Finite Group Databasebeta

← C29×#28735 #20323635

Subgroups — C29×#28735 #20323635

Order 7424.

674 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#501C211yesmaximal, characteristic, complemented
2C29×#3142C211yesmaximal, characteristic
3C29×#3141C211yesmaximal, characteristic
4C29×#2932C211yesmaximal, characteristic
5C29×#2079C212yesmaximal, complemented
6C29×#2078C212yesmaximal, complemented
7C29×#1998C211yesmaximal, characteristic, complemented
8C29×#1997C211yesmaximal, characteristic, complemented
9C29×#1816C212yesmaximal, complemented
10C29×#1815C212yesmaximal, complemented
11C29×#1778C211yesmaximal, characteristic, complemented
12C2×C29×#131C2212yes—
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C2×C29×#125C2211yescharacteristic
16C29×#501—22no—
17C29×#501—22no—
18C29×#491—21no—
19C29×#490—21no—
20C29×#489—22no—
21C29×#488—22no—
22C29×#487—21no—
23C29×#486—21no—
24C29×#435—22no—
25C29×#435—22no—
26C2×C29×#108C2212yes—
27C2×C29×#107C2211yescharacteristic
28C2×C29×#107C2211yescharacteristic
29C2×C29×#106C2211yescharacteristic
30C2×C29×#106C2211yescharacteristic
31C29×#423C2211yescharacteristic
32C29×#417C2212yes—
33C29×#417C2212yes—
34C29×#417C2212yes—
35C29×#417C2212yes—
36C29×#408C2212yes—
37C4×M16×C29C2211yescharacteristic
38C4×M16×C29C2211yescharacteristic
39C2×C29×#97C2211yescharacteristic
40C29×#343C2212yes—
41C29×#343C2212yes—
42C29×#343C2212yes—
43C29×#343C2212yes—
44C29×#341C2212yes—
45C2×#41×C29C2312yes—
46C22×Q8×C29—21no—
47C29×#131—28no—
48C2×M16×C29—22no—
49C2×M16×C29C2312yes—
50C2×M16×C29C2312yes—
51C2×M16×C29C2312yes—
52C22×C8×C29—22no—
53C22×C8×C29C2311yescharacteristic
54C22×C8×C29C2311yescharacteristic
55C29×C4⋊Q8—21no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8D411yescharacteristic
60C29×#127D411yescharacteristic
61C29×#125—21no—
62C29×#125—21no—
63C29×#125—21no—
64C29×#125—21no—
65C29×#124D412yes—
66C29×#121—21no—
67C29×#121—21no—
68C4×D4×C29—21no—
69C4×D4×C29—21no—
70C2×C4⋊C4×C29—21no—
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29C2311yescharacteristic
74C2×C4⋊C4×C29C2311yescharacteristic
75C2×C4⋊C4×C29C2311yescharacteristic
76C2×C4⋊C4×C29C2311yescharacteristic
77C2×C42×C29C2311yescharacteristic
78C29×#108—24no—
79C29×#107—22no—
80C29×#107—22no—
81C29×#106—22no—
82C29×#106—22no—
83C29×C4⋊C8—21no—
84C29×C4⋊C8—21no—
85C29×#103—22no—
86C29×#103—22no—
87C29×#103—22no—
88C29×#103—22no—
89C29×#102—22no—
90C29×#102—22no—
91C29×#102—22no—
92C29×#102—22no—
93C29×C22⋊C8—24no—
94C29×#97—21no—
95C29×#97—21no—
96C29×#97D412yes—
97C29×#97D412yes—
98C4×C8×C29—21no—
99C4×C8×C29—21no—
100#41×C29—24no—
101#41×C29—24no—
102C2×Q8×C29—41no—
103C2×Q8×C29—41no—
104C2×Q8×C29—82no—
105C2×Q8×C29C2×D412yes—
106C2×D4×C29—22no—
107C2×D4×C29—21no—
108C2×D4×C29—21no—
109C2×D4×C29C2×D412yes—
110C22×C4×C29—22no—
111C22×C4×C29—21no—
112C22×C4×C29—21no—
113C22×C4×C29—21no—
114C22×C4×C29—21no—
115C22×C4×C29#4111yescharacteristic
116C22×C4×C29#4111yescharacteristic
117C22×C4×C29C2411yescharacteristic
118M16×C29—24no—
119M16×C29—22no—
120M16×C29—22no—
121M16×C29—22no—
122M16×C29—22no—
123M16×C29—44no—
124C2×C8×C29—22no—
125C2×C8×C29—22no—
126C2×C8×C29—22no—
127C2×C8×C29—22no—
128C2×C8×C29—44no—
129C2×C8×C29C2×D412yes—
