Finite Group Databasebeta

← C29×#9164 #20304064

Subgroups — C29×#9164 #20304064

Order 7424.

458 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3112C211yesmaximal, characteristic
2C29×#2984C211yesmaximal, characteristic, complemented
3C29×#1763C211yesmaximal, characteristic, complemented
4C29×#1530C211yesmaximal, characteristic
5C29×#1502C211yesmaximal, characteristic
6C29×#1302C211yesmaximal, characteristic, complemented
7C29×#1285C211yesmaximal, characteristic, complemented
8C29×#532C2211yescharacteristic
9C2×C4×Q8×C29C2211yescharacteristic
10C29×#480—21no—
11C29×#477C411yescharacteristic, complemented
12C29×#477C411yescharacteristic, complemented
13C29×#460C411yescharacteristic, complemented
14C29×#460C411yescharacteristic, complemented
15C29×#448—21no—
16C29×#446—22no—
17C29×#446—21no—
18C8×Q8×C29—21no—
19C29×#440—21no—
20C29×#440—21no—
21C29×#432—21no—
22C29×#432C2211yescharacteristic
23C29×#432C2211yescharacteristic
24C29×#431—21no—
25C29×#431C2211yescharacteristic
26C2×C29×#103—21no—
27C2×C29×#97C2211yescharacteristic
28C4×C4⋊C4×C29C2211yescharacteristic
29C29×#340—21no—
30C29×#329—22no—
31C29×#327—21no—
32C29×#327—21no—
33C2×#41×C29—21no—
34C22×Q8×C29D411yescharacteristic
35C2×SD16×C29—21no—
36C2×SD16×C29—21no—
37C22×C8×C29—21no—
38C29×C4⋊Q8C2×C411yescharacteristic
39C29×#127C2×C411yescharacteristic
40C29×#124—21no—
41C29×#121—21no—
42C29×#121—21no—
43C4×Q8×C29—21no—
44C4×Q8×C29—21no—
45C4×Q8×C29C2×C411yescharacteristic
46C4×Q8×C29C2×C411yescharacteristic
47C4×Q8×C29D411yescharacteristic
48C4×Q8×C29D411yescharacteristic
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29D411yescharacteristic
54C2×C42×C29—21no—
55C2×C42×C29—21no—
56C2×C42×C29C2311yescharacteristic
57C29×#107—21no—
58C29×#107—21no—
59C29×C4⋊C8—22no—
60C29×C4⋊C8—22no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8C2×C411yescharacteristic
64C29×C4⋊C8C2×C411yescharacteristic
65C29×#103—24no—
66C29×#103—21no—
67C29×#103—21no—
68C29×#102—21no—
69C29×#102—21no—
70C29×C22⋊C8—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8D411yescharacteristic
73C29×C22⋊C8D411yescharacteristic
74C29×#97—22no—
75C29×#97—21no—
76C29×#97—21no—
77C29×#97—21no—
78C29×#97D412yes—
79C4×C8×C29—22no—
80C4×C8×C29—21no—
81C29×#95—21no—
82#41×C29—81no—
83#41×C29—81no—
84C2×Q8×C29—21no—
85C2×Q8×C29—22no—
86C2×Q8×C29—21no—
87C2×Q8×C29—41no—
88C2×Q8×C29C22⋊C411yescharacteristic
89C2×Q8×C29C22⋊C411yescharacteristic
90C2×D4×C29—21no—
91C2×D4×C29—21no—
92C2×D4×C29—21no—
93C2×D4×C29—41no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—41no—
97C22×C4×C29—41no—
98C22×C4×C29C2×D411yescharacteristic
99C22×C4×C29C2×D411yescharacteristic
100C22×C4×C29#4111yescharacteristic
101SD16×C29—42no—
102SD16×C29—42no—
103C2×C8×C29—22no—
104C2×C8×C29—21no—
105C2×C8×C29—21no—
106C2×C8×C29—21no—
107C2×C8×C29—21no—
108C2×C8×C29—22no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—22no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29C22⋊C411yescharacteristic
