Finite Group Databasebeta

← C29×#9240 #20304140

Subgroups — C29×#9240 #20304140

Order 7424.

452 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
1C2×C29×#485C211yesmaximal, characteristic
2C29×#2924C211yesmaximal, characteristic
3C29×#1826C211yesmaximal, characteristic
4C29×#1508C211yesmaximal, characteristic
5C29×#1472C211yesmaximal, characteristic
6C29×#1293C211yesmaximal, characteristic
7C29×#1282C211yesmaximal, characteristic
8C2×C29×C22⋊Q8C2211yescharacteristic
9C2×C29×#117C2211yescharacteristic
10C29×#485—21no—
11C29×#485—21no—
12C29×#485—21no—
13C29×#485—21no—
14C29×#433—22no—
15C29×#432—21no—
16C29×#431—21no—
17C2×C29×#107C411yescharacteristic, complemented
18C2×C29×#106C411yescharacteristic, complemented
19C29×#424—21no—
20C2×C29×#103C411yescharacteristic, complemented
21C2×C29×#103C411yescharacteristic, complemented
22C29×#407C2211yescharacteristic
23C29×#407C2211yescharacteristic
24C2×C29×C22⋊C8C2211yescharacteristic
25C2×C29×C22⋊C8C2211yescharacteristic
26C29×#405—21no—
27C4×C22⋊C4×C29C2211yescharacteristic
28C29×#339—21no—
29C29×#339—21no—
30C29×#328—22no—
31C29×#324—21no—
32C29×#324—21no—
33C22×Q8×C29C2×C411yescharacteristic
34C23×C4×C29C2311yescharacteristic
35C2×M16×C29—21no—
36C2×M16×C29—21no—
37C22×C8×C29—21no—
38C22×C8×C29C2×C411yescharacteristic
39C22×C8×C29C2×C411yescharacteristic
40C29×C22⋊Q8—21no—
41C29×C22⋊Q8—21no—
42C29×C22⋊Q8—21no—
43C29×C22⋊Q8—21no—
44C29×#117—21no—
45C29×#117—21no—
46C29×#117D411yescharacteristic
47C29×#117D411yescharacteristic
48C29×#117D411yescharacteristic
49C29×#117D411yescharacteristic
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29C2×C411yescharacteristic
52C2×C4⋊C4×C29C2×C411yescharacteristic
53C2×C4⋊C4×C29C2×C411yescharacteristic
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29—21no—
56C2×C22⋊C4×C29—21no—
57C2×C42×C29—21no—
58C2×C42×C29—21no—
59C29×#107—21no—
60C29×#107—21no—
61C29×#106—21no—
62C29×#106—21no—
63C29×C4⋊C8—22no—
64C29×C4⋊C8—22no—
65C29×#103—21no—
66C29×#103—21no—
67C29×#103—21no—
68C29×#103—21no—
69C29×C22⋊C8—21no—
70C29×C22⋊C8—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8D411yescharacteristic
76C29×C22⋊C8D411yescharacteristic
77C29×C22⋊C8D412yes—
78C29×#97—22no—
79C4×C8×C29—22no—
80C29×#95—21no—
81C24×C29#4111yescharacteristic
82C2×Q8×C29—21no—
83C2×Q8×C29—21no—
84C2×Q8×C29—41no—
85C2×Q8×C29—41no—
86C22×C4×C29—21no—
87C22×C4×C29—21no—
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—41no—
91C22×C4×C29—41no—
92C22×C4×C29—41no—
93C22×C4×C29C22×C411yescharacteristic
94C22×C4×C29C2×D411yescharacteristic
95C22×C4×C29C2×D411yescharacteristic
96C22×C4×C29C2×D411yescharacteristic
97C22×C4×C29C2×D411yescharacteristic
98C22×C4×C29#4111yescharacteristic
99M16×C29—41no—
100M16×C29—41no—
101M16×C29—41no—
102M16×C29—41no—
103C2×C8×C29—21no—
104C2×C8×C29—21no—
105C2×C8×C29—21no—
106C2×C8×C29—21no—
107C2×C8×C29—22no—
108C2×C8×C29—41no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C2×C8×C29—41no—
112C2×C8×C29—41no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—41no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29C22⋊C411yescharacteristic
120C4⋊C4×C29C22⋊C411yescharacteristic
121C4⋊C4×C29C22⋊C411yescharacteristic
122C4⋊C4×C29C22⋊C411yescharacteristic
123C22⋊C4×C29—21no—
124C22⋊C4×C29—21no—
125C22⋊C4×C29—21no—
126C22⋊C4×C29—21no—
127C22⋊C4×C29—22no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29—41no—
130C22⋊C4×C29—41no—
131C42×C29—21no—
132C42×C29—21no—
133C42×C29—21no—
134C42×C29—21no—
135C42×C29—41no—
136C42×C29—41no—
137#9240C2911yesmaximal, characteristic, direct product factor, Sylow
138C23×C29—21no—
139C23×C29—21no—
140C23×C29—41no—
141C23×C29—41no—
142C23×C29C4×D411yescharacteristic
143C23×C29#12111yescharacteristic
144C23×C29#12311yescharacteristic
145Q8×C29—41no—
146Q8×C29—41no—
147Q8×C29—81no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—41no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—42no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—81no—
169C2×C4×C29—81no—
170C2×C4×C29—81no—
171C2×C4×C29—81no—
172C2×C4×C29C2×C22⋊C411yescharacteristic
173C2×C4×C29C4×D411yescharacteristic
174C2×C4×C29#12011yescharacteristic
175C2×C4×C29#12111yescharacteristic
176C8×C29—41no—
177C8×C29—41no—
178C8×C29—42no—
179C8×C29—41no—
180C8×C29—41no—
181C8×C29—81no—
182C2×#485C2×C2911yescharacteristic
183#2924C2×C2911yescharacteristic
184#1826C2×C2911yescharacteristic
185#1508C2×C2911yescharacteristic
186#1472C2×C2911yescharacteristic
