Finite Group Databasebeta

← C29×#8955 #20303855

Subgroups — C29×#8955 #20303855

Order 7424.

488 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2989C211yesmaximal, characteristic
2C4×C29×#137C211yesmaximal, characteristic
3C29×#1984C211yesmaximal, characteristic, complemented
4C29×#1479C211yesmaximal, characteristic, complemented
5C29×#1476C211yesmaximal, characteristic
6C29×#1283C211yesmaximal, characteristic, complemented
7C29×#1278C211yesmaximal, characteristic, complemented
8C2×C29×#137C411yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C2×C4×Q8×C29C2211yescharacteristic
11C29×#446—21no—
12C29×#441—21no—
13C29×#440—21no—
14C4×Q16×C29—21no—
15C4×SD16×C29—21no—
16C29×#436—21no—
17C29×#435—22no—
18C29×#432—21no—
19C29×#431C2211yescharacteristic
20C29×#431C2211yescharacteristic
21C29×#428C411yescharacteristic
22C29×#423—21no—
23C2×C29×C4⋊C8C2211yescharacteristic
24C29×#419C411yescharacteristic
25C29×#417C411yescharacteristic
26C4×M16×C29C2211yescharacteristic
27C2×C4×C8×C29C2211yescharacteristic
28C29×#336—22no—
29C29×Q8⋊C8—21no—
30C29×Q8⋊C8—21no—
31C29×Q8⋊C8—21no—
32C29×D4⋊C8—21no—
33C2×#41×C29C2×C411yescharacteristic
34C22×Q8×C29C2×C411yescharacteristic
35C29×#137—22no—
36C29×#137—22no—
37C2×Q16×C29—21no—
38C2×SD16×C29—21no—
39C2×M16×C29—22no—
40C2×M16×C29C2×C411yescharacteristic
41C2×M16×C29C2×C411yescharacteristic
42C22×C8×C29—21no—
43C22×C8×C29D412yes—
44C4×Q8×C29—21no—
45C4×Q8×C29—21no—
46C4×Q8×C29—21no—
47C4×Q8×C29—21no—
48C4×Q8×C29D411yescharacteristic
49C4×Q8×C29D411yescharacteristic
50C4×D4×C29—21no—
51C4×D4×C29—21no—
52C4×D4×C29D411yescharacteristic
53C4×D4×C29D411yescharacteristic
54C29×#117—21no—
55C29×#117C2×C411yescharacteristic
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29C2×C411yescharacteristic
58C2×C42×C29—21no—
59C2×C42×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×#107—21no—
62C29×#106—21no—
63C29×C4⋊C8—22no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8D411yescharacteristic
68C29×C4⋊C8D411yescharacteristic
69C29×#103—21no—
70C29×#103—21no—
71C29×#103—21no—
72C29×#102—21no—
73C29×C22⋊C8—22no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8—21no—
76C29×#97—22no—
77C29×#97—21no—
78C4×C8×C29—21no—
79C4×C8×C29—21no—
80C4×C8×C29—21no—
81C4×C8×C29—21no—
82C4×C8×C29—21no—
83#41×C29—21no—
84#41×C29—21no—
85#41×C29—21no—
86#41×C29—21no—
87C2×Q8×C29—21no—
88C2×Q8×C29—21no—
89C2×Q8×C29—21no—
90C2×Q8×C29—21no—
91C2×Q8×C29—21no—
92C2×Q8×C29C22⋊C411yescharacteristic
93C2×Q8×C29M1612yescomplemented
94C2×D4×C29—21no—
95C2×D4×C29C22⋊C411yescharacteristic
96C22×C4×C29—21no—
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29C22×C411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29#4111yescharacteristic
104Q16×C29—24no—
105SD16×C29—24no—
106M16×C29—21no—
107M16×C29—21no—
108M16×C29—21no—
109M16×C29—82no—
110M16×C29M1612yescomplemented
111C2×C8×C29—21no—
112C2×C8×C29—22no—
113C2×C8×C29—21no—
114C2×C8×C29—22no—
115C2×C8×C29—21no—
116C2×C8×C29—21no—
117C2×C8×C29—41no—
118C2×C8×C29—41no—
119C2×C8×C29—42no—
120C2×C8×C29—41no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—21no—
125C4⋊C4×C29—41no—
126C4⋊C4×C29—41no—
127C4⋊C4×C29C22⋊C411yescharacteristic
128C4⋊C4×C29C22⋊C411yescharacteristic
129C22⋊C4×C29—21no—
130C22⋊C4×C29—21no—