121C4⋊C4×C29C22⋊C411yescharacteristic
122C22⋊C4×C29—41no—
123C22⋊C4×C29—41no—
124C42×C29—21no—
125C42×C29—21no—
126C42×C29—21no—
127C42×C29—21no—
128C42×C29—81no—
129C42×C29C22×C411yescharacteristic
130C42×C29C2×D411yescharacteristic
131C42×C29C2×D411yescharacteristic
132C42×C29#4111yescharacteristic
133#9164C2911yesmaximal, characteristic, direct product factor, Sylow
134C23×C29—41no—
135C23×C29#12111yescharacteristic
136Q8×C29—21no—
137Q8×C29—21no—
138Q8×C29—21no—
139Q8×C29—42no—
140Q8×C29—81no—
141Q8×C29#10412yes—
142D4×C29—41no—
143D4×C29—41no—
144D4×C29—81no—
145D4×C29—81no—
146D4×C29—81no—
147D4×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—41no—
157C2×C4×C29—42no—
158C2×C4×C29—41no—
159C2×C4×C29—41no—
160C2×C4×C29—42no—
161C2×C4×C29—41no—
162C2×C4×C29—82no—
163C2×C4×C29—81no—
164C2×C4×C29—81no—
165C2×C4×C29C2×C22⋊C411yescharacteristic
166C2×C4×C29C4×D411yescharacteristic
167C2×C4×C29C4×D411yescharacteristic
168C2×C4×C29#12011yescharacteristic
169C2×C4×C29#12111yescharacteristic
170C2×C4×C29#12311yescharacteristic
171C8×C29—41no—
172C8×C29—41no—
173C8×C29—42no—
174C8×C29—42no—
175C8×C29—41no—
176C8×C29—41no—
177#3112C2×C2911yescharacteristic
178#2984C2×C2911yescharacteristic, complemented
179#1763C2×C2911yescharacteristic, complemented
180#1530C2×C2911yescharacteristic
181#1502C2×C2911yescharacteristic
182#1302C2×C2911yescharacteristic, complemented
183#1285C2×C2911yescharacteristic, complemented
184C22×C29—21no—
185C22×C29—21no—
186C22×C29—81no—
187C22×C29—81no—
188C22×C29—81no—
189C22×C29#38611yescharacteristic
190C22×C29#47111yescharacteristic
191C22×C29#47211yescharacteristic
192C4×C29—21no—
193C4×C29—22no—
194C4×C29—21no—
195C4×C29—21no—
196C4×C29—21no—
197C4×C29—21no—
198C4×C29—41no—
199C4×C29—41no—
200C4×C29—41no—
201C4×C29—82no—
202C4×C29—81no—
203C4×C29C2×#10411yescharacteristic
204C4×C29#42111yescharacteristic
205#532C22×C2911yescharacteristic
206C2×C4×Q8C22×C2911yescharacteristic
207#480—21no—
208#477C4×C2911yescharacteristic, complemented
209#477C4×C2911yescharacteristic, complemented
210#460C4×C2911yescharacteristic, complemented
211#460C4×C2911yescharacteristic, complemented
212#448—21no—
213#446—21no—
214#446—22no—
215C8×Q8—21no—
216#440—21no—
217#440—21no—
218#432—21no—
219#432C22×C2911yescharacteristic
220#432C22×C2911yescharacteristic
221#431—21no—
222#431C22×C2911yescharacteristic
223C2×#103—21no—
224C2×#97C22×C2911yescharacteristic
225C4×C4⋊C4C22×C2911yescharacteristic
226#340—21no—
227#329—22no—
228#327—21no—
229#327—21no—
230C2×C29—21no—
231C2×C29—21no—
232C2×C29—161no—
233C2×C29#187111yescharacteristic
234C2×C29#190511yescharacteristic
235C2×C29#190711yescharacteristic
236C2×#41—21no—
237C22×Q8D4×C2911yescharacteristic
238C2×SD16—21no—
239C2×SD16—21no—
240C22×C8—21no—
241C4⋊Q8C2×C4×C2911yescharacteristic
242#127C2×C4×C2911yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8C2×C4×C2911yescharacteristic
249C4×Q8C2×C4×C2911yescharacteristic
250C4×Q8D4×C2911yescharacteristic
