Finite Group Databasebeta

← C29×#10070 #20304970

Subgroups — C29×#10070 #20304970

Order 7424.

790 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#486C211yesmaximal, characteristic, complemented
2C2×C29×#474C211yesmaximal, characteristic, complemented
3C29×#2541C211yesmaximal, characteristic
4C29×#1981C211yesmaximal, characteristic, complemented
5C2×C29×#331C211yesmaximal, characteristic, complemented
6C2×C29×D4⋊C8C211yesmaximal, characteristic, complemented
7C29×#1279C211yesmaximal, characteristic, complemented
8C2×C29×C4⋊Q8C2211yescharacteristic
9C2×C29×#127—21no—
10C2×C29×#127C2211yescharacteristic
11C2×C29×#121—22no—
12C2×C4×D4×C29C2211yescharacteristic
13C29×#486—22no—
14C29×#486—22no—
15C29×#474—22no—
16C29×#474—22no—
17C2×C29×#107—21no—
18C2×C29×C4⋊C8C2211yescharacteristic
19C2×C29×C4⋊C8C2211yescharacteristic
20C2×C29×#103—22no—
21C2×C29×#102—21no—
22C2×C29×#102—22no—
23C2×C4×C8×C29C2211yescharacteristic
24C29×#392—22no—
25C29×#390—21no—
26C4×C4⋊C4×C29C2211yescharacteristic
27C29×#331—22no—
28C29×D4⋊C8—22no—
29C22×Q8×C29—21no—
30C22×D4×C29—24no—
31C22×D4×C29—21no—
32C22×D4×C29—21no—
33C22×D4×C29D411yescharacteristic
34C22×D4×C29D412yes—
35C23×C4×C29—21no—
36C22×C8×C29—21no—
37C22×C8×C29—21no—
38C22×C8×C29—21no—
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8D412yescomplemented
43C29×#127—21no—
44C29×#127—21no—
45C29×#127—21no—
46C29×#127—21no—
47C29×#127—42no—
48C29×#127—42no—
49C29×#121—44no—
50C29×#121—44no—
51C4×D4×C29—21no—
52C4×D4×C29—21no—
53C4×D4×C29—21no—
54C4×D4×C29—21no—
55C2×C4⋊C4×C29—21no—
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29D411yescharacteristic
58C2×C4⋊C4×C29D412yes—
59C2×C22⋊C4×C29—24no—
60C2×C22⋊C4×C29—21no—
61C2×C42×C29—21no—
62C2×C42×C29C2311yescharacteristic
63C29×#107—24no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8D412yescomplemented
68C29×#103—44no—
69C29×#102—24no—
70C29×#102—28no—
71C4×C8×C29—21no—
72C4×C8×C29D412yescomplemented
73C29×#95—21no—
74C24×C29—21no—
75C24×C29—22no—
76C2×Q8×C29—22no—
77C2×Q8×C29—41no—
78C2×Q8×C29—42no—
79C2×Q8×C29—42no—
80C2×D4×C29—21no—
81C2×D4×C29—22no—
82C2×D4×C29—21no—
83C2×D4×C29—22no—
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—21no—
87C2×D4×C29—44no—
88C2×D4×C29—48no—
89C2×D4×C29—48no—
90C2×D4×C29—41no—
91C2×D4×C29—41no—
92C2×D4×C29—41no—
93C2×D4×C29—41no—
94C2×D4×C29—42no—
95C2×D4×C29—41no—
96C2×D4×C29—41no—
97C2×D4×C29—42no—
98C2×D4×C29—41no—
99C2×D4×C29—41no—
100C2×D4×C29—84no—
101C2×D4×C29SD1612yes—
102C22×C4×C29—22no—
103C22×C4×C29—21no—
104C22×C4×C29—41no—
105C22×C4×C29—41no—
106C22×C4×C29—41no—
107C22×C4×C29—42no—
108C22×C4×C29—42no—
109C22×C4×C29C2×D411yescharacteristic
110C22×C4×C29C2×D411yescharacteristic
111C22×C4×C29C2×D411yescharacteristic
112C2×C8×C29—22no—
113C2×C8×C29—22no—
114C2×C8×C29—42no—
115C2×C8×C29—41no—
116C2×C8×C29—41no—
117C2×C8×C29—41no—
118C2×C8×C29—42no—
119C4⋊C4×C29—22no—
120C4⋊C4×C29—22no—
121C4⋊C4×C29—22no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29—41no—
125C4⋊C4×C29—41no—
126C4⋊C4×C29D814yes—
127C22⋊C4×C29—48no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29—41no—
130C42×C29—41no—
131C42×C29—41no—
132C42×C29C2×D411yescharacteristic
133C42×C29C2×D411yescharacteristic
134C42×C29C2×D411yescharacteristic
135C42×C29#4111yescharacteristic
136#10070C2911yesmaximal, characteristic, direct product factor, Sylow
137C23×C29—22no—
138C23×C29—41no—
