Finite Group Databasebeta

← C29×#19351 #20314251

Subgroups — C29×#19351 #20314251

Order 7424.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3255C211yesmaximal, characteristic, complemented
2C29×#3254C211yesmaximal, characteristic
3C29×#3167C211yesmaximal, characteristic
4C29×#2960C211yesmaximal, characteristic, complemented
5C29×#1692C212yesmaximal, complemented
6C29×#1686C212yesmaximal, complemented
7C29×#1684C212yesmaximal, complemented
8C29×#1682C212yesmaximal, complemented
9C29×#1567C211yesmaximal, characteristic, complemented
10C29×#1561C211yesmaximal, characteristic, complemented
11C29×#1560C211yesmaximal, characteristic
12C29×#533C2211yescharacteristic
13C29×#533C2211yescharacteristic
14C29×#532C2211yescharacteristic
15C29×#498C2211yescharacteristic
16C29×#492C2211yescharacteristic
17C29×#487C2211yescharacteristic
18C29×#486C2211yescharacteristic
19C29×#477C2212yes—
20C29×#475—21no—
21C29×#475C2212yes—
22C29×#474—21no—
23C29×#470—22no—
24C29×#468—22no—
25C29×#465—21no—
26C29×#465—21no—
27C29×#462—21no—
28C29×#462C2212yes—
29C29×#461—21no—
30C29×#460C2212yes—
31C29×#446—21no—
32C29×#446C2212yes—
33C8×Q8×C29—21no—
34C8×Q8×C29C2212yes—
35C4×SD16×C29—21no—
36C4×SD16×C29—21no—
37C29×#424—21no—
38C29×#423C2211yescharacteristic
39C29×#423C2211yescharacteristic
40C29×#423C2211yescharacteristic
41C29×#405—21no—
42C2×C4×C8×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#335C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×Q16×C29—22no—
51C2×SD16×C29—22no—
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C2×M16×C29—21no—
55C2×M16×C29—21no—
56C2×M16×C29—21no—
57C22×C8×C29D411yescharacteristic
58C22×C8×C29D411yescharacteristic
59C29×C4⋊Q8D411yescharacteristic
60C29×C4⋊Q8D411yescharacteristic
61C29×C4⋊Q8C2311yescharacteristic
62C29×C4⋊Q8C2311yescharacteristic
63C29×C4⋊Q8C2311yescharacteristic
64C29×#127C2311yescharacteristic
65C29×#125—21no—
66C29×#125—21no—
67C29×#124—21no—
68C29×C22⋊Q8—21no—
69C29×C22⋊Q8—21no—
70C29×C22⋊Q8—21no—
71C29×C22⋊Q8D412yes—
72C29×#121—21no—
73C29×#121—21no—
74C4×Q8×C29—21no—
75C4×Q8×C29—21no—
76C4×Q8×C29—21no—
77C4×Q8×C29C2312yes—
78C4×D4×C29—21no—
79C4×D4×C29—21no—
80C29×#117—21no—
81C29×#117—21no—
82C2×C42×C29C2311yescharacteristic
83C29×#107—22no—
84C29×#106—21no—
85C29×#106—21no—
86C29×#106—22no—
87C29×C4⋊C8—22no—
88C29×C4⋊C8—22no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8—21no—
92C29×C4⋊C8C2312yes—
93C29×C4⋊C8C2312yes—
94C29×C4⋊C8C2312yes—
95C29×#103—22no—
96C29×#103—22no—
97C29×#103—21no—
98C29×#103—21no—
99C29×#103—22no—
100C29×#102—21no—
101C29×#102—21no—
102C29×#102—22no—
103C29×#97—22no—
104C4×C8×C29—22no—
105C4×C8×C29D411yescharacteristic
106C4×C8×C29D411yescharacteristic
107C4×C8×C29C2311yescharacteristic
108C4×C8×C29C2311yescharacteristic
109#41×C29—82no—
110C2×Q8×C29—21no—
111C2×Q8×C29—21no—
112C2×Q8×C29—21no—
113C2×Q8×C29—21no—
114C2×Q8×C29C2×D412yes—
115C2×D4×C29—21no—
116C2×D4×C29—21no—
117C2×D4×C29—21no—
118C2×D4×C29—41no—
119C22×C4×C29—41no—
120C22×C4×C29C2×D411yescharacteristic
121C22×C4×C29C2×D411yescharacteristic
122C22×C4×C29#4111yescharacteristic
123Q16×C29—82no—
124SD16×C29—42no—
125SD16×C29—42no—
126SD16×C29—82no—
127M16×C29—42no—
128M16×C29—81no—
129M16×C29—81no—
130C2×C8×C29—22no—
131C2×C8×C29—22no—
132C2×C8×C29—22no—
133C2×C8×C29—22no—
134C2×C8×C29—41no—
135C2×C8×C29C2×D411yescharacteristic
136C2×C8×C29C2×D411yescharacteristic
137C2×C8×C29C2×D411yescharacteristic
138C2×C8×C29C2×D411yescharacteristic