251C4×Q8D4×C2911yescharacteristic
252C4×D4—21no—
253C4×D4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C2911yescharacteristic
257C2×C42—21no—
258C2×C42—21no—
259C2×C42C23×C2911yescharacteristic
260#107—21no—
261#107—21no—
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8C2×C4×C2911yescharacteristic
267C4⋊C8C2×C4×C2911yescharacteristic
268#103—24no—
269#103—21no—
270#103—21no—
271#102—21no—
272#102—21no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8D4×C2911yescharacteristic
276C22⋊C8D4×C2911yescharacteristic
277#97—22no—
278#97—21no—
279#97—21no—
280#97—21no—
281#97D4×C2912yes—
282C4×C8—22no—
283C4×C8—21no—
284#95—21no—
285C29#916411yescharacteristic, direct product factor, Sylow
286#41—81no—
287#41—81no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8C22⋊C4×C2911yescharacteristic
293C2×Q8C22⋊C4×C2911yescharacteristic
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C2×D4×C2911yescharacteristic
303C22×C4C2×D4×C2911yescharacteristic
304C22×C4#41×C2911yescharacteristic
305SD16—42no—
306SD16—42no—
307C2×C8—22no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4C22⋊C4×C2911yescharacteristic
325C4⋊C4C22⋊C4×C2911yescharacteristic
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—81no—
333C42C22×C4×C2911yescharacteristic
334C42C2×D4×C2911yescharacteristic
335C42C2×D4×C2911yescharacteristic
336C42#41×C2911yescharacteristic
337C23—41no—
338C23C29×#12111yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—21no—
342Q8—42no—
343Q8—81no—
344Q8C29×#10412yes—
345D4—41no—
346D4—41no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4C2×C22⋊C4×C2911yescharacteristic
369C2×C4C4×D4×C2911yescharacteristic
370C2×C4C4×D4×C2911yescharacteristic
371C2×C4C29×#12011yescharacteristic
372C2×C4C29×#12111yescharacteristic
373C2×C4C29×#12311yescharacteristic
374C8—42no—
375C8—41no—
376C8—41no—
377C8—42no—
378C8—41no—
379C8—41no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C29×#38611yescharacteristic
386C22C29×#47111yescharacteristic
387C22C29×#47211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—82no—
398C4—81no—
399C4C2×C29×#10411yescharacteristic
400C4C29×#42111yescharacteristic
401C2—21no—
402C2—21no—
403C2—161no—
404C2C29×#187111yescharacteristic
405C2C29×#190511yescharacteristic
406C2C29×#190711yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×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×#2984C2semidirect
3. C29×#1763C2semidirect
6. C29×#1302C2semidirect
7. C29×#1285C2semidirect
11. C29×#477C4semidirect
12. C29×#477C4semidirect
13. C29×#460C4semidirect
14. C29×#460C4semidirect
133. #9164C29direct (N × H)
178. #2984C2×C29semidirect
179. #1763C2×C29semidirect
182. #1302C2×C29semidirect
183. #1285C2×C29semidirect
208. #477C4×C29semidirect
209. #477C4×C29semidirect
210. #460C4×C29semidirect
211. #460C4×C29semidirect
285. C29#9164direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31122
C29×#29842
C29×#17632
C29×#15302
C29×#15022
C29×#13022
C29×#12852
#916429