Finite Group Databasebeta

← C29×#19532 #20314432

Subgroups — C29×#19532 #20314432

Order 7424.

562 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3254C211yesmaximal, characteristic
2C29×#3249C211yesmaximal, characteristic, complemented
3C29×#3228C211yesmaximal, characteristic
4C29×#2985C211yesmaximal, characteristic, complemented
5C29×#1702C212yesmaximal, complemented
6C29×#1696C212yesmaximal, complemented
7C29×#1678C212yesmaximal, complemented
8C29×#1672C212yesmaximal, complemented
9C29×#1570C211yesmaximal, characteristic, complemented
10C29×#1559C211yesmaximal, characteristic, complemented
11C29×#1551C211yesmaximal, characteristic
12C29×#533C2211yescharacteristic
13C29×#533C2211yescharacteristic
14C29×#532C2211yescharacteristic
15C29×#500C2211yescharacteristic
16C29×#498C2211yescharacteristic
17C29×#486C2211yescharacteristic
18C29×#486C2211yescharacteristic
19C29×#482—22no—
20C29×#478—22no—
21C29×#477—21no—
22C29×#477C2212yes—
23C29×#477C2212yes—
24C29×#474—21no—
25C29×#468—22no—
26C29×#467—22no—
27C29×#462—21no—
28C29×#462C2212yes—
29C29×#461—21no—
30C29×#460C2212yes—
31C29×#446—22no—
32C29×#446C2212yes—
33C8×Q8×C29C2212yes—
34C29×#433—22no—
35C29×#432C2211yescharacteristic
36C29×#431C2211yescharacteristic
37C29×#423C2211yescharacteristic
38C2×C29×C4⋊C8C2211yescharacteristic
39C29×#334C2212yes—
40C29×#334C2212yes—
41C29×#333C2212yes—
42C29×#333C2212yes—
43C29×#332C2212yes—
44C29×#331C2212yes—
45C2×#41×C29—21no—
46C2×Q16×C29—22no—
47C2×SD16×C29—22no—
48C2×M16×C29—21no—
49C22×C8×C29—21no—
50C29×C4⋊Q8D411yescharacteristic
51C29×C4⋊Q8D411yescharacteristic
52C29×C4⋊Q8C2311yescharacteristic
53C29×C4⋊Q8C2311yescharacteristic
54C29×C4⋊Q8C2311yescharacteristic
55C29×#127C2311yescharacteristic
56C29×#125—21no—
57C29×#125—21no—
58C29×#124—21no—
59C29×C22⋊Q8—21no—
60C29×C22⋊Q8—21no—
61C29×C22⋊Q8—21no—
62C29×C22⋊Q8D412yes—
63C29×#121—21no—
64C29×#121—21no—
65C4×Q8×C29—21no—
66C4×Q8×C29—21no—
67C4×Q8×C29—21no—
68C4×Q8×C29C2312yes—
69C4×D4×C29—21no—
70C4×D4×C29—21no—
71C29×#117—21no—
72C29×#117—21no—
73C2×C42×C29C2311yescharacteristic
74C29×#107—22no—
75C29×#107—22no—
76C29×#107—22no—
77C29×#106—22no—
78C29×C4⋊C8—22no—
79C29×C4⋊C8—22no—
80C29×C4⋊C8—21no—
81C29×C4⋊C8—21no—
82C29×C4⋊C8D412yes—
83C29×C4⋊C8C2312yes—
84C29×C4⋊C8C2312yes—
85C29×C4⋊C8C2312yes—
86C29×#103—22no—
87C29×#103—22no—
88C29×#103—22no—
89C29×#102—22no—
90C29×#102—22no—
91C29×#102—22no—
92C29×C22⋊C8—21no—
93C29×C22⋊C8D412yes—
94C29×#97—22no—
95C29×#97—21no—
96C4×C8×C29—22no—
97C4×C8×C29C2311yescharacteristic
98C4×C8×C29C2311yescharacteristic
99#41×C29—82no—
100C2×Q8×C29—21no—
101C2×Q8×C29—21no—
102C2×Q8×C29—21no—
103C2×Q8×C29—21no—
104C2×Q8×C29C2×D412yes—
105C2×D4×C29—21no—
106C2×D4×C29—21no—
107C2×D4×C29—21no—
108C2×D4×C29—41no—
109C22×C4×C29—41no—
110C22×C4×C29C2×D411yescharacteristic
111C22×C4×C29C2×D411yescharacteristic
112C22×C4×C29#4111yescharacteristic
113Q16×C29—82no—
114SD16×C29—82no—
115M16×C29—81no—
116C2×C8×C29—22no—
117C2×C8×C29—22no—
118C2×C8×C29—22no—
119C2×C8×C29—81no—
120C2×C8×C29C2×D412yes—
121C2×C8×C29C2×D412yes—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—21no—
125C4⋊C4×C29—22no—