139C23×C29—42no—
140C23×C29—41no—
141C23×C29—42no—
142C23×C29—42no—
143C23×C29—44no—
144C23×C29—42no—
145C23×C29—42no—
146C23×C29—44no—
147C23×C29#12011yescharacteristic
148Q8×C29—44no—
149Q8×C29—81no—
150Q8×C29—81no—
151D4×C29—22no—
152D4×C29—22no—
153D4×C29—44no—
154D4×C29—41no—
155D4×C29—41no—
156D4×C29—82no—
157D4×C29—816no—
158D4×C29—81no—
159D4×C29—81no—
160D4×C29—82no—
161D4×C29—81no—
162D4×C29—81no—
163D4×C29—81no—
164D4×C29—81no—
165C2×C4×C29—22no—
166C2×C4×C29—24no—
167C2×C4×C29—42no—
168C2×C4×C29—42no—
169C2×C4×C29—41no—
170C2×C4×C29—42no—
171C2×C4×C29—42no—
172C2×C4×C29—82no—
173C2×C4×C29—82no—
174C2×C4×C29—81no—
175C2×C4×C29—81no—
176C2×C4×C29#12011yescharacteristic
177C2×C4×C29#12011yescharacteristic
178C2×C4×C29#12111yescharacteristic
179C2×C4×C29#12111yescharacteristic
180C2×C4×C29#12111yescharacteristic
181C2×C4×C29#12711yescharacteristic
182C2×C4×C29C2×D812yes—
183C2×C4×C29C2×SD1611yescharacteristic
184C2×C4×C29#13511yescharacteristic
185C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C29AGL(1,ℤ/8)12yes—
187C2×C4×C29#13711yescharacteristic
188C8×C29—42no—
189C8×C29—42no—
190C8×C29—81no—
191C2×#486C2×C2911yescharacteristic, complemented
192C2×#474C2×C2911yescharacteristic, complemented
193#2541C2×C2911yescharacteristic
194#1981C2×C2911yescharacteristic, complemented
195C2×#331C2×C2911yescharacteristic, complemented
196C2×D4⋊C8C2×C2911yescharacteristic, complemented
197#1279C2×C2911yescharacteristic, complemented
198C22×C29—44no—
199C22×C29—42no—
200C22×C29—82no—
201C22×C29—81no—
202C22×C29—81no—
203C22×C29—84no—
204C22×C29—84no—
205C22×C29—82no—
206C22×C29—82no—
207C22×C29—82no—
208C22×C29#39211yescharacteristic
209C22×C29#44712yes—
210C22×C29#45011yescharacteristic
211C22×C29#45211yescharacteristic
212C22×C29#45512yes—
213C4×C29—21no—
214C4×C29—21no—
215C4×C29—44no—
216C4×C29—81no—
217C4×C29—82no—
218C4×C29#44811yescharacteristic
219C4×C29#44911yescharacteristic
220C4×C29#45912yes—
221C4×C29#46511yescharacteristic
222C4×C29#46811yescharacteristic
223C4×C29#49311yescharacteristic
224C4×C29#49611yescharacteristic
225C2×C4⋊Q8C22×C2911yescharacteristic
226C2×#127—21no—
227C2×#127C22×C2911yescharacteristic
228C2×#121—22no—
229C2×C4×D4C22×C2911yescharacteristic
230#486—22no—
231#486—22no—
232#474—22no—
233#474—22no—
234C2×#107—21no—
235C2×C4⋊C8C22×C2911yescharacteristic
236C2×C4⋊C8C22×C2911yescharacteristic
237C2×#103—22no—
238C2×#102—22no—
239C2×#102—21no—
240C2×C4×C8C22×C2911yescharacteristic
241#392—22no—
242#390—21no—
243C4×C4⋊C4C22×C2911yescharacteristic
244#331—22no—
245D4⋊C8—22no—
246C2×C29—82no—
247C2×C29—162no—
248C2×C29#163912yes—
249C2×C29#164112yes—
250C2×C29#200011yescharacteristic
251C2×C29#200411yescharacteristic
252C2×C29#201111yescharacteristic
253C22×Q8—21no—
254C22×D4—24no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4D4×C2911yescharacteristic
258C22×D4D4×C2912yes—
259C23×C4—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8D4×C2912yescomplemented
267#127—21no—
268#127—21no—
269#127—21no—
270#127—21no—
271#127—42no—
272#127—42no—
273#121—44no—
274#121—44no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4D4×C2911yescharacteristic
282C2×C4⋊C4D4×C2912yes—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—21no—
285C2×C42—21no—
286C2×C42C23×C2911yescharacteristic
287#107—24no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8D4×C2912yescomplemented
