Finite Group Databasebeta

← C29×#8999 #20303899

Subgroups — C29×#8999 #20303899

Order 7424.

530 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#489C211yesmaximal, characteristic
2C29×#2379C211yesmaximal, characteristic
3C29×#1993C211yesmaximal, characteristic, complemented
4C29×#1960C211yesmaximal, characteristic, complemented
5C2×C29×#329C211yesmaximal, characteristic
6C29×#1295C211yesmaximal, characteristic, complemented
7C29×#1295C211yesmaximal, characteristic, complemented
8C2×C29×C4⋊Q8C2211yescharacteristic
9C2×C29×#124C2211yescharacteristic
10C29×#489—22no—
11C29×#489C414yescomplemented
12C2×C29×#103—21no—
13C2×C29×#103—21no—
14C2×C29×#103—21no—
15C2×C29×#102—21no—
16C2×C29×#97C2211yescharacteristic
17C2×C29×#97C2211yescharacteristic
18C2×C29×#97C2211yescharacteristic
19C29×#391—21no—
20C29×#388—21no—
21C29×#388—21no—
22C29×#386—21no—
23C29×#385—21no—
24C29×#385—21no—
25C29×#382C2211yescharacteristic
26C29×#382C2211yescharacteristic
27C29×#340—21no—
28C29×#340—21no—
29C29×#329—22no—
30C22×Q8×C29—21no—
31C22×Q8×C29D411yescharacteristic
32C22×D4×C29D411yescharacteristic
33C23×C4×C29—21no—
34C22×C8×C29—21no—
35C22×C8×C29—21no—
36C22×C8×C29—21no—
37C29×C4⋊Q8—21no—
38C29×C4⋊Q8—21no—
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8C2×C412yescomplemented
41C29×#124—21no—
42C29×#124—21no—
43C29×#124C2×C412yes—
44C29×#124D412yes—
45C2×C4⋊C4×C29—21no—
46C2×C4⋊C4×C29—21no—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29D411yescharacteristic
49C2×C4⋊C4×C29D411yescharacteristic
50C2×C4⋊C4×C29D411yescharacteristic
51C2×C4⋊C4×C29D411yescharacteristic
52C2×C22⋊C4×C29—21no—
53C2×C22⋊C4×C29—21no—
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29—21no—
56C2×C22⋊C4×C29—21no—
57C2×C42×C29—21no—
58C2×C42×C29C2311yescharacteristic
59C29×#103—24no—
60C29×#103—42no—
61C29×#103—42no—
62C29×#102—24no—
63C29×#97—21no—
64C29×#97—21no—
65C29×#97—21no—
66C29×#97—21no—
67C29×#97—21no—
68C29×#97C2×C412yescomplemented
69C29×#95—21no—
70C29×#95—21no—
71C29×#95—21no—
72C29×#95—21no—
73C29×#95—21no—
74C29×#95—21no—
75C24×C29—21no—
76C2×Q8×C29—21no—
77C2×Q8×C29—22no—
78C2×Q8×C29—41no—
79C2×Q8×C29—41no—
80C2×Q8×C29—41no—
81C2×Q8×C29—41no—
82C2×Q8×C29—41no—
83C2×Q8×C29—41no—
84C2×Q8×C29—41no—
85C2×Q8×C29C22⋊C412yes—
86C2×D4×C29—21no—
87C2×D4×C29—41no—
88C2×D4×C29—41no—
89C2×D4×C29C22⋊C412yes—
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29—41no—
96C22×C4×C29—81no—
97C22×C4×C29—81no—
98C22×C4×C29—81no—
99C22×C4×C29C2×D411yescharacteristic
100C22×C4×C29C2×D411yescharacteristic
101C22×C4×C29C2×D411yescharacteristic
102C2×C8×C29—22no—
103C2×C8×C29—22no—
104C2×C8×C29—22no—
105C2×C8×C29—41no—
106C2×C8×C29—41no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C4⋊C4×C29—22no—
112C4⋊C4×C29—22no—
113C4⋊C4×C29—41no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29—41no—
116C4⋊C4×C29—41no—
117C4⋊C4×C29—41no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—81no—
120C22⋊C4×C29—22no—
121C22⋊C4×C29—22no—
122C22⋊C4×C29—22no—
123C22⋊C4×C29—22no—
124C22⋊C4×C29—81no—
125C22⋊C4×C29—81no—
126C22⋊C4×C29—81no—
127C42×C29—81no—
128C42×C29C22×C411yescharacteristic
129C42×C29C2×D411yescharacteristic
130C42×C29#4111yescharacteristic
131C42×C29#4111yescharacteristic
132#8999C2911yesmaximal, characteristic, direct product factor, Sylow
133C23×C29—22no—
134C23×C29—41no—
135C23×C29—41no—
136C23×C29—41no—
137C23×C29—41no—
138C23×C29—41no—
139C23×C29—41no—
140C23×C29#12011yescharacteristic
141Q8×C29—42no—
142Q8×C29—42no—
143Q8×C29—42no—
144Q8×C29—81no—
145Q8×C29—81no—
146Q8×C29—81no—
147D4×C29—42no—
148D4×C29—81no—
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—22no—
156C2×C4×C29—41no—
157C2×C4×C29—41no—
158C2×C4×C29—42no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—84no—
172C2×C4×C29—81no—
173C2×C4×C29—81no—
174C2×C4×C29C2×C22⋊C411yescharacteristic
175C2×C4×C29C4×D411yescharacteristic
176C2×C4×C29C4×D411yescharacteristic
177C2×C4×C29#12111yescharacteristic
178C2×C4×C29#12111yescharacteristic
179C2×C4×C29#12311yescharacteristic
180C8×C29—42no—
181C8×C29—42no—
182C8×C29—42no—
183C2×#489C2×C2911yescharacteristic
184#2379C2×C2911yescharacteristic
185#1993C2×C2911yescharacteristic, complemented
186#1960C2×C2911yescharacteristic, complemented
187C2×#329C2×C2911yescharacteristic
188#1295C2×C2911yescharacteristic, complemented
189#1295C2×C2911yescharacteristic, complemented
190C22×C29—42no—
191C22×C29—42no—
192C22×C29—42no—
193C22×C29—81no—