126C4⋊C4×C29—22no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—21no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—21no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—41no—
134C4⋊C4×C29—41no—
135C4⋊C4×C29C2×D412yes—
136C22⋊C4×C29—22no—
137C22⋊C4×C29—41no—
138C22⋊C4×C29—41no—
139C22⋊C4×C29—41no—
140C42×C29—22no—
141C42×C29—41no—
142C42×C29C2×D411yescharacteristic
143C42×C29C2×D411yescharacteristic
144C42×C29#4111yescharacteristic
145C42×C29C2411yescharacteristic
146#19532C2911yesmaximal, characteristic, direct product factor, Sylow
147C23×C29—41no—
148C23×C29#12111yescharacteristic
149Q8×C29—22no—
150Q8×C29—22no—
151Q8×C29—41no—
152Q8×C29—41no—
153Q8×C29—81no—
154Q8×C29—81no—
155Q8×C29—81no—
156D4×C29—41no—
157D4×C29—41no—
158D4×C29—42no—
159D4×C29—81no—
160D4×C29—82no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—22no—
164C2×C4×C29—22no—
165C2×C4×C29—22no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—82no—
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29#12111yescharacteristic
173C2×C4×C29#12111yescharacteristic
174C2×C4×C29C22×D411yescharacteristic
175C2×C4×C29C22×D411yescharacteristic
176C2×C4×C29C2×#4111yescharacteristic
177C8×C29—22no—
178C8×C29—22no—
179C8×C29—42no—
180C8×C29—42no—
181C8×C29—42no—
182#3254C2×C2911yescharacteristic
183#3249C2×C2911yescharacteristic, complemented
184#3228C2×C2911yescharacteristic
185#2985C2×C2911yescharacteristic, complemented
186#1702C2×C2912yescomplemented
187#1696C2×C2912yescomplemented
188#1678C2×C2912yescomplemented
189#1672C2×C2912yescomplemented
190#1570C2×C2911yescharacteristic, complemented
191#1559C2×C2911yescharacteristic, complemented
192#1551C2×C2911yescharacteristic
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—81no—
197C22×C29—81no—
198C22×C29—81no—
199C22×C29C2×#12111yescharacteristic
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—42no—
205C4×C29—42no—
206C4×C29—81no—
207C4×C29—81no—
208C4×C29—81no—
209C4×C29#57711yescharacteristic
210C4×C29#57711yescharacteristic
211C4×C29#57812yes—
212#533C22×C2911yescharacteristic
213#533C22×C2911yescharacteristic
214#532C22×C2911yescharacteristic
215#500C22×C2911yescharacteristic
216#498C22×C2911yescharacteristic
217#486C22×C2911yescharacteristic
218#486C22×C2911yescharacteristic
219#482—22no—
220#478—22no—
221#477—21no—
222#477C22×C2912yes—
223#477C22×C2912yes—
224#474—21no—
225#468—22no—
226#467—22no—
227#462—21no—
228#462C22×C2912yes—
229#461—21no—
230#460C22×C2912yes—
231#446—22no—
232#446C22×C2912yes—
233C8×Q8C22×C2912yes—
234#433—22no—
235#432C22×C2911yescharacteristic
236#431C22×C2911yescharacteristic
237#423C22×C2911yescharacteristic
238C2×C4⋊C8C22×C2911yescharacteristic
239#334C22×C2912yes—
240#334C22×C2912yes—
241#333C22×C2912yes—
242#333C22×C2912yes—
243#332C22×C2912yes—
244#331C22×C2912yes—
245C2×C29—41no—
246C2×C29—161no—
247C2×C29#304411yescharacteristic
248C2×C29#306011yescharacteristic
249C2×C29#306811yescharacteristic
250C2×#41—21no—
251C2×Q16—22no—
252C2×SD16—22no—
253C2×M16—21no—
254C22×C8—21no—
255C4⋊Q8D4×C2911yescharacteristic
256C4⋊Q8D4×C2911yescharacteristic
257C4⋊Q8C23×C2911yescharacteristic
258C4⋊Q8C23×C2911yescharacteristic