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—22no—
143C4⋊C4×C29—22no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29C2×D412yes—
153C22⋊C4×C29—22no—
154C22⋊C4×C29—41no—
155C22⋊C4×C29—41no—
156C22⋊C4×C29—41no—
157C42×C29—22no—
158C42×C29—41no—
159C42×C29C2×D411yescharacteristic
160C42×C29C2×D411yescharacteristic
161C42×C29#4111yescharacteristic
162C42×C29C2411yescharacteristic
163#19351C2911yesmaximal, characteristic, direct product factor, Sylow
164C23×C29—41no—
165C23×C29#12111yescharacteristic
166Q8×C29—22no—
167Q8×C29—22no—
168Q8×C29—42no—
169Q8×C29—41no—
170Q8×C29—41no—
171Q8×C29—41no—
172Q8×C29—41no—
173Q8×C29—81no—
174D4×C29—41no—
175D4×C29—41no—
176D4×C29—41no—
177D4×C29—41no—
178D4×C29—81no—
179D4×C29—82no—
180C2×C4×C29—21no—
181C2×C4×C29—21no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—22no—
185C2×C4×C29—22no—
186C2×C4×C29—22no—
187C2×C4×C29—41no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—82no—
191C2×C4×C29#12111yescharacteristic
192C2×C4×C29#12111yescharacteristic
193C2×C4×C29#12111yescharacteristic
194C2×C4×C29C22×D411yescharacteristic
195C2×C4×C29C22×D411yescharacteristic
196C2×C4×C29C2×#4111yescharacteristic
197C8×C29—21no—
198C8×C29—21no—
199C8×C29—21no—
200C8×C29—42no—
201C8×C29—42no—
202C8×C29—42no—
203C8×C29#13712yes—
204#3255C2×C2911yescharacteristic, complemented
205#3254C2×C2911yescharacteristic
206#3167C2×C2911yescharacteristic
207#2960C2×C2911yescharacteristic, complemented
208#1692C2×C2912yescomplemented
209#1686C2×C2912yescomplemented
210#1684C2×C2912yescomplemented
211#1682C2×C2912yescomplemented
212#1567C2×C2911yescharacteristic, complemented
213#1561C2×C2911yescharacteristic, complemented
214#1560C2×C2911yescharacteristic
215C22×C29—21no—
216C22×C29—21no—
217C22×C29—21no—
218C22×C29—81no—
219C22×C29—81no—
220C22×C29—81no—
221C22×C29C2×#12111yescharacteristic
222C4×C29—21no—
223C4×C29—21no—
224C4×C29—21no—
225C4×C29—42no—
226C4×C29—42no—
227C4×C29—81no—
228C4×C29—81no—
229C4×C29—81no—
230C4×C29#47112yes—
231C4×C29C2×#13711yescharacteristic
232C4×C29#57511yescharacteristic
233C4×C29#57611yescharacteristic
234C4×C29#57811yescharacteristic
235#533C22×C2911yescharacteristic
236#533C22×C2911yescharacteristic
237#532C22×C2911yescharacteristic
238#498C22×C2911yescharacteristic
239#492C22×C2911yescharacteristic
240#487C22×C2911yescharacteristic
241#486C22×C2911yescharacteristic
242#477C22×C2912yes—
243#475—21no—
244#475C22×C2912yes—
245#474—21no—
246#470—22no—
247#468—22no—
248#465—21no—
249#465—21no—
250#462—21no—
251#462C22×C2912yes—
252#461—21no—
253#460C22×C2912yes—
254#446—21no—
255#446C22×C2912yes—
256C8×Q8—21no—
257C8×Q8C22×C2912yes—
258C4×SD16—21no—
259C4×SD16—21no—
260#424—21no—
261#423C22×C2911yescharacteristic
262#423C22×C2911yescharacteristic
263#423C22×C2911yescharacteristic
264#405—21no—
265C2×C4×C8C22×C2911yescharacteristic
266#335C22×C2912yes—
267#335C22×C2912yes—
268#333C22×C2912yes—
269#332C22×C2912yes—
270#332C22×C2912yes—
271#331C22×C2912yes—
272C2×C29—41no—
273C2×C29—161no—
274C2×C29#303711yescharacteristic
275C2×C29#306111yescharacteristic
276C2×C29C2×#47111yescharacteristic
277C2×#41—21no—
278C2×Q16—22no—
279C2×SD16—22no—
280C2×SD16—21no—
281C2×SD16—21no—
282C2×M16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C22×C8D4×C2911yescharacteristic
286C22×C8D4×C2911yescharacteristic
287C4⋊Q8D4×C2911yescharacteristic
288C4⋊Q8D4×C2911yescharacteristic
289C4⋊Q8C23×C2911yescharacteristic
