Finite Group Databasebeta

← C29×#19507 #20314407

Subgroups — C29×#19507 #20314407

Order 7424.

588 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3235C211yesmaximal, characteristic
2C29×#3226C211yesmaximal, characteristic
3C29×#3209C211yesmaximal, characteristic, complemented
4C29×#2981C211yesmaximal, characteristic
5C29×#1703C212yesmaximal, complemented
6C29×#1689C212yesmaximal, complemented
7C29×#1683C212yesmaximal, complemented
8C29×#1669C212yesmaximal, complemented
9C29×#1572C211yesmaximal, characteristic, complemented
10C29×#1556C211yesmaximal, characteristic, complemented
11C29×#1554C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C29×#501—21no—
16C29×#500—21no—
17C29×#494C2211yescharacteristic
18C29×#494C2211yescharacteristic
19C29×#490—21no—
20C29×#487C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#486—21no—
23C29×#482—22no—
24C29×#480—22no—
25C29×#476C2212yes—
26C29×#474C2212yes—
27C29×#474C2212yes—
28C29×#474C2212yes—
29C29×#462—22no—
30C29×#451—22no—
31C29×#436C2212yes—
32C29×#435—22no—
33C8×D4×C29C2212yes—
34C29×#432C2211yescharacteristic
35C29×#432C2211yescharacteristic
36C29×#431C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C29×#408—22no—
39C29×#335C2212yes—
40C29×#334C2212yes—
41C29×#333C2212yes—
42C29×#332C2212yes—
43C29×#332C2212yes—
44C29×#332C2212yes—
45C2×#41×C29—21no—
46C22×Q8×C29—21no—
47C2×Q16×C29—22no—
48C2×Q16×C29—22no—
49C2×M16×C29—22no—
50C22×C8×C29—22no—
51C29×C4⋊Q8—21no—
52C29×C4⋊Q8—21no—
53C29×C4⋊Q8—21no—
54C29×C4⋊Q8D411yescharacteristic
55C29×C4⋊Q8C2311yescharacteristic
56C29×C4⋊Q8C2311yescharacteristic
57C29×C4⋊Q8C2311yescharacteristic
58C29×C4⋊Q8C2311yescharacteristic
59C29×#127D411yescharacteristic
60C29×#125—21no—
61C29×#124—21no—
62C29×C22⋊Q8—21no—
63C29×C22⋊Q8—21no—
64C29×#121—21no—
65C29×#121D412yes—
66C4×Q8×C29—21no—
67C4×Q8×C29—21no—
68C4×D4×C29—21no—
69C4×D4×C29C2312yes—
70C29×#117—21no—
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—21no—
73C2×C42×C29C2311yescharacteristic
74C29×#107—22no—
75C29×#107—22no—
76C29×#107—22no—
77C29×#106—22no—
78C29×C4⋊C8D412yes—
79C29×C4⋊C8C2312yes—
80C29×C4⋊C8C2312yes—
81C29×C4⋊C8C2312yes—
82C29×#103—22no—
83C29×#103—22no—
84C29×#102—22no—
85C29×#102—22no—
86C29×#102—22no—
87C29×#102—22no—
88C29×C22⋊C8—21no—
89C29×C22⋊C8—21no—
90C29×C22⋊C8—21no—
91C29×C22⋊C8—22no—
92C29×C22⋊C8—22no—
93C29×C22⋊C8D412yes—
94C29×#97—21no—
95C29×#97—21no—
96C4×C8×C29—21no—
97C4×C8×C29C2311yescharacteristic
98C4×C8×C29C2311yescharacteristic
99#41×C29—82no—
100C2×Q8×C29—21no—
101C2×Q8×C29—21no—
102C2×Q8×C29—21no—
103C2×Q8×C29—21no—
104C2×Q8×C29—21no—
105C2×Q8×C29—41no—
106C2×Q8×C29—82no—
107C2×D4×C29—22no—
108C2×D4×C29—21no—
109C2×D4×C29—21no—
110C2×D4×C29C2×D412yes—
111C22×C4×C29—22no—
112C22×C4×C29—41no—
113C22×C4×C29C2×D411yescharacteristic
114C22×C4×C29C2×D411yescharacteristic
115C22×C4×C29#4111yescharacteristic
116Q16×C29—82no—
117Q16×C29—82no—
118M16×C29—82no—
119C2×C8×C29—22no—
120C2×C8×C29—22no—
121C2×C8×C29—22no—
122C2×C8×C29—82no—
123C2×C8×C29C2×D412yes—