259C4⋊Q8C23×C2911yescharacteristic
260#127C23×C2911yescharacteristic
261#125—21no—
262#125—21no—
263#124—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8D4×C2912yes—
268#121—21no—
269#121—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8C23×C2912yes—
274C4×D4—21no—
275C4×D4—21no—
276#117—21no—
277#117—21no—
278C2×C42C23×C2911yescharacteristic
279#107—22no—
280#107—22no—
281#107—22no—
282#106—22no—
283C4⋊C8—22no—
284C4⋊C8—22no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8D4×C2912yes—
288C4⋊C8C23×C2912yes—
289C4⋊C8C23×C2912yes—
290C4⋊C8C23×C2912yes—
291#103—22no—
292#103—22no—
293#103—22no—
294#102—22no—
295#102—22no—
296#102—22no—
297C22⋊C8—21no—
298C22⋊C8D4×C2912yes—
299#97—22no—
300#97—21no—
301C4×C8—22no—
302C4×C8C23×C2911yescharacteristic
303C4×C8C23×C2911yescharacteristic
304C29#1953211yescharacteristic, direct product factor, Sylow
305#41—82no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8C2×D4×C2912yes—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C22×C4—41no—
316C22×C4C2×D4×C2911yescharacteristic
317C22×C4C2×D4×C2911yescharacteristic
318C22×C4#41×C2911yescharacteristic
319Q16—82no—
320SD16—82no—
321M16—81no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—81no—
326C2×C8C2×D4×C2912yes—
327C2×C8C2×D4×C2912yes—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4C2×D4×C2912yes—
342C22⋊C4—22no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—22no—
347C42—41no—
348C42C2×D4×C2911yescharacteristic
349C42C2×D4×C2911yescharacteristic
350C42#41×C2911yescharacteristic
351C42C24×C2911yescharacteristic
352C23—41no—
353C23C29×#12111yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358Q8—81no—
359Q8—81no—
360Q8—81no—
361D4—41no—
362D4—41no—
363D4—42no—
364D4—81no—
365D4—82no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4C29×#12111yescharacteristic
377C2×C4C29×#12111yescharacteristic
378C2×C4C29×#12111yescharacteristic
379C2×C4C22×D4×C2911yescharacteristic
380C2×C4C22×D4×C2911yescharacteristic
381C2×C4C2×#41×C2911yescharacteristic
382C8—22no—
383C8—22no—
384C8—42no—
385C8—42no—
386C8—42no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22C2×C29×#12111yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—42no—
399C4—42no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4C29×#57711yescharacteristic
404C4C29×#57711yescharacteristic
405C4C29×#57812yes—
406C2—41no—
407C2—161no—
408C2C29×#304411yescharacteristic
409C2C29×#306011yescharacteristic
410C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3249C2semidirect
4. C29×#2985C2semidirect
5. C29×#1702C2semidirect
6. C29×#1696C2semidirect
7. C29×#1678C2semidirect
8. C29×#1672C2semidirect
9. C29×#1570C2semidirect
10. C29×#1559C2semidirect
146. #19532C29direct (N × H)
183. #3249C2×C29semidirect
185. #2985C2×C29semidirect
186. #1702C2×C29semidirect
187. #1696C2×C29semidirect
188. #1678C2×C29semidirect
189. #1672C2×C29semidirect
190. #1570C2×C29semidirect
191. #1559C2×C29semidirect
304. C29#19532direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32542
C29×#32492
C29×#32282
C29×#29852
C29×#17022
C29×#16962
C29×#16782
C29×#16722
C29×#15702
C29×#15592
C29×#15512
#1953229