Finite Group Databasebeta

← C29×#9432 #20304332

Subgroups — C29×#9432 #20304332

Order 7424.

436 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3180C211yesmaximal, characteristic
2C29×#2968C211yesmaximal, characteristic, complemented
3C29×#1530C211yesmaximal, characteristic, complemented
4C29×#1517C211yesmaximal, characteristic, complemented
5C29×#1512C211yesmaximal, characteristic, complemented
6C29×#1302C211yesmaximal, characteristic, complemented
7C29×#1295C211yesmaximal, characteristic, complemented
8C29×#532C2211yescharacteristic
9C29×#529C2211yescharacteristic
10C29×#501C411yescharacteristic, complemented
11C29×#496C411yescharacteristic, complemented
12C29×#490C411yescharacteristic, complemented
13C29×#489C411yescharacteristic, complemented
14C29×#466—21no—
15C29×#465—21no—
16C29×#446—21no—
17C29×#442—21no—
18C29×#440—21no—
19C29×#435—21no—
20C29×#435—21no—
21C8×D4×C29—21no—
22C29×#433—21no—
23C29×#432C2211yescharacteristic
24C29×#431C2211yescharacteristic
25C29×#405—21no—
26C2×C29×#97C2211yescharacteristic
27C2×C29×#97C2211yescharacteristic
28C29×#382C2211yescharacteristic
29C29×#329—21no—
30C29×#329—21no—
31C29×#328—21no—
32C29×#327—21no—
33C29×#327—21no—
34C29×#327—21no—
35C2×#41×C29—21no—
36C2×SD16×C29—21no—
37C2×D8×C29—21no—
38C2×M16×C29—21no—
39C22×C8×C29—21no—
40C22×C8×C29—21no—
41C22×C8×C29—21no—
42C29×C4⋊Q8C2×C411yescharacteristic
43C29×#127C2×C411yescharacteristic
44C29×#126—21no—
45C29×#125C2×C411yescharacteristic
46C29×#124—21no—
47C29×#124C2×C411yescharacteristic
48C29×#123—21no—
49C29×C22⋊Q8D411yescharacteristic
50C29×#121—21no—
51C29×#121—21no—
52C29×#121D411yescharacteristic
53C4×Q8×C29D411yescharacteristic
54C4×D4×C29—21no—
55C4×D4×C29—21no—
56C4×D4×C29—21no—
57C4×D4×C29D411yescharacteristic
58C29×#117—21no—
59C2×C4⋊C4×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×#107—21no—
62C29×#106—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×#103—21no—
68C29×#102—21no—
69C29×#102—21no—
70C29×#102—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8D411yescharacteristic
75C29×C22⋊C8D411yescharacteristic
76C29×#97—21no—
77C29×#97—21no—
78C29×#97—21no—
79C29×#97—21no—
80C29×#97C2×C411yescharacteristic
81C29×#97C2×C411yescharacteristic
82C29×#97D411yescharacteristic
83C29×#97D411yescharacteristic
84C4×C8×C29—21no—
85C4×C8×C29—21no—
86C29×#95—21no—
87C29×#95—21no—
88#41×C29—81no—
89#41×C29—81no—
90C2×Q8×C29—21no—
91C2×Q8×C29C22⋊C411yescharacteristic
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29—21no—
95C2×D4×C29—21no—
96C2×D4×C29—41no—
97C2×D4×C29C22⋊C411yescharacteristic
98C22×C4×C29—21no—
99C22×C4×C29—41no—
100C22×C4×C29—41no—
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29#4111yescharacteristic
104SD16×C29—42no—
105D8×C29—42no—
106M16×C29—42no—
107C2×C8×C29—21no—
108C2×C8×C29—21no—
109C2×C8×C29—21no—
110C2×C8×C29—21no—
111C2×C8×C29—21no—
112C2×C8×C29—21no—
113C2×C8×C29—42no—
114C2×C8×C29—42no—
115C2×C8×C29—42no—
116C2×C8×C29—41no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—81no—
124C4⋊C4×C29C22⋊C411yescharacteristic
125C4⋊C4×C29C22⋊C411yescharacteristic
126C22⋊C4×C29—21no—
127C22⋊C4×C29—21no—
128C22⋊C4×C29—21no—
129C22⋊C4×C29—21no—
130C22⋊C4×C29—21no—
131C22⋊C4×C29—41no—
132C22⋊C4×C29—41no—
133C42×C29—21no—
134C42×C29C22×C411yescharacteristic
135C42×C29C2×D411yescharacteristic
136C42×C29C2×D411yescharacteristic
137C42×C29#4111yescharacteristic
138#9432C2911yesmaximal, characteristic, direct product factor, Sylow
139C23×C29—21no—
140C23×C29—41no—
141C23×C29#12111yescharacteristic
142Q8×C29—41no—
143Q8×C29—81no—
144D4×C29—41no—
145D4×C29—41no—
146D4×C29—41no—
147D4×C29—41no—
148D4×C29—41no—
149D4×C29—81no—
150D4×C29—81no—
151D4×C29—81no—
152D4×C29—81no—
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—82no—
164C2×C4×C29—81no—
165C2×C4×C29—81no—
166C2×C4×C29—81no—
167C2×C4×C29C2×C22⋊C411yescharacteristic
168C2×C4×C29C4×D411yescharacteristic
169C2×C4×C29C4×D411yescharacteristic
170C2×C4×C29#12011yescharacteristic
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29#12311yescharacteristic
173C8×C29—22no—
174C8×C29—22no—
175C8×C29—41no—
176C8×C29—41no—
177C8×C29—41no—
178C8×C29—41no—
179C8×C29—81no—
180#3180C2×C2911yescharacteristic
181#2968C2×C2911yescharacteristic, complemented
182#1530C2×C2911yescharacteristic, complemented
183#1517C2×C2911yescharacteristic, complemented
184#1512C2×C2911yescharacteristic, complemented
185#1302C2×C2911yescharacteristic, complemented
186#1295C2×C2911yescharacteristic, complemented
187C22×C29—21no—
188C22×C29—21no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29—41no—
