharacteristic
418C4C29×#43511yescharacteristic
419C4C29×#47111yescharacteristic
420C4C29×#47311yescharacteristic
421C2—21no—
422C2—21no—
423C2—42no—
424C2C29×#186911yescharacteristic
425C2C29×#190611yescharacteristic
426C2C29×#190811yescharacteristic
subgroupG/H
centerC2×C4×C29#121
commutatorC2×C4C22×C8×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC2×#41×C29C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C29×Q8⋊C8C2semidirect
5. C29×#1461C2semidirect
6. C29×#1283C2semidirect
7. C29×#1278C2semidirect
36. C29×#137C8semidirect
93. C2×Q8×C29C2×C8semidirect
109. M16×C29C2×C8semidirect
140. #9096C29direct (N × H)
189. C2×Q8⋊C8C2×C29semidirect
190. #1461C2×C29semidirect
191. #1283C2×C29semidirect
192. #1278C2×C29semidirect
249. #137C8×C29semidirect
296. C29#9096direct (N × H)
307. C2×Q8C2×C8×C29semidirect
323. M16C2×C8×C29semidirect

Maximal subgroups

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

subgroupindex
C8×#41×C292
C4×C29×#1372
C29×#14772
C2×C29×Q8⋊C82
C29×#14612
C29×#12832
C29×#12782
#909629