130C2×C8×C29C2×D412yes—
131C2×C8×C29#4114yes—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—21no—
136C4⋊C4×C29—21no—
137C4⋊C4×C29—21no—
138C4⋊C4×C29—21no—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—41no—
143C4⋊C4×C29—41no—
144C4⋊C4×C29—41no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C22⋊C4×C29—22no—
149C22⋊C4×C29—22no—
150C42×C29C2×D411yescharacteristic
151C42×C29C2×D411yescharacteristic
152C42×C29C2×D411yescharacteristic
153C42×C29C2×D411yescharacteristic
154#28735C2911yesmaximal, characteristic, direct product factor, Sylow
155C23×C29—22no—
156C23×C29C2×#4111yescharacteristic
157Q8×C29—24no—
158Q8×C29—82no—
159Q8×C29—82no—
160D4×C29—24no—
161D4×C29—44no—
162D4×C29—81no—
163D4×C29—81no—
164C2×C4×C29—22no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—42no—
168C2×C4×C29—42no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—41no—
173C2×C4×C29—81no—
174C2×C4×C29—81no—
175C2×C4×C29—81no—
176C2×C4×C29—81no—
177C2×C4×C29#12111yescharacteristic
178C2×C4×C29#12111yescharacteristic
179C2×C4×C29#12111yescharacteristic
180C2×C4×C29#12111yescharacteristic
181C2×C4×C29C22×D411yescharacteristic
182C2×C4×C29C22×D411yescharacteristic
183C2×C4×C29C2×#4112yes—
184C2×C4×C292−1+412yes—
185C8×C29—22no—
186C8×C29—42no—
187C8×C29—42no—
188C8×C29—42no—
189C8×C29#12414yes—
190C2×#501C2×C2911yescharacteristic, complemented
191#3142C2×C2911yescharacteristic
192#3141C2×C2911yescharacteristic
193#2932C2×C2911yescharacteristic
194#2079C2×C2912yescomplemented
195#2078C2×C2912yescomplemented
196#1998C2×C2911yescharacteristic, complemented
197#1997C2×C2911yescharacteristic, complemented
198#1816C2×C2912yescomplemented
199#1815C2×C2912yescomplemented
200#1778C2×C2911yescharacteristic, complemented
201C22×C29—21no—
202C22×C29—21no—
203C22×C29—42no—
204C22×C29—42no—
205C22×C29—42no—
206C22×C29C2×#12111yescharacteristic
207C22×C29#55612yes—
208C4×C29—21no—
209C4×C29—21no—
210C4×C29—21no—
211C4×C29—21no—
212C4×C29—42no—
213C4×C29—81no—
214C4×C29—81no—
215C4×C29—81no—
216C4×C29—81no—
217C4×C29C2×#12411yescharacteristic
218C4×C29#53611yescharacteristic
219C4×C29#54712yes—
220C2×#131C22×C2912yes—
221#532C22×C2911yescharacteristic
222C2×C4⋊Q8C22×C2911yescharacteristic
223C2×#125C22×C2911yescharacteristic
224#501—22no—
225#501—22no—
226#491—21no—
227#490—21no—
228#489—22no—
229#488—22no—
230#487—21no—
231#486—21no—
232#435—22no—
233#435—22no—
234C2×#108C22×C2912yes—
235C2×#107C22×C2911yescharacteristic
236C2×#107C22×C2911yescharacteristic
237C2×#106C22×C2911yescharacteristic
238C2×#106C22×C2911yescharacteristic
239#423C22×C2911yescharacteristic
240#417C22×C2912yes—
241#417C22×C2912yes—
242#417C22×C2912yes—
243#417C22×C2912yes—
244#408C22×C2912yes—
245C4×M16C22×C2911yescharacteristic
246C4×M16C22×C2911yescharacteristic
247C2×#97C22×C2911yescharacteristic
248#343C22×C2912yes—
249#343C22×C2912yes—
250#343C22×C2912yes—
251#343C22×C2912yes—
252#341C22×C2912yes—
253C2×C29—22no—
254C2×C29—82no—
255C2×C29#254711yescharacteristic
256C2×C29#306811yescharacteristic
257C2×C29#306911yescharacteristic
258C2×#41C23×C2912yes—
259C22×Q8—21no—
260#131—28no—
261C2×M16—22no—
262C2×M16C23×C2912yes—
263C2×M16C23×C2912yes—
264C2×M16C23×C2912yes—
265C22×C8—22no—