192C22×C29—81no—
193C22×C29—81no—
194C22×C29—81no—
195C22×C29#38611yescharacteristic
196C22×C29#47111yescharacteristic
197C22×C29#47211yescharacteristic
198C4×C29—21no—
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—41no—
205C4×C29—41no—
206C4×C29—41no—
207C4×C29—81no—
208C4×C29—161no—
209#532C22×C2911yescharacteristic
210#529C22×C2911yescharacteristic
211#501C4×C2911yescharacteristic, complemented
212#496C4×C2911yescharacteristic, complemented
213#490C4×C2911yescharacteristic, complemented
214#489C4×C2911yescharacteristic, complemented
215#466—21no—
216#465—21no—
217#446—21no—
218#442—21no—
219#440—21no—
220#435—21no—
221#435—21no—
222C8×D4—21no—
223#433—21no—
224#432C22×C2911yescharacteristic
225#431C22×C2911yescharacteristic
226#405—21no—
227C2×#97C22×C2911yescharacteristic
228C2×#97C22×C2911yescharacteristic
229#382C22×C2911yescharacteristic
230#329—21no—
231#329—21no—
232#328—21no—
233#327—21no—
234#327—21no—
235#327—21no—
236C2×C29—21no—
237C2×C29—21no—
238C2×C29—81no—
239C2×C29—161no—
240C2×C29#188411yescharacteristic
241C2×C29#190611yescharacteristic
242C2×C29#190711yescharacteristic
243C2×#41—21no—
244C2×SD16—21no—
245C2×D8—21no—
246C2×M16—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C4⋊Q8C2×C4×C2911yescharacteristic
251#127C2×C4×C2911yescharacteristic
252#126—21no—
253#125C2×C4×C2911yescharacteristic
254#124—21no—
255#124C2×C4×C2911yescharacteristic
256#123—21no—
257C22⋊Q8D4×C2911yescharacteristic
258#121—21no—
259#121—21no—
260#121D4×C2911yescharacteristic
261C4×Q8D4×C2911yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4D4×C2911yescharacteristic
266#117—21no—
267C2×C4⋊C4—21no—
268C2×C42C23×C2911yescharacteristic
269#107—21no—
270#106—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275#103—21no—
276#102—21no—
277#102—21no—
278#102—21no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8D4×C2911yescharacteristic
283C22⋊C8D4×C2911yescharacteristic
284#97—21no—
285#97—21no—
286#97—21no—
287#97—21no—
288#97C2×C4×C2911yescharacteristic
289#97C2×C4×C2911yescharacteristic
290#97D4×C2911yescharacteristic
291#97D4×C2911yescharacteristic
292C4×C8—21no—
293C4×C8—21no—
294#95—21no—
295#95—21no—
296C29#943211yescharacteristic, direct product factor, Sylow
297#41—81no—
298#41—81no—
299C2×Q8—21no—
300C2×Q8C22⋊C4×C2911yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4C22⋊C4×C2911yescharacteristic
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4C2×D4×C2911yescharacteristic
311C22×C4C2×D4×C2911yescharacteristic
312C22×C4#41×C2911yescharacteristic
313SD16—42no—
314D8—42no—
315M16—42no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—81no—
333C4⋊C4C22⋊C4×C2911yescharacteristic
334C4⋊C4C22⋊C4×C2911yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—21no—
343C42C22×C4×C2911yescharacteristic
344C42C2×D4×C2911yescharacteristic
345C42C2×D4×C2911yescharacteristic
346C42#41×C2911yescharacteristic
347C23—21no—
348C23—41no—
349C23C29×#12111yescharacteristic
350Q8—41no—
351Q8—81no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—82no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C2×C22⋊C4×C2911yescharacteristic
376C2×C4C4×D4×C2911yescharacteristic
377C2×C4C4×D4×C2911yescharacteristic
378C2×C4C29×#12011yescharacteristic
379C2×C4C29×#12111yescharacteristic
380C2×C4C29×#12311yescharacteristic
381C8—22no—
382C8—22no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—41no—
387C8—81no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C29×#38611yescharacteristic
397C22C29×#47111yescharacteristic
398C22C29×#47211yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—81no—
409C4—161no—
410C2—21no—
411C2—21no—
412C2—81no—
413C2—161no—
414C2C29×#188411yescharacteristic
415C2C29×#190611yescharacteristic
416C2C29×#190711yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3180C2
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×#2968C2semidirect
3. C29×#1530C2semidirect
4. C29×#1517C2semidirect
5. C29×#1512C2semidirect
6. C29×#1302C2semidirect
7. C29×#1295C2semidirect
10. C29×#501C4semidirect
11. C29×#496C4semidirect
12. C29×#490C4semidirect
13. C29×#489C4semidirect
138. #9432C29direct (N × H)
181. #2968C2×C29semidirect
182. #1530C2×C29semidirect
183. #1517C2×C29semidirect
184. #1512C2×C29semidirect
185. #1302C2×C29semidirect
186. #1295C2×C29semidirect
211. #501C4×C29semidirect
212. #496C4×C29semidirect
213. #490C4×C29semidirect
214. #489C4×C29semidirect
296. C29#9432direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31802
C29×#29682
C29×#15302
C29×#15172
C29×#15122
C29×#13022
C29×#12952
#943229