Finite Group Databasebeta

← C29×#10192 #20305092

Subgroups — C29×#10192 #20305092

Order 7424.

678 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3245C211yesmaximal, characteristic, complemented
2C29×#3205C211yesmaximal, characteristic, complemented
3C29×#3151C211yesmaximal, characteristic, complemented
4C29×#1982C211yesmaximal, characteristic, complemented
5C29×#1980C211yesmaximal, characteristic, complemented
6C29×#1502C211yesmaximal, characteristic, complemented
7C29×#1283C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—22no—
9C29×#532C2211yescharacteristic
10C29×#532C2211yescharacteristic
11C2×C29×#127C2211yescharacteristic
12C29×#496—22no—
13C29×#493—21no—
14C29×#493—21no—
15C29×#492—21no—
16C29×#486—21no—
17C29×#474—21no—
18C29×#474—21no—
19C29×#466—22no—
20C29×#459—22no—
21C29×#459—21no—
22C29×#459—21no—
23C29×#447—22no—
24C29×#431C2211yescharacteristic
25C2×C29×C4⋊C8C2211yescharacteristic
26C2×C29×#104—22no—
27C2×C29×#102—22no—
28C4×M16×C29C2211yescharacteristic
29C4×C4⋊C4×C29C2211yescharacteristic
30C29×#327—22no—
31C2×#41×C29—21no—
32C2×#41×C29—21no—
33C22×D4×C29—21no—
34C22×D4×C29—21no—
35C22×D4×C29—21no—
36C29×AGL(1,ℤ/8)—44no—
37C29×AGL(1,ℤ/8)—44no—
38C2×SD16×C29—24no—
39C2×D8×C29—24no—
40C2×D8×C29—24no—
41C2×D8×C29—22no—
42C2×M16×C29D412yes—
43C22×C8×C29D412yes—
44C29×C4⋊Q8D411yescharacteristic
45C29×C4⋊Q8D411yescharacteristic
46C29×#127—21no—
47C29×#127—21no—
48C29×#127—21no—
49C29×#127D411yescharacteristic
50C29×#127D411yescharacteristic
51C29×#127D412yes—
52C29×#124—21no—
53C29×#124—21no—
54C29×#121—21no—
55C29×#121—21no—
56C29×#121—21no—
57C29×#121—21no—
58C4×D4×C29—21no—
59C4×D4×C29—21no—
60C4×D4×C29—21no—
61C4×D4×C29—21no—
62C2×C4⋊C4×C29—21no—
63C2×C42×C29—21no—
64C2×C42×C29C2311yescharacteristic
65C29×#107—22no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×C4⋊C8—21no—
69C29×#104—44no—
70C29×#102—24no—
71C29×#102—22no—
72C29×#102—22no—
73C29×#102—44no—
74C29×C22⋊C8D412yes—
75C29×#97—21no—
76C4×C8×C29—21no—
77C4×C8×C29—21no—
78C29×#95—21no—
79C24×C29—41no—
80#41×C29—42no—
81#41×C29—42no—
82#41×C29—42no—
83#41×C29—42no—
84C2×Q8×C29—21no—
85C2×Q8×C29—21no—
86C2×D4×C29—21no—
87C2×D4×C29—21no—
88C2×D4×C29—21no—
89C2×D4×C29—21no—
90C2×D4×C29—22no—
91C2×D4×C29—22no—
92C2×D4×C29—21no—
93C2×D4×C29—22no—
94C2×D4×C29—21no—
95C2×D4×C29—42no—
96C2×D4×C29—42no—
97C2×D4×C29—41no—
98C2×D4×C29—41no—
99C2×D4×C29—41no—
100C2×D4×C29—41no—
101C2×D4×C29—41no—
102C2×D4×C29—42no—
103C2×D4×C29—42no—
104C2×D4×C29—82no—
105C22×C4×C29—41no—
106C22×C4×C29—41no—
107C22×C4×C29—41no—
108C22×C4×C29C2×D411yescharacteristic
109C22×C4×C29C2×D411yescharacteristic
110C22×C4×C29C2×D411yescharacteristic
111SD16×C29—48no—
112D8×C29—48no—
113D8×C29—84no—
114D8×C29—82no—
115M16×C29—22no—
116M16×C29D814yescomplemented
117C2×C8×C29—22no—
118C2×C8×C29—22no—
119C2×C8×C29—22no—
120C2×C8×C29—42no—
121C4⋊C4×C29—22no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—21no—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—41no—
127C22⋊C4×C29—41no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29—41no—
130C22⋊C4×C29—41no—
131C42×C29—42no—