266C22×C8C23×C2911yescharacteristic
267C22×C8C23×C2911yescharacteristic
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8D4×C2911yescharacteristic
273#127D4×C2911yescharacteristic
274#125—21no—
275#125—21no—
276#125—21no—
277#125—21no—
278#124D4×C2912yes—
279#121—21no—
280#121—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4C23×C2911yescharacteristic
287C2×C4⋊C4C23×C2911yescharacteristic
288C2×C4⋊C4C23×C2911yescharacteristic
289C2×C4⋊C4C23×C2911yescharacteristic
290C2×C42C23×C2911yescharacteristic
291#108—24no—
292#107—22no—
293#107—22no—
294#106—22no—
295#106—22no—
296C4⋊C8—21no—
297C4⋊C8—21no—
298#103—22no—
299#103—22no—
300#103—22no—
301#103—22no—
302#102—22no—
303#102—22no—
304#102—22no—
305#102—22no—
306C22⋊C8—24no—
307#97—21no—
308#97—21no—
309#97D4×C2912yes—
310#97D4×C2912yes—
311C4×C8—21no—
312C4×C8—21no—
313C29#2873511yescharacteristic, direct product factor, Sylow
314#41—24no—
315#41—24no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—82no—
319C2×Q8C2×D4×C2912yes—
320C2×D4—22no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4C2×D4×C2912yes—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4#41×C2911yescharacteristic
330C22×C4#41×C2911yescharacteristic
331C22×C4C24×C2911yescharacteristic
332M16—22no—
333M16—22no—
334M16—24no—
335M16—22no—
336M16—22no—
337M16—44no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—44no—
343C2×C8C2×D4×C2912yes—
344C2×C8C2×D4×C2912yes—
345C2×C8#41×C2914yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C42C2×D4×C2911yescharacteristic
365C42C2×D4×C2911yescharacteristic
366C42C2×D4×C2911yescharacteristic
367C42C2×D4×C2911yescharacteristic
368C23—22no—
369C23C2×#41×C2911yescharacteristic
370Q8—24no—
371Q8—82no—
372Q8—82no—
373D4—24no—
374D4—44no—
375D4—81no—
376D4—81no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4C29×#12111yescharacteristic
391C2×C4C29×#12111yescharacteristic
392C2×C4C29×#12111yescharacteristic
393C2×C4C29×#12111yescharacteristic
394C2×C4C22×D4×C2911yescharacteristic
395C2×C4C22×D4×C2911yescharacteristic
396C2×C4C2×#41×C2912yes—
397C2×C4C29×2−1+412yes—
398C8—22no—
399C8—42no—
400C8—42no—
401C8—42no—
402C8C29×#12414yes—
403C22—21no—
404C22—21no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22C2×C29×#12111yescharacteristic
409C22C29×#55612yes—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4C2×C29×#12411yescharacteristic
420C4C29×#53611yescharacteristic
421C4C29×#54712yes—
422C2—22no—
423C2—82no—
424C2C29×#254711yescharacteristic
425C2C29×#306811yescharacteristic
426C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#501C2semidirect
5. C29×#2079C2semidirect
6. C29×#2078C2semidirect
7. C29×#1998C2semidirect
8. C29×#1997C2semidirect
9. C29×#1816C2semidirect
10. C29×#1815C2semidirect
11. C29×#1778C2semidirect
154. #28735C29direct (N × H)
190. C2×#501C2×C29semidirect
194. #2079C2×C29semidirect
195. #2078C2×C29semidirect
196. #1998C2×C29semidirect
197. #1997C2×C29semidirect
198. #1816C2×C29semidirect
199. #1815C2×C29semidirect
200. #1778C2×C29semidirect
313. C29#28735direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5012
C29×#31422
C29×#31412
C29×#29322
C29×#20792
C29×#20782
C29×#19982
C29×#19972
C29×#18162
C29×#18152
C29×#17782
#2873529