131C22⋊C4×C29—21no—
132C42×C29—21no—
133C42×C29—21no—
134C42×C29—21no—
135C42×C29—41no—
136C42×C29—41no—
137C42×C29C2×D411yescharacteristic
138C42×C29C2×D411yescharacteristic
139C42×C29C2×D411yescharacteristic
140C42×C29#4111yescharacteristic
141#8955C2911yesmaximal, characteristic, direct product factor, Sylow
142C23×C29—21no—
143C23×C29C4×D411yescharacteristic
144Q8×C29—22no—
145Q8×C29—21no—
146Q8×C29—21no—
147Q8×C29—22no—
148Q8×C29—41no—
149Q8×C29—41no—
150D4×C29—21no—
151D4×C29—21no—
152D4×C29—41no—
153D4×C29—41no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—22no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—42no—
168C2×C4×C29—41no—
169C2×C4×C29—81no—
170C2×C4×C29C2×C22⋊C411yescharacteristic
171C2×C4×C29C4×D411yescharacteristic
172C2×C4×C29#12011yescharacteristic
173C2×C4×C29#12111yescharacteristic
174C2×C4×C29#12111yescharacteristic
175C2×C4×C29#12311yescharacteristic
176C2×C4×C29C2×M1611yescharacteristic
177C2×C4×C29C2×M1611yescharacteristic
178C2×C4×C29#13111yescharacteristic
179C2×C4×C29#13111yescharacteristic
180C8×C29—22no—
181C8×C29—42no—
182C8×C29—41no—
183C8×C29—42no—
184C8×C29—41no—
185C8×C29—41no—
186C8×C29—81no—
187#2989C2×C2911yescharacteristic
188C4×#137C2×C2911yescharacteristic
189#1984C2×C2911yescharacteristic, complemented
190#1479C2×C2911yescharacteristic, complemented
191#1476C2×C2911yescharacteristic
192#1283C2×C2911yescharacteristic, complemented
193#1278C2×C2911yescharacteristic, complemented
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—41no—
197C22×C29—41no—
198C22×C29—41no—
199C22×C29#38611yescharacteristic
200C22×C29#43511yescharacteristic
201C22×C29#43611yescharacteristic
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—21no—
205C4×C29—41no—
206C4×C29—42no—
207C4×C29—41no—
208C4×C29—41no—
209C4×C29—81no—
210C4×C29#40711yescharacteristic
211C4×C29#40811yescharacteristic
212C4×C29#43511yescharacteristic
213C4×C29#43611yescharacteristic
214C4×C29#45511yescharacteristic
215C4×C29#45611yescharacteristic
216C2×#137C4×C2911yescharacteristic
217C4×#41C22×C2911yescharacteristic
218C2×C4×Q8C22×C2911yescharacteristic
219#446—21no—
220#441—21no—
221#440—21no—
222C4×Q16—21no—
223C4×SD16—21no—
224#436—21no—
225#435—22no—
226#432—21no—
227#431C22×C2911yescharacteristic
228#431C22×C2911yescharacteristic
229#428C4×C2911yescharacteristic
230#423—21no—
231C2×C4⋊C8C22×C2911yescharacteristic
232#419C4×C2911yescharacteristic
233#417C4×C2911yescharacteristic
234C4×M16C22×C2911yescharacteristic
235C2×C4×C8C22×C2911yescharacteristic
236#336—22no—
237Q8⋊C8—21no—
238Q8⋊C8—21no—
239Q8⋊C8—21no—
240D4⋊C8—21no—
241C2×C29—21no—
242C2×C29—21no—
243C2×C29—81no—
244C2×C29#187011yescharacteristic
245C2×C29#188111yescharacteristic
246C2×C29#188211yescharacteristic
247C2×#41C2×C4×C2911yescharacteristic
248C22×Q8C2×C4×C2911yescharacteristic
249#137—22no—
250#137—22no—
251C2×Q16—21no—
252C2×SD16—21no—
253C2×M16—22no—
254C2×M16C2×C4×C2911yescharacteristic
255C2×M16C2×C4×C2911yescharacteristic
256C22×C8—21no—
257C22×C8D4×C2912yes—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8D4×C2911yescharacteristic
263C4×Q8D4×C2911yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4D4×C2911yescharacteristic
267C4×D4D4×C2911yescharacteristic
268#117—21no—
