Finite Group Databasebeta

← C29×#13334 #20308234

Subgroups — C29×#13334 #20308234

Order 7424.

568 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3414C211yesmaximal, characteristic, complemented
2C2×C29×#509C211yesmaximal, characteristic, complemented
3C29×#3155C211yesmaximal, characteristic, complemented
4C29×#2145C211yesmaximal, characteristic, complemented
5C29×#2140C211yesmaximal, characteristic, complemented
6C29×#1976C211yesmaximal, characteristic, complemented
7C29×#1378C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—21no—
9C2×C29×#135C2211yescharacteristic
10C2×C29×#135C2211yescharacteristic
11C22×D8×C29C2211yescharacteristic
12C29×#535—21no—
13C29×#510—21no—
14C29×#510—21no—
15C29×#509—22no—
16C29×#509—22no—
17C29×#509—21no—
18C29×#509—21no—
19C29×#508—22no—
20C2×C29×SD32—21no—
21C2×C29×D16—21no—
22C2×C29×M32C2211yescharacteristic
23C2×C29×M32C2211yescharacteristic
24C29×#496—22no—
25C29×#495—21no—
26C29×#493—21no—
27C29×#427C2211yescharacteristic
28C29×#421—21no—
29C29×#410—21no—
30C29×#405C2211yescharacteristic
31C29×#360—22no—
32C29×#357—22no—
33C2×#41×C29—21no—
34C2×#41×C29—21no—
35C22×D4×C29—21no—
36C29×AGL(1,ℤ/8)—42no—
37C29×AGL(1,ℤ/8)—42no—
38C29×#135—21no—
39C29×#135—21no—
40C29×#135—21no—
41C29×#135—21no—
42C29×#135—21no—
43C29×#135—21no—
44C29×#135—21no—
45C29×#135—21no—
46C2×Q16×C29D411yescharacteristic
47C2×Q16×C29D411yescharacteristic, complemented
48C2×SD16×C29—22no—
49C2×SD16×C29—21no—
50C2×SD16×C29—21no—
51C2×D8×C29—22no—
52C2×D8×C29—21no—
53C2×D8×C29—21no—
54C2×D8×C29—21no—
55C2×D8×C29—21no—
56C2×D8×C29—21no—
57C2×D8×C29D411yescharacteristic
58C2×D8×C29D412yes—
59C2×D8×C29D411yescharacteristic, complemented
60C2×M16×C29D411yescharacteristic
61C22×C8×C29C2311yescharacteristic
62C29×#127—22no—
63C29×#124—22no—
64C29×#121—42no—
65C29×#120—42no—
66C29×#117—21no—
67C29×#117D411yescharacteristic
68C29×Q32—22no—
69C29×SD32—24no—
70C29×SD32—22no—
71C29×SD32—22no—
72C29×D16—24no—
73C29×D16—22no—
74C29×M32—21no—
75C29×M32—21no—
76C29×M32—21no—
77C29×M32D412yescomplemented
78C2×C16×C29—21no—
79C2×C16×C29D412yescomplemented
80C29×#107—21no—
81C29×#106—21no—
82C29×#104—42no—
83C29×#99—42no—
84C29×#97—21no—
85C4×C8×C29—21no—
86C24×C29—41no—
87#41×C29—41no—
88#41×C29—41no—
89#41×C29—41no—
90#41×C29—41no—
91#41×C29—41no—
92#41×C29—41no—
93#41×C29—41no—
94#41×C29—41no—
95C2×Q8×C29—21no—
96C2×Q8×C29—21no—
97C2×D4×C29—22no—
98C2×D4×C29—21no—
99C2×D4×C29—21no—
100C2×D4×C29—44no—
101C2×D4×C29—41no—
102C2×D4×C29—41no—
103C2×D4×C29—41no—
104C2×D4×C29—41no—
105C2×D4×C29—41no—
106C2×D4×C29—41no—
107C2×D4×C29—41no—
108C22×C4×C29—41no—
109C22×C4×C29—41no—
110C22×C4×C29C2×D411yescharacteristic
111Q16×C29—21no—
112Q16×C29—21no—
113Q16×C29—21no—
114Q16×C29—21no—
115SD16×C29—44no—
116SD16×C29—41no—
117SD16×C29—41no—
118SD16×C29—41no—
119SD16×C29—41no—
120D8×C29—22no—
121D8×C29—21no—
122D8×C29—21no—
123D8×C29—21no—
124D8×C29—22no—
125D8×C29—21no—
126D8×C29—44no—
127D8×C29—41no—
128D8×C29—41no—
129M16×C29—21no—
130M16×C29D812yes—
131C2×C8×C29—21no—
132C2×C8×C29C2×D411yescharacteristic
133C2×C8×C29C2×D411yescharacteristic
134C2×C8×C29C2×D411yescharacteristic
135C2×C8×C29C2×D411yescharacteristic
136C2×C8×C29C2×D411yescharacteristic
137C2×C8×C29#4111yescharacteristic
138C4⋊C4×C29—21no—
139C4⋊C4×C29—41no—
140C22⋊C4×C29—44no—