187#1293C2×C2911yescharacteristic
188#1282C2×C2911yescharacteristic
189C22×C29—21no—
190C22×C29—21no—
191C22×C29—21no—
192C22×C29—21no—
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—21no—
197C22×C29—81no—
198C22×C29—81no—
199C22×C29#38611yescharacteristic
200C22×C29#44311yescharacteristic
201C22×C29#44411yescharacteristic
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—21no—
205C4×C29—41no—
206C4×C29—41no—
207C4×C29—41no—
208C4×C29—41no—
209C4×C29—82no—
210C4×C29—81no—
211C4×C29—81no—
212C4×C29#41011yescharacteristic
213C4×C29#41011yescharacteristic
214C2×C22⋊Q8C22×C2911yescharacteristic
215C2×#117C22×C2911yescharacteristic
216#485—21no—
217#485—21no—
218#485—21no—
219#485—21no—
220#433—22no—
221#432—21no—
222#431—21no—
223C2×#107C4×C2911yescharacteristic, complemented
224C2×#106C4×C2911yescharacteristic, complemented
225#424—21no—
226C2×#103C4×C2911yescharacteristic, complemented
227C2×#103C4×C2911yescharacteristic, complemented
228#407C22×C2911yescharacteristic
229#407C22×C2911yescharacteristic
230C2×C22⋊C8C22×C2911yescharacteristic
231C2×C22⋊C8C22×C2911yescharacteristic
232#405—21no—
233C4×C22⋊C4C22×C2911yescharacteristic
234#339—21no—
235#339—21no—
236#328—22no—
237#324—21no—
238#324—21no—
239C2×C29—21no—
240C2×C29—21no—
241C2×C29—41no—
242C2×C29—41no—
243C2×C29#187611yescharacteristic
244C2×C29#189911yescharacteristic
245C2×C29#190211yescharacteristic
246C22×Q8C2×C4×C2911yescharacteristic
247C23×C4C23×C2911yescharacteristic
248C2×M16—21no—
249C2×M16—21no—
250C22×C8—21no—
251C22×C8C2×C4×C2911yescharacteristic
252C22×C8C2×C4×C2911yescharacteristic
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257#117—21no—
258#117—21no—
259#117D4×C2911yescharacteristic
260#117D4×C2911yescharacteristic
261#117D4×C2911yescharacteristic
262#117D4×C2911yescharacteristic
263C2×C4⋊C4—21no—
264C2×C4⋊C4C2×C4×C2911yescharacteristic
265C2×C4⋊C4C2×C4×C2911yescharacteristic
266C2×C4⋊C4C2×C4×C2911yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271C2×C42—21no—
272#107—21no—
273#107—21no—
274#106—21no—
275#106—21no—
276C4⋊C8—22no—
277C4⋊C8—22no—
278#103—21no—
279#103—21no—
280#103—21no—
281#103—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8D4×C2911yescharacteristic
289C22⋊C8D4×C2911yescharacteristic
290C22⋊C8D4×C2912yes—
291#97—22no—
292C4×C8—22no—
293#95—21no—
294C29#924011yescharacteristic, direct product factor, Sylow
295C24#41×C2911yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4C22×C4×C2911yescharacteristic
308C22×C4C2×D4×C2911yescharacteristic
309C22×C4C2×D4×C2911yescharacteristic
310C22×C4C2×D4×C2911yescharacteristic
311C22×C4C2×D4×C2911yescharacteristic
312C22×C4#41×C2911yescharacteristic
313M16—41no—
314M16—41no—
315M16—41no—
316M16—41no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—22no—
321C2×C8—21no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊C4×C2911yescharacteristic
334C4⋊C4C22⋊C4×C2911yescharacteristic
335C4⋊C4C22⋊C4×C2911yescharacteristic
336C4⋊C4C22⋊C4×C2911yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—22no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—41no—
350C42—41no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23C4×D4×C2911yescharacteristic
356C23C29×#12111yescharacteristic
357C23C29×#12311yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C2×C22⋊C4×C2911yescharacteristic
386C2×C4C4×D4×C2911yescharacteristic
387C2×C4C29×#12011yescharacteristic
388C2×C4C29×#12111yescharacteristic
389C8—41no—
390C8—41no—
391C8—42no—
392C8—41no—
393C8—41no—
394C8—81no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22C29×#38611yescharacteristic
406C22C29×#44311yescharacteristic
407C22C29×#44411yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—82no—
416C4—81no—
417C4—81no—
418C4C29×#41011yescharacteristic
419C4C29×#41011yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2C29×#187611yescharacteristic
425C2C29×#189911yescharacteristic
426C2C29×#190211yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC24×C29#41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
17. C2×C29×#107C4semidirect
18. C2×C29×#106C4semidirect
20. C2×C29×#103C4semidirect
21. C2×C29×#103C4semidirect
137. #9240C29direct (N × H)
223. C2×#107C4×C29semidirect
224. C2×#106C4×C29semidirect
226. C2×#103C4×C29semidirect
227. C2×#103C4×C29semidirect
294. C29#9240direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4852
C29×#29242
C29×#18262
C29×#15082
C29×#14722
C29×#12932
C29×#12822
#924029