269#117C2×C4×C2911yescharacteristic
270C2×C4⋊C4—21no—
271C2×C4⋊C4C2×C4×C2911yescharacteristic
272C2×C42—21no—
273C2×C42—21no—
274C2×C42C23×C2911yescharacteristic
275#107—21no—
276#106—21no—
277C4⋊C8—22no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8D4×C2911yescharacteristic
282C4⋊C8D4×C2911yescharacteristic
283#103—21no—
284#103—21no—
285#103—21no—
286#102—21no—
287C22⋊C8—22no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290#97—22no—
291#97—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—21no—
296C4×C8—21no—
297C29#895511yescharacteristic, direct product factor, Sylow
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8C22⋊C4×C2911yescharacteristic
308C2×Q8M16×C2912yescomplemented
309C2×D4—21no—
310C2×D4C22⋊C4×C2911yescharacteristic
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4C22×C4×C2911yescharacteristic
317C22×C4C2×D4×C2911yescharacteristic
318C22×C4#41×C2911yescharacteristic
319Q16—24no—
320SD16—24no—
321M16—21no—
322M16—21no—
323M16—21no—
324M16—82no—
325M16M16×C2912yescomplemented
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—42no—
335C2×C8—41no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4C22⋊C4×C2911yescharacteristic
343C4⋊C4C22⋊C4×C2911yescharacteristic
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C42—41no—
351C42—41no—
352C42C2×D4×C2911yescharacteristic
353C42C2×D4×C2911yescharacteristic
354C42C2×D4×C2911yescharacteristic
355C42#41×C2911yescharacteristic
356C23—21no—
357C23C4×D4×C2911yescharacteristic
358Q8—22no—
359Q8—22no—
360Q8—21no—
361Q8—21no—
362Q8—41no—
363Q8—41no—
364D4—21no—
365D4—21no—
366D4—41no—
367D4—41no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4C2×C22⋊C4×C2911yescharacteristic
385C2×C4C4×D4×C2911yescharacteristic
386C2×C4C29×#12011yescharacteristic
387C2×C4C29×#12111yescharacteristic
388C2×C4C29×#12111yescharacteristic
389C2×C4C29×#12311yescharacteristic
390C2×C4C2×M16×C2911yescharacteristic
391C2×C4C2×M16×C2911yescharacteristic
392C2×C4C29×#13111yescharacteristic
393C2×C4C29×#13111yescharacteristic
394C8—22no—
395C8—42no—
396C8—42no—
397C8—41no—
398C8—41no—
399C8—41no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22C29×#38611yescharacteristic
407C22C29×#43511yescharacteristic
408C22C29×#43611yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—41no—
413C4—42no—
414C4—41no—
415C4—41no—
416C4—81no—
417C4C29×#40711yescharacteristic
418C4C29×#40811yescharacteristic
419C4C29×#43511yescharacteristic
420C4C29×#43611yescharacteristic
421C4C29×#45511yescharacteristic
422C4C29×#45611yescharacteristic
423C2—21no—
424C2—21no—
425C2—81no—
426C2C29×#187011yescharacteristic
427C2C29×#188111yescharacteristic
428C2C29×#188211yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC2×#41×C29C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1984C2semidirect
4. C29×#1479C2semidirect
6. C29×#1283C2semidirect
7. C29×#1278C2semidirect
93. C2×Q8×C29M16semidirect
110. M16×C29M16semidirect
141. #8955C29direct (N × H)
189. #1984C2×C29semidirect
190. #1479C2×C29semidirect
192. #1283C2×C29semidirect
193. #1278C2×C29semidirect
297. C29#8955direct (N × H)
308. C2×Q8M16×C29semidirect
325. M16M16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#29892
C4×C29×#1372
C29×#19842
C29×#14792
C29×#14762
C29×#12832
C29×#12782
#895529