141C22⋊C4×C29—41no—
142C22⋊C4×C29D812yes—
143C42×C29—21no—
144C42×C29—41no—
145C16×C29—22no—
146C16×C29—22no—
147#13334C2911yesmaximal, characteristic, direct product factor, Sylow
148C23×C29—42no—
149C23×C29—41no—
150C23×C29—41no—
151C23×C29—81no—
152C23×C29—81no—
153C23×C29—162no—
154C23×C29C2×D811yescharacteristic
155Q8×C29—41no—
156Q8×C29—41no—
157Q8×C29—41no—
158Q8×C29—41no—
159D4×C29—42no—
160D4×C29—41no—
161D4×C29—41no—
162D4×C29—41no—
163D4×C29—42no—
164D4×C29—41no—
165D4×C29—81no—
166D4×C29—81no—
167D4×C29—81no—
168D4×C29—81no—
169D4×C29—81no—
170D4×C29—81no—
171D4×C29—164no—
172C2×C4×C29—22no—
173C2×C4×C29—41no—
174C2×C4×C29—41no—
175C2×C4×C29—81no—
176C2×C4×C29—81no—
177C2×C4×C29—81no—
178C2×C4×C29—81no—
179C2×C4×C29—81no—
180C2×C4×C29#12011yescharacteristic
181C2×C4×C29#12111yescharacteristic
182C2×C4×C29#12711yescharacteristic
183C2×C4×C29C2×D811yescharacteristic
184C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
186C8×C29—22no—
187C8×C29#12011yescharacteristic
188C8×C29#12011yescharacteristic
189C8×C29#12111yescharacteristic
190C8×C29#12111yescharacteristic
191#3414C2×C2911yescharacteristic, complemented
192C2×#509C2×C2911yescharacteristic, complemented
193#3155C2×C2911yescharacteristic, complemented
194#2145C2×C2911yescharacteristic, complemented
195#2140C2×C2911yescharacteristic, complemented
196#1976C2×C2911yescharacteristic, complemented
197#1378C2×C2911yescharacteristic, complemented
198C22×C29—41no—
199C22×C29—82no—
200C22×C29—84no—
201C22×C29—81no—
202C22×C29—81no—
203C22×C29—82no—
204C22×C29—161no—
205C22×C29—162no—
206C22×C29—162no—
207C22×C29#44711yescharacteristic
208C22×C29#45911yescharacteristic
209C22×C29#49311yescharacteristic
210C4×C29—42no—
211C4×C29—81no—
212C4×C29—81no—
213C4×C29—161no—
214C4×C29#39211yescharacteristic
215C4×C29#44711yescharacteristic
216C4×C29#45911yescharacteristic
217C4×C29#49611yescharacteristic
218C2×AGL(1,ℤ/8)—21no—
219C2×#135C22×C2911yescharacteristic
220C2×#135C22×C2911yescharacteristic
221C22×D8C22×C2911yescharacteristic
222#535—21no—
223#510—21no—
224#510—21no—
225#509—22no—
226#509—21no—
227#509—21no—
228#509—22no—
229#508—22no—
230C2×SD32—21no—
231C2×D16—21no—
232C2×M32C22×C2911yescharacteristic
233C2×M32C22×C2911yescharacteristic
234#496—22no—
235#495—21no—
236#493—21no—
237#427C22×C2911yescharacteristic
238#421—21no—
239#410—21no—
240#405C22×C2911yescharacteristic
241#360—22no—
242#357—22no—
243C2×C29—21no—
244C2×C29—21no—
245C2×C29—21no—
246C2×C29—161no—
247C2×C29—162no—
248C2×C29—161no—
249C2×C29#201111yescharacteristic
250C2×#41—21no—
251C2×#41—21no—
252C22×D4—21no—
253AGL(1,ℤ/8)—42no—
254AGL(1,ℤ/8)—42no—
255#135—21no—
256#135—21no—
257#135—21no—
258#135—21no—
259#135—21no—
260#135—21no—
261#135—21no—
262#135—21no—
263C2×Q16D4×C2911yescharacteristic
264C2×Q16D4×C2911yescharacteristic, complemented
265C2×SD16—22no—
266C2×SD16—21no—
267C2×SD16—21no—
268C2×D8—22no—
269C2×D8—21no—
270C2×D8—21no—
271C2×D8—21no—
272C2×D8—21no—
273C2×D8—21no—
274C2×D8D4×C2912yes—
275C2×D8D4×C2911yescharacteristic
276C2×D8D4×C2911yescharacteristic, complemented
277C2×M16D4×C2911yescharacteristic
278C22×C8C23×C2911yescharacteristic
279#127—22no—
280#124—22no—
281#121—42no—
282#120—42no—
283#117—21no—
284#117D4×C2911yescharacteristic
285Q32—22no—
286SD32—24no—
287SD32—22no—
288SD32—22no—
