Finite Group Databasebeta

← C29×#10033 #20304933

Subgroups — C29×#10033 #20304933

Order 7424.

550 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3135C211yesmaximal, characteristic, complemented
2C29×#3101C211yesmaximal, characteristic, complemented
3C29×#3100C211yesmaximal, characteristic
4C29×#1955C211yesmaximal, characteristic, complemented
5C29×#1481C211yesmaximal, characteristic, complemented
6C29×#1480C211yesmaximal, characteristic, complemented
7C29×#1275C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C29×#532C2211yescharacteristic
10C2×C4×D4×C29C2211yescharacteristic
11C29×#491—21no—
12C29×#490—21no—
13C29×#489—21no—
14C29×#489—21no—
15C29×#483—21no—
16C29×#480—21no—
17C29×#476—21no—
18C29×#474—21no—
19C29×#461—21no—
20C29×#459—21no—
21C29×#450—21no—
22C29×#447—21no—
23C4×SD16×C29—22no—
24C4×D8×C29—22no—
25C29×#431C2211yescharacteristic
26C29×#431C2211yescharacteristic
27C2×C29×C4⋊C8C2211yescharacteristic
28C29×#416—22no—
29C2×C29×C22⋊C8—22no—
30C2×C29×#97C2211yescharacteristic
31C29×Q8⋊C8—22no—
32C29×D4⋊C8—22no—
33C2×#41×C29—21no—
34C22×D4×C29D411yescharacteristic
35C23×C4×C29—21no—
36C2×SD16×C29—22no—
37C2×D8×C29—22no—
38C22×C8×C29—21no—
39C22×C8×C29D412yes—
40C29×C4⋊Q8D411yescharacteristic
41C29×C4⋊Q8D411yescharacteristic
42C29×C4⋊Q8D411yescharacteristic
43C29×#127D411yescharacteristic
44C29×#125—21no—
45C29×#124—21no—
46C29×C22⋊Q8—21no—
47C29×C22⋊Q8—21no—
48C29×#121—21no—
49C29×#121—21no—
50C4×Q8×C29—21no—
51C4×Q8×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29—21no—
54C4×D4×C29—21no—
55C4×D4×C29—21no—
56C4×D4×C29—21no—
57C4×D4×C29—21no—
58C29×#117—21no—
59C2×C4⋊C4×C29D411yescharacteristic
60C2×C22⋊C4×C29—21no—
61C2×C42×C29C2311yescharacteristic
62C29×#107—22no—
63C29×#106—22no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×#103—22no—
69C29×#103—22no—
70C29×#103—22no—
71C29×#102—22no—
72C29×#102—22no—
73C29×#102—22no—
74C29×#102—22no—
75C29×#102—22no—
76C29×C22⋊C8—21no—
77C29×C22⋊C8—21no—
78C29×C22⋊C8—44no—
79C29×#97—21no—
80C29×#97—21no—
81C4×C8×C29D412yes—
82C4×C8×C29D412yes—
83C24×C29—21no—
84#41×C29—42no—
85#41×C29—42no—
86C2×Q8×C29—21no—
87C2×Q8×C29—21no—
88C2×Q8×C29—21no—
89C2×D4×C29—21no—
90C2×D4×C29—21no—
91C2×D4×C29—21no—
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29—42no—
95C2×D4×C29—41no—
96C22×C4×C29—21no—
97C22×C4×C29—41no—
98C22×C4×C29—41no—
99C22×C4×C29—41no—
100C22×C4×C29—42no—
101C22×C4×C29—42no—
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29C2×D411yescharacteristic
104C22×C4×C29#4111yescharacteristic
105SD16×C29—44no—
106D8×C29—44no—
107C2×C8×C29—22no—
108C2×C8×C29—22no—
109C2×C8×C29—22no—
110C2×C8×C29—22no—
111C2×C8×C29—22no—
112C2×C8×C29—41no—
113C2×C8×C29—42no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—21no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—41no—
123C4⋊C4×C29—41no—
124C22⋊C4×C29—41no—
125C22⋊C4×C29—41no—
126C22⋊C4×C29—41no—
127C22⋊C4×C29—41no—
128C22⋊C4×C29—41no—
129C42×C29—41no—
130C42×C29C2×D411yescharacteristic
131C42×C29C2×D411yescharacteristic
132C42×C29C2×D411yescharacteristic
133C42×C29C2×D411yescharacteristic
134#10033C2911yesmaximal, characteristic, direct product factor, Sylow
135C23×C29—22no—
136C23×C29—41no—
137C23×C29—42no—
138C23×C29—41no—
139C23×C29—42no—
140C23×C29—41no—
141C23×C29#12111yescharacteristic
142Q8×C29—42no—
143Q8×C29—42no—
144Q8×C29—42no—
145D4×C29—22no—
146D4×C29—22no—
147D4×C29—41no—
148D4×C29—41no—
149D4×C29—42no—
150D4×C29—42no—
151D4×C29—42no—
152D4×C29—82no—
153C2×C4×C29—41no—
154C2×C4×C29—41no—
155C2×C4×C29—41no—
156C2×C4×C29—41no—
157C2×C4×C29—41no—
158C2×C4×C29—41no—
159C2×C4×C29—42no—
160C2×C4×C29—82no—
161C2×C4×C29—81no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29—81no—
165C2×C4×C29#12011yescharacteristic
166C2×C4×C29#12011yescharacteristic
167C2×C4×C29#12011yescharacteristic
168C2×C4×C29#12111yescharacteristic
169C2×C4×C29#12111yescharacteristic
170C2×C4×C29#12711yescharacteristic
171C2×C4×C29#13512yes—
172C2×C4×C29AGL(1,ℤ/8)12yes—
173C8×C29—42no—
174C8×C29—42no—
175C8×C29—42no—
176C8×C29—81no—
177#3135C2×C2911yescharacteristic, complemented
178#3101C2×C2911yescharacteristic, complemented
179#3100C2×C2911yescharacteristic
180#1955C2×C2911yescharacteristic, complemented
181#1481C2×C2911yescharacteristic, complemented
182#1480C2×C2911yescharacteristic, complemented