290C4⋊Q8C23×C2911yescharacteristic
291C4⋊Q8C23×C2911yescharacteristic
292#127C23×C2911yescharacteristic
293#125—21no—
294#125—21no—
295#124—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8D4×C2912yes—
300#121—21no—
301#121—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8C23×C2912yes—
306C4×D4—21no—
307C4×D4—21no—
308#117—21no—
309#117—21no—
310C2×C42C23×C2911yescharacteristic
311#107—22no—
312#106—21no—
313#106—21no—
314#106—22no—
315C4⋊C8—22no—
316C4⋊C8—22no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8C23×C2912yes—
321C4⋊C8C23×C2912yes—
322C4⋊C8C23×C2912yes—
323#103—22no—
324#103—22no—
325#103—21no—
326#103—21no—
327#103—22no—
328#102—21no—
329#102—21no—
330#102—22no—
331#97—22no—
332C4×C8—22no—
333C4×C8D4×C2911yescharacteristic
334C4×C8D4×C2911yescharacteristic
335C4×C8C23×C2911yescharacteristic
336C4×C8C23×C2911yescharacteristic
337C29#1935111yescharacteristic, direct product factor, Sylow
338#41—82no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C2×D4×C2912yes—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C22×C4—41no—
349C22×C4C2×D4×C2911yescharacteristic
350C22×C4C2×D4×C2911yescharacteristic
351C22×C4#41×C2911yescharacteristic
352Q16—82no—
353SD16—42no—
354SD16—42no—
355SD16—82no—
356M16—42no—
357M16—81no—
358M16—81no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8C2×D4×C2911yescharacteristic
365C2×C8C2×D4×C2911yescharacteristic
366C2×C8C2×D4×C2911yescharacteristic
367C2×C8C2×D4×C2911yescharacteristic
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4C2×D4×C2912yes—
382C22⋊C4—22no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C42—22no—
387C42—41no—
388C42C2×D4×C2911yescharacteristic
389C42C2×D4×C2911yescharacteristic
390C42#41×C2911yescharacteristic
391C42C24×C2911yescharacteristic
392C23—41no—
393C23C29×#12111yescharacteristic
394Q8—22no—
395Q8—22no—
396Q8—42no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—81no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—81no—
407D4—82no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4C29×#12111yescharacteristic
420C2×C4C29×#12111yescharacteristic
421C2×C4C29×#12111yescharacteristic
422C2×C4C22×D4×C2911yescharacteristic
423C2×C4C22×D4×C2911yescharacteristic
424C2×C4C2×#41×C2911yescharacteristic
425C8—21no—
426C8—21no—
427C8—21no—
428C8—42no—
429C8—42no—
430C8—42no—
431C8C29×#13712yes—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22C2×C29×#12111yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4C29×#47112yes—
448C4C2×C29×#13711yescharacteristic
449C4C29×#57511yescharacteristic
450C4C29×#57611yescharacteristic
451C4C29×#57811yescharacteristic
452C2—41no—
453C2—161no—
454C2C29×#303711yescharacteristic
455C2C29×#306111yescharacteristic
456C2C2×C29×#47111yescharacteristic
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
1. C29×#3255C2semidirect
4. C29×#2960C2semidirect
5. C29×#1692C2semidirect
6. C29×#1686C2semidirect
7. C29×#1684C2semidirect
8. C29×#1682C2semidirect
9. C29×#1567C2semidirect
10. C29×#1561C2semidirect
163. #19351C29direct (N × H)
204. #3255C2×C29semidirect
207. #2960C2×C29semidirect
208. #1692C2×C29semidirect
209. #1686C2×C29semidirect
210. #1684C2×C29semidirect
211. #1682C2×C29semidirect
212. #1567C2×C29semidirect
213. #1561C2×C29semidirect
337. C29#19351direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32552
C29×#32542
C29×#31672
C29×#29602
C29×#16922
C29×#16862
C29×#16842
C29×#16822
C29×#15672
C29×#15612
C29×#15602
#1935129