Finite Group Databasebeta

← C29×#19477 #20314377

Subgroups — C29×#19477 #20314377

Order 7424.

598 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×#3226C211yesmaximal, characteristic
2C29×#3112C211yesmaximal, characteristic
3C2×C29×#477C211yesmaximal, characteristic, complemented
4C29×#2984C211yesmaximal, characteristic, complemented
5C29×#1698C212yesmaximal, complemented
6C29×#1696C212yesmaximal, complemented
7C29×#1678C212yesmaximal, complemented
8C29×#1676C212yesmaximal, complemented
9C29×#1573C211yesmaximal, characteristic, complemented
10C29×#1558C211yesmaximal, characteristic, complemented
11C29×#1551C211yesmaximal, characteristic
12C29×#532C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C29C2211yescharacteristic
15C29×#500C2212yes—
16C29×#486C2212yes—
17C29×#480—21no—
18C29×#480—21no—
19C29×#480—21no—
20C29×#477—21no—
21C29×#477—21no—
22C29×#477C2211yescharacteristic
23C29×#477C2212yes—
24C29×#477C2211yescharacteristic
25C29×#477C2212yes—
26C29×#474—22no—
27C29×#460C2211yescharacteristic
28C29×#460C2211yescharacteristic
29C29×#448—21no—
30C29×#446—22no—
31C29×#446C2212yes—
32C8×Q8×C29C2212yes—
33C29×#440—21no—
34C29×#440—21no—
35C29×#432—21no—
36C29×#432C2211yescharacteristic
37C29×#432C2211yescharacteristic
38C29×#431—21no—
39C29×#431C2211yescharacteristic
40C2×C29×#107—21no—
41C2×C29×C4⋊C8C2211yescharacteristic
42C2×C29×#103—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#333C2212yes—
47C29×#333C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C22×Q8×C29—21no—
51C22×Q8×C29D411yescharacteristic
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C22×C8×C29—21no—
55C29×C4⋊Q8—21no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8C2312yes—
59C29×C4⋊Q8C2311yescharacteristic
60C29×#127C2311yescharacteristic
61C29×#124—21no—
62C29×#121—21no—
63C29×#121—21no—
64C4×Q8×C29—21no—
65C4×Q8×C29—21no—
66C4×Q8×C29D411yescharacteristic
67C4×Q8×C29D411yescharacteristic
68C4×Q8×C29C2311yescharacteristic
69C4×Q8×C29C2311yescharacteristic
70C4×D4×C29—21no—
71C4×D4×C29—21no—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29D411yescharacteristic
76C2×C42×C29—21no—
77C2×C42×C29C2311yescharacteristic
78C29×#107—22no—
79C29×#107—22no—
80C29×#107—22no—
81C29×#107—22no—
82C29×#107—21no—
83C29×#107—21no—
84C29×C4⋊C8—22no—
85C29×C4⋊C8—22no—
86C29×C4⋊C8—21no—
87C29×C4⋊C8D412yes—
88C29×C4⋊C8C2312yes—
89C29×C4⋊C8C2311yescharacteristic
90C29×C4⋊C8C2311yescharacteristic
91C29×C4⋊C8C2312yes—
92C29×#103—21no—
93C29×#103—21no—
94C29×#103—22no—
95C29×#103—22no—
96C29×#102—22no—
97C29×#102—22no—
98C29×#102—21no—
99C29×#102—21no—
100C29×C22⋊C8—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8D411yescharacteristic
103C29×C22⋊C8D411yescharacteristic
104C29×#97—22no—
105C29×#97—21no—
106C29×#97—21no—
107C4×C8×C29—22no—
108C4×C8×C29C2312yes—
109#41×C29—82no—
110C2×Q8×C29—21no—
111C2×Q8×C29—22no—
112C2×Q8×C29—21no—
113C2×Q8×C29—22no—
114C2×Q8×C29—41no—
115C2×Q8×C29—41no—
116C2×Q8×C29—82no—
117C2×Q8×C29C2×D411yescharacteristic
118C2×Q8×C29C2×D411yescharacteristic
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—41no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—41no—
126C22×C4×C29—41no—
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29#4111yescharacteristic
130SD16×C29—42no—
131SD16×C29—42no—
132C2×C8×C29—22no—
133C2×C8×C29—21no—
134C2×C8×C29—21no—
135C2×C8×C29—22no—
136C2×C8×C29—42no—
137C2×C8×C29C2×D412yes—
138C2×C8×C29C2×D412yes—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—22no—