183#1275C2×C2911yescharacteristic, complemented
184C22×C29—21no—
185C22×C29—21no—
186C22×C29—44no—
187C22×C29—42no—
188C22×C29—82no—
189C22×C29—81no—
190C22×C29—81no—
191C22×C29—81no—
192C22×C29—81no—
193C22×C29—81no—
194C22×C29#39211yescharacteristic
195C22×C29#46312yes—
196C4×C29—21no—
197C4×C29—21no—
198C4×C29—21no—
199C4×C29—21no—
200C4×C29—81no—
201C4×C29—81no—
202C4×C29—81no—
203C4×C29—81no—
204C4×C29#44912yes—
205C4×C29#49511yescharacteristic
206C4×C29#49611yescharacteristic
207#533C22×C2911yescharacteristic
208#532C22×C2911yescharacteristic
209C2×C4×D4C22×C2911yescharacteristic
210#491—21no—
211#490—21no—
212#489—21no—
213#489—21no—
214#483—21no—
215#480—21no—
216#476—21no—
217#474—21no—
218#461—21no—
219#459—21no—
220#450—21no—
221#447—21no—
222C4×SD16—22no—
223C4×D8—22no—
224#431C22×C2911yescharacteristic
225#431C22×C2911yescharacteristic
226C2×C4⋊C8C22×C2911yescharacteristic
227#416—22no—
228C2×C22⋊C8—22no—
229C2×#97C22×C2911yescharacteristic
230Q8⋊C8—22no—
231D4⋊C8—22no—
232C2×C29—22no—
233C2×C29—82no—
234C2×C29—161no—
235C2×C29#201011yescharacteristic
236C2×C29#201211yescharacteristic
237C2×C29#201711yescharacteristic
238C2×#41—21no—
239C22×D4D4×C2911yescharacteristic
240C23×C4—21no—
241C2×SD16—22no—
242C2×D8—22no—
243C22×C8—21no—
244C22×C8D4×C2912yes—
245C4⋊Q8D4×C2911yescharacteristic
246C4⋊Q8D4×C2911yescharacteristic
247C4⋊Q8D4×C2911yescharacteristic
248#127D4×C2911yescharacteristic
249#125—21no—
250#124—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253#121—21no—
254#121—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263#117—21no—
264C2×C4⋊C4D4×C2911yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C23×C2911yescharacteristic
267#107—22no—
268#106—22no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273#103—22no—
274#103—22no—
275#103—22no—
276#102—22no—
277#102—22no—
278#102—22no—
279#102—22no—
280#102—22no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—44no—
284#97—21no—
285#97—21no—
286C4×C8D4×C2912yes—
287C4×C8D4×C2912yes—
288C29#1003311yescharacteristic, direct product factor, Sylow
289C24—21no—
290#41—42no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—41no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4C2×D4×C2911yescharacteristic
309C22×C4C2×D4×C2911yescharacteristic
310C22×C4#41×C2911yescharacteristic
311SD16—44no—
312D8—44no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—41no—
319C2×C8—42no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42—41no—
336C42C2×D4×C2911yescharacteristic
337C42C2×D4×C2911yescharacteristic
338C42C2×D4×C2911yescharacteristic
339C42C2×D4×C2911yescharacteristic
340C23—22no—
341C23—41no—
342C23—42no—
343C23—42no—
344C23—41no—
345C23—41no—
346C23C29×#12111yescharacteristic
347Q8—42no—
348Q8—42no—
349Q8—42no—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—82no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4C29×#12011yescharacteristic
371C2×C4C29×#12011yescharacteristic
372C2×C4C29×#12011yescharacteristic
373C2×C4C29×#12111yescharacteristic
374C2×C4C29×#12111yescharacteristic
375C2×C4C29×#12711yescharacteristic
376C2×C4C29×#13512yes—
377C2×C4C29×AGL(1,ℤ/8)12yes—
378C8—42no—
379C8—42no—
380C8—42no—
381C8—81no—
382C22—21no—
383C22—21no—
384C22—44no—
385C22—42no—
386C22—82no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C29×#39211yescharacteristic
393C22C29×#46312yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4C29×#44912yes—
403C4C29×#49511yescharacteristic
404C4C29×#49611yescharacteristic
405C2—22no—
406C2—82no—
407C2—161no—
408C2C29×#201011yescharacteristic
409C2C29×#201211yescharacteristic
410C2C29×#201711yescharacteristic
subgroupG/H
centerC2×C4×C29#127
commutator, Frattini, cosocleC2×C42C23×C29
socleC22×C29#392
prime radicalC29×#3100C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C29×#3135C2semidirect
2. C29×#3101C2semidirect
4. C29×#1955C2semidirect
5. C29×#1481C2semidirect
6. C29×#1480C2semidirect
7. C29×#1275C2semidirect
134. #10033C29direct (N × H)
177. #3135C2×C29semidirect
178. #3101C2×C29semidirect
180. #1955C2×C29semidirect
181. #1481C2×C29semidirect
182. #1480C2×C29semidirect
183. #1275C2×C29semidirect
288. C29#10033direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31352
C29×#31012
C29×#31002
C29×#19552
C29×#14812
C29×#14802
C29×#12752
#1003329