132C42×C29C2×D411yescharacteristic
133C42×C29C2×D411yescharacteristic
134C42×C29C2×D411yescharacteristic
135C42×C29#4111yescharacteristic
136#10192C2911yesmaximal, characteristic, direct product factor, Sylow
137C23×C29—41no—
138C23×C29—41no—
139C23×C29—42no—
140C23×C29—82no—
141C23×C29—82no—
142C23×C29—81no—
143C23×C29—81no—
144C23×C29#12711yescharacteristic
145Q8×C29—42no—
146Q8×C29—42no—
147D4×C29—42no—
148D4×C29—44no—
149D4×C29—44no—
150D4×C29—42no—
151D4×C29—44no—
152D4×C29—41no—
153D4×C29—41no—
154D4×C29—41no—
155D4×C29—41no—
156D4×C29—42no—
157D4×C29—81no—
158D4×C29—82no—
159D4×C29—81no—
160D4×C29—81no—
161D4×C29—81no—
162D4×C29—81no—
163D4×C29—81no—
164D4×C29—81no—
165D4×C29—82no—
166C2×C4×C29—21no—
167C2×C4×C29—21no—
168C2×C4×C29—41no—
169C2×C4×C29—42no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—81no—
173C2×C4×C29—81no—
174C2×C4×C29—82no—
175C2×C4×C29—82no—
176C2×C4×C29#12011yescharacteristic
177C2×C4×C29#12011yescharacteristic
178C2×C4×C29#12011yescharacteristic
179C2×C4×C29#12111yescharacteristic
180C2×C4×C29#12111yescharacteristic
181C2×C4×C29#12111yescharacteristic
182C2×C4×C29C2×D812yes—
183C2×C4×C29AGL(1,ℤ/8)12yes—
184C8×C29—24no—
185C8×C29—42no—
186C8×C29—42no—
187#3245C2×C2911yescharacteristic, complemented
188#3205C2×C2911yescharacteristic, complemented
189#3151C2×C2911yescharacteristic, complemented
190#1982C2×C2911yescharacteristic, complemented
191#1980C2×C2911yescharacteristic, complemented
192#1502C2×C2911yescharacteristic, complemented
193#1283C2×C2911yescharacteristic, complemented
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—82no—
197C22×C29—81no—
198C22×C29—81no—
199C22×C29—82no—
200C22×C29—81no—
201C22×C29—81no—
202C22×C29—81no—
203C22×C29—81no—
204C22×C29—82no—
205C22×C29—162no—
206C22×C29—162no—
207C22×C29#39211yescharacteristic
208C22×C29#49311yescharacteristic
209C22×C29#49611yescharacteristic
210C4×C29—21no—
211C4×C29—21no—
212C4×C29—21no—
213C4×C29—82no—
214C4×C29—81no—
215C4×C29—81no—
216C4×C29#44712yes—
217C4×C29#45311yescharacteristic
218C4×C29#45411yescharacteristic
219C4×C29#45912yes—
220C2×AGL(1,ℤ/8)—22no—
221#532C22×C2911yescharacteristic
222#532C22×C2911yescharacteristic
223C2×#127C22×C2911yescharacteristic
224#496—22no—
225#493—21no—
226#493—21no—
227#492—21no—
228#486—21no—
229#474—21no—
230#474—21no—
231#466—22no—
232#459—22no—
233#459—21no—
234#459—21no—
235#447—22no—
236#431C22×C2911yescharacteristic
237C2×C4⋊C8C22×C2911yescharacteristic
238C2×#104—22no—
239C2×#102—22no—
240C4×M16C22×C2911yescharacteristic
241C4×C4⋊C4C22×C2911yescharacteristic
242#327—22no—
243C2×C29—21no—
244C2×C29—21no—
245C2×C29—161no—
246C2×C29—161no—
247C2×C29—162no—
248C2×C29#200611yescharacteristic
249C2×C29#200811yescharacteristic
250C2×C29#201111yescharacteristic
251C2×#41—21no—
252C2×#41—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256AGL(1,ℤ/8)—44no—
257AGL(1,ℤ/8)—44no—
258C2×SD16—24no—
259C2×D8—24no—
260C2×D8—24no—
261C2×D8—22no—
262C2×M16D4×C2912yes—
263C22×C8D4×C2912yes—
264C4⋊Q8D4×C2911yescharacteristic
265C4⋊Q8D4×C2911yescharacteristic
266#127—21no—
267#127—21no—
268#127—21no—
269#127D4×C2912yes—