145C4⋊C4×C29—22no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29C2×D411yescharacteristic
151C4⋊C4×C29C2×D411yescharacteristic
152C22⋊C4×C29—41no—
153C22⋊C4×C29—41no—
154C42×C29—21no—
155C42×C29—21no—
156C42×C29—21no—
157C42×C29—21no—
158C42×C29C2×D411yescharacteristic
159C42×C29C2×D411yescharacteristic
160C42×C29#4111yescharacteristic
161C42×C29C2411yescharacteristic
162#19477C2911yesmaximal, characteristic, direct product factor, Sylow
163C23×C29—41no—
164C23×C29#12111yescharacteristic
165Q8×C29—21no—
166Q8×C29—21no—
167Q8×C29—21no—
168Q8×C29—42no—
169Q8×C29—82no—
170Q8×C29—81no—
171Q8×C29—82no—
172Q8×C29#13712yes—
173D4×C29—41no—
174D4×C29—41no—
175D4×C29—42no—
176D4×C29—81no—
177D4×C29—82no—
178C2×C4×C29—21no—
179C2×C4×C29—22no—
180C2×C4×C29—21no—
181C2×C4×C29—21no—
182C2×C4×C29—22no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—42no—
187C2×C4×C29—42no—
188C2×C4×C29—41no—
189C2×C4×C29—42no—
190C2×C4×C29—82no—
191C2×C4×C29—82no—
192C2×C4×C29#12111yescharacteristic
193C2×C4×C29#12111yescharacteristic
194C2×C4×C29#12111yescharacteristic
195C2×C4×C29C22×D411yescharacteristic
196C2×C4×C29C22×D411yescharacteristic
197C2×C4×C29C2×#4111yescharacteristic
198C8×C29—22no—
199C8×C29—22no—
200C8×C29—41no—
201C8×C29—42no—
202C8×C29—41no—
203C8×C29—42no—
204#3226C2×C2911yescharacteristic
205#3112C2×C2911yescharacteristic
206C2×#477C2×C2911yescharacteristic, complemented
207#2984C2×C2911yescharacteristic, complemented
208#1698C2×C2912yescomplemented
209#1696C2×C2912yescomplemented
210#1678C2×C2912yescomplemented
211#1676C2×C2912yescomplemented
212#1573C2×C2911yescharacteristic, complemented
213#1558C2×C2911yescharacteristic, complemented
214#1551C2×C2911yescharacteristic
215C22×C29—21no—
216C22×C29—21no—
217C22×C29—81no—
218C22×C29—81no—
219C22×C29—81no—
220C22×C29#47212yes—
221C22×C29C2×#12111yescharacteristic
222C4×C29—21no—
223C4×C29—21no—
224C4×C29—22no—
225C4×C29—21no—
226C4×C29—21no—
227C4×C29—41no—
228C4×C29—41no—
229C4×C29—41no—
230C4×C29—81no—
231C4×C29—82no—
232C4×C29C2×#13711yescharacteristic
233C4×C29#57511yescharacteristic
234C4×C29#57812yes—
235#532C22×C2911yescharacteristic
236C2×C4⋊Q8C22×C2911yescharacteristic
237C2×C4×Q8C22×C2911yescharacteristic
238#500C22×C2912yes—
239#486C22×C2912yes—
240#480—21no—
241#480—21no—
242#480—21no—
243#477—21no—
244#477—21no—
245#477C22×C2912yes—
246#477C22×C2912yes—
247#477C22×C2911yescharacteristic
248#477C22×C2911yescharacteristic
249#474—22no—
250#460C22×C2911yescharacteristic
251#460C22×C2911yescharacteristic
252#448—21no—
253#446—22no—
254#446C22×C2912yes—
255C8×Q8C22×C2912yes—
256#440—21no—
257#440—21no—
258#432—21no—
259#432C22×C2911yescharacteristic
260#432C22×C2911yescharacteristic
261#431—21no—
262#431C22×C2911yescharacteristic
263C2×#107—21no—
264C2×C4⋊C8C22×C2911yescharacteristic
265C2×#103—21no—
266#335C22×C2912yes—
267#334C22×C2912yes—
268#333C22×C2912yes—
269#333C22×C2912yes—
270#333C22×C2912yes—
271#331C22×C2912yes—
272C2×C29—22no—
273C2×C29—161no—
274C2×C29#304411yescharacteristic
275C2×C29#305611yescharacteristic
276C2×C29C2×#47211yescharacteristic
277C2×#41—21no—
278C22×Q8—21no—
279C22×Q8D4×C2911yescharacteristic
280C2×SD16—21no—
281C2×SD16—21no—
282C22×C8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8C23×C2912yes—
287C4⋊Q8C23×C2911yescharacteristic
288#127C23×C2911yescharacteristic
289#124—21no—
290#121—21no—
291#121—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8D4×C2911yescharacteristic