289D16—24no—
290D16—22no—
291M32—21no—
292M32—21no—
293M32—21no—
294M32D4×C2912yescomplemented
295C2×C16—21no—
296C2×C16D4×C2912yescomplemented
297#107—21no—
298#106—21no—
299#104—42no—
300#99—42no—
301#97—21no—
302C4×C8—21no—
303C29#1333411yescharacteristic, direct product factor, Sylow
304C24—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—41no—
312#41—41no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—44no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4C2×D4×C2911yescharacteristic
329Q16—21no—
330Q16—21no—
331Q16—21no—
332Q16—21no—
333SD16—44no—
334SD16—41no—
335SD16—41no—
336SD16—41no—
337SD16—41no—
338D8—21no—
339D8—22no—
340D8—21no—
341D8—21no—
342D8—22no—
343D8—21no—
344D8—44no—
345D8—41no—
346D8—41no—
347M16—21no—
348M16D8×C2912yes—
349C2×C8—21no—
350C2×C8C2×D4×C2911yescharacteristic
351C2×C8C2×D4×C2911yescharacteristic
352C2×C8C2×D4×C2911yescharacteristic
353C2×C8C2×D4×C2911yescharacteristic
354C2×C8C2×D4×C2911yescharacteristic
355C2×C8#41×C2911yescharacteristic
356C4⋊C4—21no—
357C4⋊C4—41no—
358C22⋊C4—44no—
359C22⋊C4—41no—
360C22⋊C4D8×C2912yes—
361C42—21no—
362C42—41no—
363C16—22no—
364C16—22no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—81no—
369C23—81no—
370C23—162no—
371C23C2×D8×C2911yescharacteristic
372Q8—41no—
373Q8—41no—
374Q8—41no—
375Q8—41no—
376D4—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—41no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—81no—
388D4—164no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4C29×#12011yescharacteristic
398C2×C4C29×#12111yescharacteristic
399C2×C4C29×#12711yescharacteristic
400C2×C4C2×D8×C2911yescharacteristic
401C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
402C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
403C8—22no—
404C8C29×#12011yescharacteristic
405C8C29×#12011yescharacteristic
406C8C29×#12111yescharacteristic
407C8C29×#12111yescharacteristic
408C22—41no—
409C22—82no—
410C22—84no—
411C22—81no—
412C22—81no—
413C22—82no—
414C22—161no—
415C22—162no—
416C22—162no—
417C22C29×#44711yescharacteristic
418C22C29×#45911yescharacteristic
419C22C29×#49311yescharacteristic
420C4—42no—
421C4—81no—
422C4—81no—
423C4—161no—
424C4C29×#39211yescharacteristic
425C4C29×#44711yescharacteristic
426C4C29×#45911yescharacteristic
427C4C29×#49611yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—162no—
432C2—161no—
433C2—161no—
434C2C29×#201111yescharacteristic
subgroupG/H
center, socleC2×C29#2011
commutator, Frattini, cosocleC22×C8C23×C29
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3414C2semidirect
2. C2×C29×#509C2semidirect
3. C29×#3155C2semidirect
4. C29×#2145C2semidirect
5. C29×#2140C2semidirect
6. C29×#1976C2semidirect
7. C29×#1378C2semidirect
47. C2×Q16×C29D4semidirect
59. C2×D8×C29D4semidirect
77. C29×M32D4semidirect
79. C2×C16×C29D4semidirect
147. #13334C29direct (N × H)
191. #3414C2×C29semidirect
192. C2×#509C2×C29semidirect
193. #3155C2×C29semidirect
194. #2145C2×C29semidirect
195. #2140C2×C29semidirect
196. #1976C2×C29semidirect
197. #1378C2×C29semidirect
264. C2×Q16D4×C29semidirect
276. C2×D8D4×C29semidirect
294. M32D4×C29semidirect
296. C2×C16D4×C29semidirect
303. C29#13334direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34142
C2×C29×#5092
C29×#31552
C29×#21452
C29×#21402
C29×#19762
C29×#13782
#1333429