292#103—44no—
293#102—24no—
294#102—28no—
295C4×C8—21no—
296C4×C8D4×C2912yescomplemented
297#95—21no—
298C29#1007011yescharacteristic, direct product factor, Sylow
299C24—21no—
300C24—22no—
301C2×Q8—22no—
302C2×Q8—41no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—44no—
313C2×D4—48no—
314C2×D4—48no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—42no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—42no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—84no—
326C2×D4SD16×C2912yes—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4C2×D4×C2911yescharacteristic
335C22×C4C2×D4×C2911yescharacteristic
336C22×C4C2×D4×C2911yescharacteristic
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—42no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4D8×C2914yes—
352C22⋊C4—48no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—41no—
356C42—41no—
357C42C2×D4×C2911yescharacteristic
358C42C2×D4×C2911yescharacteristic
359C42C2×D4×C2911yescharacteristic
360C42#41×C2911yescharacteristic
361C23—22no—
362C23—42no—
363C23—41no—
364C23—42no—
365C23—41no—
366C23—44no—
367C23—42no—
368C23—42no—
369C23—44no—
370C23—42no—
371C23C29×#12011yescharacteristic
372Q8—44no—
373Q8—81no—
374Q8—81no—
375D4—22no—
376D4—22no—
377D4—44no—
378D4—41no—
379D4—41no—
380D4—82no—
381D4—816no—
382D4—81no—
383D4—81no—
384D4—82no—
385D4—81no—
386D4—81no—
387D4—81no—
388D4—81no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4C29×#12011yescharacteristic
401C2×C4C29×#12011yescharacteristic
402C2×C4C29×#12111yescharacteristic
403C2×C4C29×#12111yescharacteristic
404C2×C4C29×#12111yescharacteristic
405C2×C4C29×#12711yescharacteristic
406C2×C4C2×D8×C2912yes—
407C2×C4C2×SD16×C2911yescharacteristic
408C2×C4C29×#13511yescharacteristic
409C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
410C2×C4C29×AGL(1,ℤ/8)12yes—
411C2×C4C29×#13711yescharacteristic
412C8—42no—
413C8—42no—
414C8—81no—
415C22—42no—
416C22—44no—
417C22—81no—
418C22—81no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22—84no—
424C22—84no—
425C22C29×#39211yescharacteristic
426C22C29×#44712yes—
427C22C29×#45011yescharacteristic
428C22C29×#45211yescharacteristic
429C22C29×#45512yes—
430C4—21no—
431C4—21no—
432C4—44no—
433C4—81no—
434C4—82no—
435C4C29×#44811yescharacteristic
436C4C29×#44911yescharacteristic
437C4C29×#45912yes—
438C4C29×#46511yescharacteristic
439C4C29×#46811yescharacteristic
440C4C29×#49311yescharacteristic
441C4C29×#49611yescharacteristic
442C2—82no—
443C2—162no—
444C2C29×#163912yes—
445C2C29×#164112yes—
446C2C29×#200011yescharacteristic
447C2C29×#200411yescharacteristic
448C2C29×#201111yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#2541C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#486C2semidirect
2. C2×C29×#474C2semidirect
4. C29×#1981C2semidirect
5. C2×C29×#331C2semidirect
6. C2×C29×D4⋊C8C2semidirect
7. C29×#1279C2semidirect
42. C29×C4⋊Q8D4semidirect
67. C29×C4⋊C8D4semidirect
72. C4×C8×C29D4semidirect
136. #10070C29direct (N × H)
191. C2×#486C2×C29semidirect
192. C2×#474C2×C29semidirect
194. #1981C2×C29semidirect
195. C2×#331C2×C29semidirect
196. C2×D4⋊C8C2×C29semidirect
197. #1279C2×C29semidirect
266. C4⋊Q8D4×C29semidirect
291. C4⋊C8D4×C29semidirect
296. C4×C8D4×C29semidirect
298. C29#10070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4862
C2×C29×#4742
C29×#25412
C29×#19812
C2×C29×#3312
C2×C29×D4⋊C82
C29×#12792
#1007029