270#127D4×C2911yescharacteristic
271#127D4×C2911yescharacteristic
272#124—21no—
273#124—21no—
274#121—21no—
275#121—21no—
276#121—21no—
277#121—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C2×C4⋊C4—21no—
283C2×C42—21no—
284C2×C42C23×C2911yescharacteristic
285#107—22no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289#104—44no—
290#102—24no—
291#102—22no—
292#102—22no—
293#102—44no—
294C22⋊C8D4×C2912yes—
295#97—21no—
296C4×C8—21no—
297C4×C8—21no—
298#95—21no—
299C29#1019211yescharacteristic, direct product factor, Sylow
300C24—41no—
301#41—42no—
302#41—42no—
303#41—42no—
304#41—42no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—82no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4C2×D4×C2911yescharacteristic
330C22×C4C2×D4×C2911yescharacteristic
331C22×C4C2×D4×C2911yescharacteristic
332SD16—48no—
333D8—48no—
334D8—84no—
335D8—82no—
336M16—22no—
337M16D8×C2914yescomplemented
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—42no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—42no—
353C42C2×D4×C2911yescharacteristic
354C42C2×D4×C2911yescharacteristic
355C42C2×D4×C2911yescharacteristic
356C42#41×C2911yescharacteristic
357C23—41no—
358C23—41no—
359C23—42no—
360C23—82no—
361C23—82no—
362C23—81no—
363C23—81no—
364C23C29×#12711yescharacteristic
365Q8—42no—
366Q8—42no—
367D4—42no—
368D4—44no—
369D4—44no—
370D4—42no—
371D4—44no—
372D4—41no—
373D4—41no—
374D4—41no—
375D4—41no—
376D4—42no—
377D4—81no—
378D4—82no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—82no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4C29×#12011yescharacteristic
397C2×C4C29×#12011yescharacteristic
398C2×C4C29×#12011yescharacteristic
399C2×C4C29×#12111yescharacteristic
400C2×C4C29×#12111yescharacteristic
401C2×C4C29×#12111yescharacteristic
402C2×C4C2×D8×C2912yes—
403C2×C4C29×AGL(1,ℤ/8)12yes—
404C8—24no—
405C8—42no—
406C8—42no—
407C22—21no—
408C22—21no—
409C22—82no—
410C22—81no—
411C22—81no—
412C22—82no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—82no—
418C22—162no—
419C22—162no—
420C22C29×#39211yescharacteristic
421C22C29×#49311yescharacteristic
422C22C29×#49611yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—82no—
427C4—81no—
428C4—81no—
429C4C29×#44712yes—
430C4C29×#45311yescharacteristic
431C4C29×#45411yescharacteristic
432C4C29×#45912yes—
433C2—21no—
434C2—21no—
435C2—162no—
436C2—161no—
437C2—161no—
438C2C29×#200611yescharacteristic
439C2C29×#200811yescharacteristic
440C2C29×#201111yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3245C2semidirect
2. C29×#3205C2semidirect
3. C29×#3151C2semidirect
4. C29×#1982C2semidirect
5. C29×#1980C2semidirect
6. C29×#1502C2semidirect
7. C29×#1283C2semidirect
116. M16×C29D8semidirect
136. #10192C29direct (N × H)
187. #3245C2×C29semidirect
188. #3205C2×C29semidirect
189. #3151C2×C29semidirect
190. #1982C2×C29semidirect
191. #1980C2×C29semidirect
192. #1502C2×C29semidirect
193. #1283C2×C29semidirect
299. C29#10192direct (N × H)
337. M16D8×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#32452
C29×#32052
C29×#31512
C29×#19822
C29×#19802
C29×#15022
C29×#12832
#1019229