Finite Group Databasebeta

← C29×#9348 #20304248

Subgroups — C29×#9348 #20304248

Order 7424.

470 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3094C211yesmaximal, characteristic
2C29×#2924C211yesmaximal, characteristic, complemented
3C29×#1825C211yesmaximal, characteristic, complemented
4C29×#1519C211yesmaximal, characteristic
5C29×#1471C211yesmaximal, characteristic
6C29×#1305C211yesmaximal, characteristic, complemented
7C29×#1298C211yesmaximal, characteristic, complemented
8C2×C29×#121C2211yescharacteristic
9C2×C29×#117C2211yescharacteristic
10C29×#482—21no—
11C29×#482—21no—
12C29×#481—21no—
13C29×#480—21no—
14C29×#433—22no—
15C29×#432—21no—
16C29×#431—21no—
17C29×#428C411yescharacteristic, complemented
18C29×#428C411yescharacteristic, complemented
19C29×#424—21no—
20C29×#418C411yescharacteristic, complemented
21C29×#418C411yescharacteristic, complemented
22C29×#407C2211yescharacteristic
23C29×#407C2211yescharacteristic
24C2×C29×C22⋊C8C2211yescharacteristic
25C2×C29×C22⋊C8C2211yescharacteristic
26C29×#405—21no—
27C29×#380C2211yescharacteristic
28C29×#340—21no—
29C29×#340—21no—
30C29×#327—21no—
31C29×#327—21no—
32C29×#323—22no—
33C22×D4×C29—21no—
34C22×D4×C29C2×C411yescharacteristic
35C23×C4×C29C2311yescharacteristic
36C2×M16×C29—21no—
37C2×M16×C29C2×C411yescharacteristic
38C2×M16×C29C2×C411yescharacteristic
39C22×C8×C29—21no—
40C22×C8×C29—21no—
41C29×#121—21no—
42C29×#121—21no—
43C29×#121—21no—
44C29×#121—21no—
45C29×#117—21no—
46C29×#117—21no—
47C29×#117C2×C411yescharacteristic
48C29×#117C2×C411yescharacteristic
49C29×#117D411yescharacteristic
50C29×#117D411yescharacteristic
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29C2×C411yescharacteristic
53C2×C4⋊C4×C29D411yescharacteristic
54C2×C4⋊C4×C29D411yescharacteristic
55C2×C22⋊C4×C29—21no—
56C2×C22⋊C4×C29—21no—
57C2×C22⋊C4×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×#102—21no—
66C29×#102—21no—
67C29×#102—21no—
68C29×#102—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—21no—
82C24×C29#4111yescharacteristic
83C2×D4×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—41no—
86C2×D4×C29—41no—
87C2×D4×C29—41no—
88C2×D4×C29—41no—
89C2×D4×C29—81no—
90C2×D4×C29—81no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—41no—
95C22×C4×C29—41no—
96C22×C4×C29—41no—
97C22×C4×C29C22×C411yescharacteristic
98C22×C4×C29C2×D411yescharacteristic
99C22×C4×C29C2×D411yescharacteristic
100C22×C4×C29C2×D411yescharacteristic
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29#4111yescharacteristic
103M16×C29—41no—
104M16×C29—41no—
105M16×C29—41no—
106M16×C29—41no—
107C2×C8×C29—21no—
108C2×C8×C29—21no—
109C2×C8×C29—21no—
110C2×C8×C29—21no—
111C2×C8×C29—22no—
112C2×C8×C29—41no—
113C2×C8×C29—41no—
114C2×C8×C29—41no—
115C2×C8×C29—41no—
116C2×C8×C29—41no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29—41no—
123C4⋊C4×C29C22⋊C411yescharacteristic
124C4⋊C4×C29C22⋊C411yescharacteristic
125C4⋊C4×C29C22⋊C411yescharacteristic
126C4⋊C4×C29C22⋊C411yescharacteristic
127C22⋊C4×C29—21no—
128C22⋊C4×C29—21no—
129C22⋊C4×C29—21no—
130C22⋊C4×C29—21no—
131C22⋊C4×C29—41no—
132C22⋊C4×C29—41no—
133C22⋊C4×C29—81no—
134C42×C29—21no—
135C42×C29—21no—
136C42×C29—21no—
137C42×C29—21no—
138#9348C2911yesmaximal, characteristic, direct product factor, Sylow
139C23×C29—21no—
140C23×C29—21no—
141C23×C29—41no—
142C23×C29—41no—
143C23×C29—42no—
144C23×C29—41no—
145C23×C29—81no—
146C23×C29—81no—
147C23×C29C4×D411yescharacteristic
148C23×C29#12111yescharacteristic
149C23×C29#12311yescharacteristic
150D4×C29—41no—
151D4×C29—41no—
152D4×C29—81no—
153D4×C29—82no—
154D4×C29—81no—
155D4×C29—81no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—21no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—81no—
173C2×C4×C29—81no—
174C2×C4×C29—81no—
175C2×C4×C29—81no—
176C2×C4×C29—81no—
177C2×C4×C29C2×C22⋊C411yescharacteristic
178C2×C4×C29C4×D411yescharacteristic
179C2×C4×C29#12011yescharacteristic
180C2×C4×C29#12111yescharacteristic
181C8×C29—41no—
182C8×C29—41no—
183C8×C29—42no—
184C8×C29—41no—
185C8×C29—41no—
186C8×C29—81no—
187#3094C2×C2911yescharacteristic
188#2924C2×C2911yescharacteristic, complemented
189#1825C2×C2911yescharacteristic, complemented
190#1519C2×C2911yescharacteristic
191#1471C2×C2911yescharacteristic
192#1305C2×C2911yescharacteristic, complemented
193#1298C2×C2911yescharacteristic, complemented
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—21no—
197C22×C29—21no—
198C22×C29—21no—
199C22×C29—21no—
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—81no—