124C2×C8×C29C2×D412yes—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—21no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—21no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—41no—
135C4⋊C4×C29—41no—
136C4⋊C4×C29—41no—
137C4⋊C4×C29—41no—
138C4⋊C4×C29C2×D412yes—
139C22⋊C4×C29—22no—
140C22⋊C4×C29—22no—
141C22⋊C4×C29—41no—
142C42×C29—41no—
143C42×C29C2×D411yescharacteristic
144C42×C29C2×D411yescharacteristic
145C42×C29#4111yescharacteristic
146C42×C29C2411yescharacteristic
147#19507C2911yesmaximal, characteristic, direct product factor, Sylow
148C23×C29—22no—
149C23×C29#12111yescharacteristic
150Q8×C29—42no—
151Q8×C29—42no—
152Q8×C29—42no—
153Q8×C29—81no—
154Q8×C29—81no—
155Q8×C29—82no—
156D4×C29—24no—
157D4×C29—81no—
158D4×C29—81no—
159D4×C29—82no—
160C2×C4×C29—22no—
161C2×C4×C29—22no—
162C2×C4×C29—22no—
163C2×C4×C29—41no—
164C2×C4×C29—42no—
165C2×C4×C29—42no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—82no—
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29#12111yescharacteristic
173C2×C4×C29#12111yescharacteristic
174C2×C4×C29C22×D411yescharacteristic
175C2×C4×C29C22×D411yescharacteristic
176C2×C4×C29C2×#4111yescharacteristic
177C8×C29—22no—
178C8×C29—22no—
179C8×C29—42no—
180C8×C29—42no—
181C8×C29—42no—
182#3235C2×C2911yescharacteristic
183#3226C2×C2911yescharacteristic
184#3209C2×C2911yescharacteristic, complemented
185#2981C2×C2911yescharacteristic
186#1703C2×C2912yescomplemented
187#1689C2×C2912yescomplemented
188#1683C2×C2912yescomplemented
189#1669C2×C2912yescomplemented
190#1572C2×C2911yescharacteristic, complemented
191#1556C2×C2911yescharacteristic, complemented
192#1554C2×C2911yescharacteristic, complemented
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—42no—
197C22×C29—42no—
198C22×C29—42no—
199C22×C29C2×#12111yescharacteristic
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—42no—
205C4×C29—81no—
206C4×C29—81no—
207C4×C29—81no—
208C4×C29—81no—
209C4×C29#57612yes—
210C4×C29#57812yes—
211#533C22×C2911yescharacteristic
212#532C22×C2911yescharacteristic
213C2×C4⋊Q8C22×C2911yescharacteristic
214#501—21no—
215#500—21no—
216#494C22×C2911yescharacteristic
217#494C22×C2911yescharacteristic
218#490—21no—
219#487C22×C2911yescharacteristic
220#487C22×C2911yescharacteristic
221#486—21no—
222#482—22no—
223#480—22no—
224#476C22×C2912yes—
225#474C22×C2912yes—
226#474C22×C2912yes—
227#474C22×C2912yes—
228#462—22no—
229#451—22no—
230#436C22×C2912yes—
231#435—22no—
232C8×D4C22×C2912yes—
233#432C22×C2911yescharacteristic
234#432C22×C2911yescharacteristic
235#431C22×C2911yescharacteristic
236#431C22×C2911yescharacteristic
237#408—22no—
238#335C22×C2912yes—
239#334C22×C2912yes—
240#333C22×C2912yes—
241#332C22×C2912yes—
242#332C22×C2912yes—
243#332C22×C2912yes—
244C2×C29—41no—
245C2×C29—82no—
246C2×C29#304111yescharacteristic
247C2×C29#305911yescharacteristic
248C2×C29#306911yescharacteristic
249C2×#41—21no—
250C22×Q8—21no—
251C2×Q16—22no—
252C2×Q16—22no—
253C2×M16—22no—
254C22×C8—22no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8D4×C2911yescharacteristic
259C4⋊Q8C23×C2911yescharacteristic
260C4⋊Q8C23×C2911yescharacteristic
