Finite Group Databasebeta

← C29×#19288 #20314188

Subgroups — C29×#19288 #20314188

Order 7424.

608 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3167C211yesmaximal, characteristic
2C29×#3113C211yesmaximal, characteristic, complemented
3C29×#3112C211yesmaximal, characteristic
4C2×C29×#446C211yesmaximal, characteristic, complemented
5C29×#1704C212yesmaximal, complemented
6C29×#1702C212yesmaximal, complemented
7C29×#1692C212yesmaximal, complemented
8C29×#1686C212yesmaximal, complemented
9C29×#1568C211yesmaximal, characteristic, complemented
10C29×#1552C211yesmaximal, characteristic, complemented
11C29×#1551C211yesmaximal, characteristic
12C29×#533C2211yescharacteristic
13C29×#532C2211yescharacteristic
14C2×C4×Q8×C29C2211yescharacteristic
15C29×#498C2211yescharacteristic
16C29×#492C2211yescharacteristic
17C29×#487C2211yescharacteristic
18C29×#486C2211yescharacteristic
19C29×#483—21no—
20C29×#480—21no—
21C29×#477C2212yes—
22C29×#475C2212yes—
23C29×#465—21no—
24C29×#465—21no—
25C29×#462C2212yes—
26C29×#460C2212yes—
27C29×#451—21no—
28C29×#448—21no—
29C29×#446—21no—
30C29×#446—21no—
31C29×#446C2212yes—
32C29×#446C2212yes—
33C29×#441—22no—
34C29×#440—22no—
35C4×SD16×C29—21no—
36C4×SD16×C29—21no—
37C29×#432C2211yescharacteristic
38C29×#432C2211yescharacteristic
39C2×C29×C4⋊C8—21no—
40C2×C29×C4⋊C8C2211yescharacteristic
41C2×C29×#97—21no—
42C2×C4×C8×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C22×Q8×C29D411yescharacteristic
51C2×Q16×C29—22no—
52C2×SD16×C29—22no—
53C2×SD16×C29—21no—
54C2×SD16×C29—21no—
55C22×C8×C29—21no—
56C22×C8×C29D411yescharacteristic
57C22×C8×C29D411yescharacteristic
58C29×C4⋊Q8C2311yescharacteristic
59C29×C4⋊Q8C2311yescharacteristic
60C29×C4⋊Q8C2311yescharacteristic
61C29×#127C2311yescharacteristic
62C29×#125—21no—
63C29×#124—21no—
64C29×C22⋊Q8—21no—
65C29×C22⋊Q8—21no—
66C29×#121—21no—
67C29×#121—21no—
68C4×Q8×C29—21no—
69C4×Q8×C29—21no—
70C4×Q8×C29—21no—
71C4×Q8×C29—21no—
72C4×Q8×C29D412yes—
73C4×Q8×C29C2312yes—
74C4×D4×C29—21no—
75C4×D4×C29—21no—
76C29×#117—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29D411yescharacteristic
79C2×C42×C29—21no—
80C2×C42×C29C2311yescharacteristic
81C29×#107—22no—
82C29×#106—21no—
83C29×#106—21no—
84C29×#106—22no—
85C29×C4⋊C8—22no—
86C29×C4⋊C8—22no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8C2312yes—
89C29×C4⋊C8C2312yes—
90C29×C4⋊C8C2312yes—
91C29×#103—22no—
92C29×#103—22no—
93C29×#103—21no—
94C29×#103—21no—
95C29×#103—22no—
96C29×#102—21no—
97C29×#102—21no—
98C29×#102—22no—
99C29×C22⋊C8—21no—
100C29×C22⋊C8—21no—
101C29×#97—22no—
102C29×#97—22no—
103C29×#97—21no—
104C29×#97—21no—
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×C29—42no—
115C2×Q8×C29C2×D412yes—
116C2×D4×C29—21no—
117C2×D4×C29—21no—
118C2×D4×C29—21no—
119C2×D4×C29—41no—
120C22×C4×C29—21no—
121C22×C4×C29—21no—
122C22×C4×C29—41no—
123C22×C4×C29C2×D411yescharacteristic
124C22×C4×C29C2×D411yescharacteristic
125C22×C4×C29#4111yescharacteristic
126Q16×C29—44no—
127SD16×C29—42no—
128SD16×C29—44no—
129SD16×C29—42no—
130C2×C8×C29—22no—
131C2×C8×C29—22no—
132C2×C8×C29—22no—
133C2×C8×C29—22no—
134C2×C8×C29—41no—
135C2×C8×C29—42no—
136C2×C8×C29C2×D411yescharacteristic
137C2×C8×C29C2×D411yescharacteristic
138C2×C8×C29C2×D411yescharacteristic
139C2×C8×C29C2×D411yescharacteristic
140C4⋊C4×C29—22no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—22no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29C2×D412yes—