194C22×C29—81no—
195C22×C29—81no—
196C22×C29—81no—
197C22×C29#38611yescharacteristic
198C22×C29#45311yescharacteristic
199C22×C29#45411yescharacteristic
200C22×C29#45511yescharacteristic
201C22×C29#45511yescharacteristic
202C22×C29#45511yescharacteristic
203C22×C29#45611yescharacteristic
204C4×C29—21no—
205C4×C29—21no—
206C4×C29—21no—
207C4×C29—21no—
208C4×C29—21no—
209C4×C29—21no—
210C4×C29—42no—
211C4×C29—82no—
212C4×C29—81no—
213C4×C29—81no—
214C4×C29—81no—
215C4×C29—81no—
216C2×C4⋊Q8C22×C2911yescharacteristic
217C2×#124C22×C2911yescharacteristic
218#489—22no—
219#489C4×C2914yescomplemented
220C2×#103—21no—
221C2×#103—21no—
222C2×#103—21no—
223C2×#102—21no—
224C2×#97C22×C2911yescharacteristic
225C2×#97C22×C2911yescharacteristic
226C2×#97C22×C2911yescharacteristic
227#391—21no—
228#388—21no—
229#388—21no—
230#386—21no—
231#385—21no—
232#385—21no—
233#382C22×C2911yescharacteristic
234#382C22×C2911yescharacteristic
235#340—21no—
236#340—21no—
237#329—22no—
238C2×C29—82no—
239C2×C29#165911yescharacteristic
240C2×C29#166111yescharacteristic
241C2×C29#166211yescharacteristic
242C2×C29#166411yescharacteristic
243C2×C29#188211yescharacteristic
244C2×C29#188311yescharacteristic
245C2×C29#188511yescharacteristic
246C22×Q8—21no—
247C22×Q8D4×C2911yescharacteristic
248C22×D4D4×C2911yescharacteristic
249C23×C4—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8C2×C4×C2912yescomplemented
257#124—21no—
258#124—21no—
259#124C2×C4×C2912yes—
260#124D4×C2912yes—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4D4×C2911yescharacteristic
265C2×C4⋊C4D4×C2911yescharacteristic
266C2×C4⋊C4D4×C2911yescharacteristic
267C2×C4⋊C4D4×C2911yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C42—21no—
274C2×C42C23×C2911yescharacteristic
275#103—24no—
276#103—42no—
277#103—42no—
278#102—24no—
279#97—21no—
280#97—21no—
281#97—21no—
282#97—21no—
283#97—21no—
284#97C2×C4×C2912yescomplemented
285#95—21no—
286#95—21no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—21no—
291C29#899911yescharacteristic, direct product factor, Sylow
292C24—21no—
293C2×Q8—21no—
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8C22⋊C4×C2912yes—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4C22⋊C4×C2912yes—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—81no—
314C22×C4—81no—
315C22×C4—81no—
316C22×C4C2×D4×C2911yescharacteristic
317C22×C4C2×D4×C2911yescharacteristic
318C22×C4C2×D4×C2911yescharacteristic
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—81no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—81no—
342C22⋊C4—81no—
343C22⋊C4—81no—
344C42—81no—
345C42C22×C4×C2911yescharacteristic
346C42C2×D4×C2911yescharacteristic
347C42#41×C2911yescharacteristic
348C42#41×C2911yescharacteristic
349C23—22no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23C29×#12011yescharacteristic
357Q8—42no—
358Q8—42no—
359Q8—42no—
360Q8—81no—
361Q8—81no—
362Q8—81no—
363D4—42no—
364D4—81no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—84no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4C2×C22⋊C4×C2911yescharacteristic
391C2×C4C4×D4×C2911yescharacteristic
392C2×C4C4×D4×C2911yescharacteristic
393C2×C4C29×#12111yescharacteristic
394C2×C4C29×#12111yescharacteristic
395C2×C4C29×#12311yescharacteristic
396C8—42no—
397C8—42no—
398C8—42no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C29×#38611yescharacteristic
407C22C29×#45311yescharacteristic
408C22C29×#45411yescharacteristic
409C22C29×#45511yescharacteristic
410C22C29×#45511yescharacteristic
411C22C29×#45511yescharacteristic
412C22C29×#45611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—82no—
425C2—82no—
426C2C29×#165911yescharacteristic
427C2C29×#166111yescharacteristic
428C2C29×#166211yescharacteristic
429C2C29×#166411yescharacteristic
430C2C29×#188211yescharacteristic
431C2C29×#188311yescharacteristic
432C2C29×#188511yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1993C2semidirect
4. C29×#1960C2semidirect
6. C29×#1295C2semidirect
7. C29×#1295C2semidirect
11. C29×#489C4semidirect
40. C29×C4⋊Q8C2×C4semidirect
68. C29×#97C2×C4semidirect
132. #8999C29direct (N × H)
185. #1993C2×C29semidirect
186. #1960C2×C29semidirect
188. #1295C2×C29semidirect
189. #1295C2×C29semidirect
219. #489C4×C29semidirect
256. C4⋊Q8C2×C4×C29semidirect
284. #97C2×C4×C29semidirect
291. C29#8999direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4892
C29×#23792
C29×#19932
C29×#19602
C2×C29×#3292
C29×#12952
#899929