203C22×C29—81no—
204C22×C29—81no—
205C22×C29—81no—
206C22×C29—81no—
207C22×C29—162no—
208C22×C29#38611yescharacteristic
209C22×C29#47111yescharacteristic
210C22×C29#47211yescharacteristic
211C4×C29—21no—
212C4×C29—21no—
213C4×C29—21no—
214C4×C29—41no—
215C4×C29—41no—
216C4×C29—41no—
217C4×C29—41no—
218C4×C29—81no—
219C4×C29—161no—
220C4×C29#41011yescharacteristic
221C4×C29#41011yescharacteristic
222C2×#121C22×C2911yescharacteristic
223C2×#117C22×C2911yescharacteristic
224#482—21no—
225#482—21no—
226#481—21no—
227#480—21no—
228#433—22no—
229#432—21no—
230#431—21no—
231#428C4×C2911yescharacteristic, complemented
232#428C4×C2911yescharacteristic, complemented
233#424—21no—
234#418C4×C2911yescharacteristic, complemented
235#418C4×C2911yescharacteristic, complemented
236#407C22×C2911yescharacteristic
237#407C22×C2911yescharacteristic
238C2×C22⋊C8C22×C2911yescharacteristic
239C2×C22⋊C8C22×C2911yescharacteristic
240#405—21no—
241#380C22×C2911yescharacteristic
242#340—21no—
243#340—21no—
244#327—21no—
245#327—21no—
246#323—22no—
247C2×C29—21no—
248C2×C29—21no—
249C2×C29—41no—
250C2×C29—41no—
251C2×C29—161no—
252C2×C29#188111yescharacteristic
253C2×C29#189911yescharacteristic
254C2×C29#190711yescharacteristic
255C22×D4—21no—
256C22×D4C2×C4×C2911yescharacteristic
257C23×C4C23×C2911yescharacteristic
258C2×M16—21no—
259C2×M16C2×C4×C2911yescharacteristic
260C2×M16C2×C4×C2911yescharacteristic
261C22×C8—21no—
262C22×C8—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267#117—21no—
268#117—21no—
269#117C2×C4×C2911yescharacteristic
270#117C2×C4×C2911yescharacteristic
271#117D4×C2911yescharacteristic
272#117D4×C2911yescharacteristic
273C2×C4⋊C4—21no—
274C2×C4⋊C4C2×C4×C2911yescharacteristic
275C2×C4⋊C4D4×C2911yescharacteristic
276C2×C4⋊C4D4×C2911yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C42—21no—
281#107—21no—
282#107—21no—
283#106—21no—
284#106—21no—
285C4⋊C8—22no—
286C4⋊C8—22no—
287#102—21no—
288#102—21no—
289#102—21no—
290#102—21no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8D4×C2912yes—
298C22⋊C8D4×C2911yescharacteristic
299C22⋊C8D4×C2911yescharacteristic
300#97—22no—
301C4×C8—22no—
302#95—21no—
303C29#934811yescharacteristic, direct product factor, Sylow
304C24—21no—
305C24#41×C2911yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—81no—
313C2×D4—81no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C22×C4×C2911yescharacteristic
321C22×C4C2×D4×C2911yescharacteristic
322C22×C4C2×D4×C2911yescharacteristic
323C22×C4C2×D4×C2911yescharacteristic
324C22×C4C2×D4×C2911yescharacteristic
325C22×C4#41×C2911yescharacteristic
326M16—41no—
327M16—41no—
328M16—41no—
329M16—41no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4C22⋊C4×C2911yescharacteristic
347C4⋊C4C22⋊C4×C2911yescharacteristic
348C4⋊C4C22⋊C4×C2911yescharacteristic
349C4⋊C4C22⋊C4×C2911yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—81no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23C4×D4×C2911yescharacteristic
370C23C29×#12111yescharacteristic
371C23C29×#12311yescharacteristic
372D4—41no—
373D4—41no—
374D4—81no—
375D4—82no—
376D4—81no—
377D4—81no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C2×C22⋊C4×C2911yescharacteristic
400C2×C4C4×D4×C2911yescharacteristic
401C2×C4C29×#12011yescharacteristic
402C2×C4C29×#12111yescharacteristic
403C8—41no—
404C8—41no—
405C8—42no—
406C8—41no—
407C8—41no—
408C8—81no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—162no—
423C22C29×#38611yescharacteristic
424C22C29×#47111yescharacteristic
425C22C29×#47211yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—161no—
435C4C29×#41011yescharacteristic
436C4C29×#41011yescharacteristic
437C2—21no—
438C2—21no—
439C2—41no—
440C2—41no—
441C2—161no—
442C2C29×#188111yescharacteristic
443C2C29×#189911yescharacteristic
444C2C29×#190711yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#121C22
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
2. C29×#2924C2semidirect
3. C29×#1825C2semidirect
6. C29×#1305C2semidirect
7. C29×#1298C2semidirect
17. C29×#428C4semidirect
18. C29×#428C4semidirect
20. C29×#418C4semidirect
21. C29×#418C4semidirect
138. #9348C29direct (N × H)
188. #2924C2×C29semidirect
189. #1825C2×C29semidirect
192. #1305C2×C29semidirect
193. #1298C2×C29semidirect
231. #428C4×C29semidirect
232. #428C4×C29semidirect
234. #418C4×C29semidirect
235. #418C4×C29semidirect
303. C29#9348direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30942
C29×#29242
C29×#18252
C29×#15192
C29×#14712
C29×#13052
C29×#12982
#934829