152C22⋊C4×C29—41no—
153C22⋊C4×C29—41no—
154C22⋊C4×C29—41no—
155C42×C29—22no—
156C42×C29—22no—
157C42×C29—41no—
158C42×C29C2×D411yescharacteristic
159C42×C29C2×D411yescharacteristic
160C42×C29#4111yescharacteristic
161C42×C29C2411yescharacteristic
162#19288C2911yesmaximal, characteristic, direct product factor, Sylow
163C23×C29—41no—
164C23×C29#12111yescharacteristic
165Q8×C29—22no—
166Q8×C29—22no—
167Q8×C29—42no—
168Q8×C29—41no—
169Q8×C29—41no—
170Q8×C29—42no—
171Q8×C29—81no—
172D4×C29—41no—
173D4×C29—41no—
174D4×C29—42no—
175D4×C29—81no—
176D4×C29—82no—
177C2×C4×C29—22no—
178C2×C4×C29—21no—
179C2×C4×C29—21no—
180C2×C4×C29—22no—
181C2×C4×C29—22no—
182C2×C4×C29—22no—
183C2×C4×C29—42no—
184C2×C4×C29—42no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—41no—
188C2×C4×C29—82no—
189C2×C4×C29#12111yescharacteristic
190C2×C4×C29#12111yescharacteristic
191C2×C4×C29#12111yescharacteristic
192C2×C4×C29C22×D411yescharacteristic
193C2×C4×C29C22×D411yescharacteristic
194C2×C4×C29C2×#4111yescharacteristic
195C8×C29—21no—
196C8×C29—21no—
197C8×C29—21no—
198C8×C29—42no—
199C8×C29—42no—
200C8×C29—42no—
201C8×C29#13712yes—
202#3167C2×C2911yescharacteristic
203#3113C2×C2911yescharacteristic, complemented
204#3112C2×C2911yescharacteristic
205C2×#446C2×C2911yescharacteristic, complemented
206#1704C2×C2912yescomplemented
207#1702C2×C2912yescomplemented
208#1692C2×C2912yescomplemented
209#1686C2×C2912yescomplemented
210#1568C2×C2911yescharacteristic, complemented
211#1552C2×C2911yescharacteristic, complemented
212#1551C2×C2911yescharacteristic
213C22×C29—21no—
214C22×C29—21no—
215C22×C29—81no—
216C22×C29—81no—
217C22×C29—81no—
218C22×C29#47112yes—
219C22×C29C2×#12111yescharacteristic
220C4×C29—21no—
221C4×C29—21no—
222C4×C29—21no—
223C4×C29—21no—
224C4×C29—42no—
225C4×C29—42no—
226C4×C29—81no—
227C4×C29—81no—
228C4×C29—81no—
229C4×C29C2×#13711yescharacteristic
230C4×C29#57511yescharacteristic
231C4×C29#57512yes—
232#533C22×C2911yescharacteristic
233#532C22×C2911yescharacteristic
234C2×C4×Q8C22×C2911yescharacteristic
235#498C22×C2911yescharacteristic
236#492C22×C2911yescharacteristic
237#487C22×C2911yescharacteristic
238#486C22×C2911yescharacteristic
239#483—21no—
240#480—21no—
241#477C22×C2912yes—
242#475C22×C2912yes—
243#465—21no—
244#465—21no—
245#462C22×C2912yes—
246#460C22×C2912yes—
247#451—21no—
248#448—21no—
249#446—21no—
250#446—21no—
251#446C22×C2912yes—
252#446C22×C2912yes—
253#441—22no—
254#440—22no—
255C4×SD16—21no—
256C4×SD16—21no—
257#432C22×C2911yescharacteristic
258#432C22×C2911yescharacteristic
259C2×C4⋊C8—21no—
260C2×C4⋊C8C22×C2911yescharacteristic
261C2×#97—21no—
262C2×C4×C8C22×C2911yescharacteristic
263#335C22×C2912yes—
264#334C22×C2912yes—
265#333C22×C2912yes—
266#332C22×C2912yes—
267#332C22×C2912yes—
268#331C22×C2912yes—
269C2×C29—22no—
270C2×C29—161no—
271C2×C29#303711yescharacteristic
272C2×C29#305411yescharacteristic
273C2×C29C2×#47111yescharacteristic
274C2×#41—21no—
275C22×Q8D4×C2911yescharacteristic
276C2×Q16—22no—
277C2×SD16—22no—
278C2×SD16—21no—
279C2×SD16—21no—
280C22×C8—21no—
281C22×C8D4×C2911yescharacteristic
282C22×C8D4×C2911yescharacteristic
283C4⋊Q8C23×C2911yescharacteristic
284C4⋊Q8C23×C2911yescharacteristic
285C4⋊Q8C23×C2911yescharacteristic
286#127C23×C2911yescharacteristic
287#125—21no—