295C4×Q8D4×C2911yescharacteristic
296C4×Q8C23×C2911yescharacteristic
297C4×Q8C23×C2911yescharacteristic
298C4×D4—21no—
299C4×D4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4D4×C2911yescharacteristic
304C2×C42—21no—
305C2×C42C23×C2911yescharacteristic
306#107—22no—
307#107—22no—
308#107—22no—
309#107—22no—
310#107—21no—
311#107—21no—
312C4⋊C8—22no—
313C4⋊C8—22no—
314C4⋊C8—21no—
315C4⋊C8D4×C2912yes—
316C4⋊C8C23×C2912yes—
317C4⋊C8C23×C2912yes—
318C4⋊C8C23×C2911yescharacteristic
319C4⋊C8C23×C2911yescharacteristic
320#103—22no—
321#103—22no—
322#103—21no—
323#103—21no—
324#102—22no—
325#102—22no—
326#102—21no—
327#102—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8D4×C2911yescharacteristic
331C22⋊C8D4×C2911yescharacteristic
332#97—22no—
333#97—21no—
334#97—21no—
335C4×C8—22no—
336C4×C8C23×C2912yes—
337C29#1947711yescharacteristic, direct product factor, Sylow
338#41—82no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—82no—
346C2×Q8C2×D4×C2911yescharacteristic
347C2×Q8C2×D4×C2911yescharacteristic
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4C2×D4×C2911yescharacteristic
357C22×C4C2×D4×C2911yescharacteristic
358C22×C4#41×C2911yescharacteristic
359SD16—42no—
360SD16—42no—
361C2×C8—22no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—22no—
365C2×C8—42no—
366C2×C8C2×D4×C2912yes—
367C2×C8C2×D4×C2912yes—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C2×D4×C2911yescharacteristic
380C4⋊C4C2×D4×C2911yescharacteristic
381C22⋊C4—41no—
382C22⋊C4—41no—
383C42—21no—
384C42—21no—
385C42—21no—
386C42—21no—
387C42C2×D4×C2911yescharacteristic
388C42C2×D4×C2911yescharacteristic
389C42#41×C2911yescharacteristic
390C42C24×C2911yescharacteristic
391C23—41no—
392C23C29×#12111yescharacteristic
393Q8—21no—
394Q8—21no—
395Q8—21no—
396Q8—42no—
397Q8—82no—
398Q8—81no—
399Q8—82no—
400Q8C29×#13712yes—
401D4—41no—
402D4—41no—
403D4—42no—
404D4—81no—
405D4—82no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4C29×#12111yescharacteristic
421C2×C4C29×#12111yescharacteristic
422C2×C4C29×#12111yescharacteristic
423C2×C4C22×D4×C2911yescharacteristic
424C2×C4C22×D4×C2911yescharacteristic
425C2×C4C2×#41×C2911yescharacteristic
426C8—22no—
427C8—22no—
428C8—41no—
429C8—42no—
430C8—41no—
431C8—42no—
432C22—21no—
433C22—21no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22C29×#47212yes—
438C22C2×C29×#12111yescharacteristic
439C4—21no—
440C4—21no—
441C4—22no—
442C4—21no—
443C4—21no—
444C4—41no—
445C4—41no—
446C4—41no—
447C4—81no—
448C4—82no—
449C4C2×C29×#13711yescharacteristic
450C4C29×#57511yescharacteristic
451C4C29×#57812yes—
452C2—22no—
453C2—161no—
454C2C29×#304411yescharacteristic
455C2C29×#305611yescharacteristic
456C2C2×C29×#47211yescharacteristic
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
3. C2×C29×#477C2semidirect
4. C29×#2984C2semidirect
5. C29×#1698C2semidirect
6. C29×#1696C2semidirect
7. C29×#1678C2semidirect
8. C29×#1676C2semidirect
9. C29×#1573C2semidirect
10. C29×#1558C2semidirect
162. #19477C29direct (N × H)
206. C2×#477C2×C29semidirect
207. #2984C2×C29semidirect
208. #1698C2×C29semidirect
209. #1696C2×C29semidirect
210. #1678C2×C29semidirect
211. #1676C2×C29semidirect
212. #1573C2×C29semidirect
213. #1558C2×C29semidirect
337. C29#19477direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32262
C29×#31122
C2×C29×#4772
C29×#29842
C29×#16982
C29×#16962
C29×#16782
C29×#16762
C29×#15732
C29×#15582
C29×#15512
#1947729