261C4⋊Q8C23×C2911yescharacteristic
262C4⋊Q8C23×C2911yescharacteristic
263#127D4×C2911yescharacteristic
264#125—21no—
265#124—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—21no—
269#121D4×C2912yes—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×D4—21no—
273C4×D4C23×C2912yes—
274#117—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C42C23×C2911yescharacteristic
278#107—22no—
279#107—22no—
280#107—22no—
281#106—22no—
282C4⋊C8D4×C2912yes—
283C4⋊C8C23×C2912yes—
284C4⋊C8C23×C2912yes—
285C4⋊C8C23×C2912yes—
286#103—22no—
287#103—22no—
288#102—22no—
289#102—22no—
290#102—22no—
291#102—22no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—22no—
296C22⋊C8—22no—
297C22⋊C8D4×C2912yes—
298#97—21no—
299#97—21no—
300C4×C8—21no—
301C4×C8C23×C2911yescharacteristic
302C4×C8C23×C2911yescharacteristic
303C29#1950711yescharacteristic, direct product factor, Sylow
304#41—82no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—41no—
311C2×Q8—82no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4C2×D4×C2912yes—
316C22×C4—22no—
317C22×C4—41no—
318C22×C4C2×D4×C2911yescharacteristic
319C22×C4C2×D4×C2911yescharacteristic
320C22×C4#41×C2911yescharacteristic
321Q16—82no—
322Q16—82no—
323M16—82no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—82no—
328C2×C8C2×D4×C2912yes—
329C2×C8C2×D4×C2912yes—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4C2×D4×C2912yes—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C42—41no—
348C42C2×D4×C2911yescharacteristic
349C42C2×D4×C2911yescharacteristic
350C42#41×C2911yescharacteristic
351C42C24×C2911yescharacteristic
352C23—22no—
353C23C29×#12111yescharacteristic
354Q8—42no—
355Q8—42no—
356Q8—42no—
357Q8—81no—
358Q8—81no—
359Q8—82no—
360D4—24no—
361D4—81no—
362D4—81no—
363D4—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—82no—
375C2×C4C29×#12111yescharacteristic
376C2×C4C29×#12111yescharacteristic
377C2×C4C29×#12111yescharacteristic
378C2×C4C22×D4×C2911yescharacteristic
379C2×C4C22×D4×C2911yescharacteristic
380C2×C4C2×#41×C2911yescharacteristic
381C8—22no—
382C8—22no—
383C8—42no—
384C8—42no—
385C8—42no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22C2×C29×#12111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4C29×#57612yes—
403C4C29×#57812yes—
404C2—41no—
405C2—82no—
406C2C29×#304111yescharacteristic
407C2C29×#305911yescharacteristic
408C2C29×#306911yescharacteristic
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. C29×#3209C2semidirect
5. C29×#1703C2semidirect
6. C29×#1689C2semidirect
7. C29×#1683C2semidirect
8. C29×#1669C2semidirect
9. C29×#1572C2semidirect
10. C29×#1556C2semidirect
11. C29×#1554C2semidirect
147. #19507C29direct (N × H)
184. #3209C2×C29semidirect
186. #1703C2×C29semidirect
187. #1689C2×C29semidirect
188. #1683C2×C29semidirect
189. #1669C2×C29semidirect
190. #1572C2×C29semidirect
191. #1556C2×C29semidirect
192. #1554C2×C29semidirect
303. C29#19507direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32352
C29×#32262
C29×#32092
C29×#29812
C29×#17032
C29×#16892
C29×#16832
C29×#16692
C29×#15722
C29×#15562
C29×#15542
#1950729