288#124—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291#121—21no—
292#121—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8D4×C2912yes—
298C4×Q8C23×C2912yes—
299C4×D4—21no—
300C4×D4—21no—
301#117—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4D4×C2911yescharacteristic
304C2×C42—21no—
305C2×C42C23×C2911yescharacteristic
306#107—22no—
307#106—21no—
308#106—21no—
309#106—22no—
310C4⋊C8—22no—
311C4⋊C8—22no—
312C4⋊C8—21no—
313C4⋊C8C23×C2912yes—
314C4⋊C8C23×C2912yes—
315C4⋊C8C23×C2912yes—
316#103—22no—
317#103—22no—
318#103—21no—
319#103—21no—
320#103—22no—
321#102—21no—
322#102—21no—
323#102—22no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326#97—22no—
327#97—22no—
328#97—21no—
329#97—21no—
330C4×C8D4×C2911yescharacteristic
331C4×C8D4×C2911yescharacteristic
332C4×C8C23×C2911yescharacteristic
333C4×C8C23×C2911yescharacteristic
334C29#1928811yescharacteristic, direct product factor, Sylow
335#41—82no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C2×Q8C2×D4×C2912yes—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4C2×D4×C2911yescharacteristic
350C22×C4C2×D4×C2911yescharacteristic
351C22×C4#41×C2911yescharacteristic
352Q16—44no—
353SD16—42no—
354SD16—44no—
355SD16—42no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—41no—
361C2×C8—42no—
362C2×C8C2×D4×C2911yescharacteristic
363C2×C8C2×D4×C2911yescharacteristic
364C2×C8C2×D4×C2911yescharacteristic
365C2×C8C2×D4×C2911yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4C2×D4×C2912yes—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C42—22no—
382C42—22no—
383C42—41no—
384C42C2×D4×C2911yescharacteristic
385C42C2×D4×C2911yescharacteristic
386C42#41×C2911yescharacteristic
387C42C24×C2911yescharacteristic
388C23—41no—
389C23C29×#12111yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—42no—
393Q8—41no—
394Q8—41no—
395Q8—42no—
396Q8—81no—
397D4—41no—
398D4—41no—
399D4—42no—
400D4—81no—
401D4—82no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4C29×#12111yescharacteristic
415C2×C4C29×#12111yescharacteristic
416C2×C4C29×#12111yescharacteristic
417C2×C4C22×D4×C2911yescharacteristic
418C2×C4C22×D4×C2911yescharacteristic
419C2×C4C2×#41×C2911yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8—42no—
424C8—42no—
425C8—42no—
426C8C29×#13712yes—
427C22—21no—
428C22—21no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22C29×#47112yes—
433C22C2×C29×#12111yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—42no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4C2×C29×#13711yescharacteristic
444C4C29×#57511yescharacteristic
445C4C29×#57512yes—
446C2—22no—
447C2—161no—
448C2C29×#303711yescharacteristic
449C2C29×#305411yescharacteristic
450C2C2×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
2. C29×#3113C2semidirect
4. C2×C29×#446C2semidirect
5. C29×#1704C2semidirect
6. C29×#1702C2semidirect
7. C29×#1692C2semidirect
8. C29×#1686C2semidirect
9. C29×#1568C2semidirect
10. C29×#1552C2semidirect
162. #19288C29direct (N × H)
203. #3113C2×C29semidirect
205. C2×#446C2×C29semidirect
206. #1704C2×C29semidirect
207. #1702C2×C29semidirect
208. #1692C2×C29semidirect
209. #1686C2×C29semidirect
210. #1568C2×C29semidirect
211. #1552C2×C29semidirect
334. C29#19288direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31672
C29×#31132
C29×#31122
C2×C29×#4462
C29×#17042
C29×#17022
C29×#16922
C29×#16862
C29×#15682
C29×#15522
C29×#15512
#1928829