Finite Group Databasebeta

← C29×#33223 #20328123

Subgroups — C29×#33223 #20328123

Order 7424.

714 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#501C211yesmaximal, characteristic, complemented
2C29×#3080C211yesmaximal, characteristic
3C29×#3079C211yesmaximal, characteristic
4C29×#2875C211yesmaximal, characteristic
5C29×#1998C211yesmaximal, characteristic, complemented
6C29×#1997C211yesmaximal, characteristic, complemented
7C29×#1952C212yesmaximal, complemented
8C29×#1951C212yesmaximal, complemented
9C29×#1849C211yesmaximal, characteristic, complemented
10C29×#1816C212yesmaximal
11C29×#1815C212yesmaximal
12C2×C29×#131C2212yes—
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C29×#125C2211yescharacteristic
15C4×#41×C29C2211yescharacteristic
16C29×#501—21no—
17C29×#501—21no—
18C29×#501—22no—
19C29×#479—21no—
20C29×#479—21no—
21C29×#478—21no—
22C29×#478—21no—
23C29×#477—21no—
24C29×#476—21no—
25C29×#475—21no—
26C29×#474—21no—
27C2×C29×#108C2212yes—
28C2×C29×#108C2212yes—
29C29×#428C2211yescharacteristic
30C29×#428C2212yes—
31C29×#428C2211yescharacteristic
32C2×C29×#107C2212yes—
33C2×C29×#106C2212yes—
34C29×#423C2211yescharacteristic
35C29×#423C2211yescharacteristic
36C29×#417C2212yes—
37C29×#417C2211yescharacteristic
38C29×#417C2211yescharacteristic
39C29×#405—22no—
40C29×#405C2212yes—
41C4×M16×C29—21no—
42C4×M16×C29C2211yescharacteristic
43C2×C29×#97—21no—
44C2×C29×#97C2211yescharacteristic
45C29×#343C2212yes—
46C29×#343C2212yes—
47C29×#343C2212yes—
48C29×#343C2212yes—
49C2×#41×C29C2311yescharacteristic
50C22×Q8×C29—21no—
51C29×#131—24no—
52C29×#131Q818yescomplemented
53C2×M16×C29—22no—
54C2×M16×C29C2311yescharacteristic
55C2×M16×C29C2312yes—
56C2×M16×C29C2311yescharacteristic
57C2×M16×C29C2312yes—
58C22×C8×C29—22no—
59C22×C8×C29C2312yes—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×#125—21no—
65C29×#125—21no—
66C29×#125—21no—
67C29×#125—21no—
68C4×Q8×C29D411yescharacteristic
69C4×Q8×C29D411yescharacteristic
70C4×D4×C29—21no—
71C4×D4×C29—21no—
72C4×D4×C29D411yescharacteristic
73C4×D4×C29D411yescharacteristic
74C29×#117—21no—
75C29×#117C2311yescharacteristic
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29C2311yescharacteristic
80C2×C4⋊C4×C29C2312yes—
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C42×C29—21no—
83C2×C42×C29C2311yescharacteristic
84C29×#108—24no—
85C29×#108—24no—
86C29×#107—22no—
87C29×#107—22no—
88C29×#107—22no—
89C29×#107—21no—
90C29×#107—21no—
91C29×#106—22no—
92C29×#106—22no—
93C29×#106—22no—
94C29×#106—21no—
95C29×#106—21no—
96C29×C4⋊C8—21no—
97C29×C4⋊C8—21no—
98C29×C4⋊C8—21no—
99C29×C4⋊C8—21no—
100C29×#103—22no—
101C29×#103—21no—
102C29×#103—21no—
103C29×#102—22no—
104C29×#102—21no—
105C29×#102—21no—
106C29×#97—22no—
107C29×#97—21no—
108C29×#97D411yescharacteristic
109C29×#97D411yescharacteristic
110C29×#97D412yes—
111C4×C8×C29—22no—
112C4×C8×C29—21no—
113#41×C29—22no—
114#41×C29C2×Q814yes—
115C2×Q8×C29—41no—
116C2×Q8×C29—41no—
117C2×Q8×C29—82no—
118C2×Q8×C29C2×D411yescharacteristic
119C2×D4×C29—21no—
120C2×D4×C29C2×D411yescharacteristic
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—22no—
127C22×C4×C29#4111yescharacteristic
128C22×C4×C29#4111yescharacteristic
129C22×C4×C29C2411yescharacteristic
130M16×C29—22no—
131M16×C29—28no—
132M16×C29—22no—
133M16×C29—22no—
134M16×C29—22no—
135M16×C29—22no—
136M16×C29C2×Q814yes—
137C2×C8×C29—22no—
138C2×C8×C29—28no—
139C2×C8×C29—22no—
140C2×C8×C29—21no—
141C2×C8×C29—21no—
142C2×C8×C29C2×D412yes—
143C2×C8×C29C2×D412yes—
144C2×C8×C29C2×Q814yes—
145C2×C8×C29#4114yes—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—22no—
153C4⋊C4×C29—22no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29—41no—
157C4⋊C4×C29—41no—
158C4⋊C4×C29—41no—
159C4⋊C4×C29—41no—
160C4⋊C4×C29C2×D411yescharacteristic
161C4⋊C4×C29C2×D411yescharacteristic
162C22⋊C4×C29—21no—
163C22⋊C4×C29—21no—
164C22⋊C4×C29—21no—
165C42×C29—21no—
166C42×C29—21no—
167C42×C29—21no—
168C42×C29C2×D411yescharacteristic
169C42×C29C2×D411yescharacteristic
170C42×C29C2×D411yescharacteristic
171C42×C29C2×D411yescharacteristic
172#33223C2911yesmaximal, characteristic, direct product factor, Sylow
173C23×C29—21no—
174C23×C29C2×#4111yescharacteristic
175Q8×C29—21no—
176Q8×C29—82no—
177Q8×C29—82no—
178Q8×C29C4⋊Q812yes—
179D4×C29—24no—
180D4×C29—21no—
181D4×C29C4⋊Q812yes—
182C2×C4×C29—21no—
183C2×C4×C29—24no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—41no—
187C2×C4×C29—41no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—42no—
191C2×C4×C29—81no—
192C2×C4×C29—81no—
193C2×C4×C29—81no—
194C2×C4×C29—81no—
195C2×C4×C29—82no—
196C2×C4×C29#12111yescharacteristic
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29#12111yescharacteristic
200C2×C4×C29C22×D411yescharacteristic
201C2×C4×C29C22×D411yescharacteristic
202C2×C4×C29C22×Q812yes—
203C2×C4×C29C2×#4112yes—
204C8×C29—24no—
205C8×C29—42no—
206C8×C29—41no—
207C8×C29—41no—
208C8×C29C22⋊Q814yes—
209C8×C29C22⋊Q814yes—
210C2×#501C2×C2911yescharacteristic, complemented
211#3080C2×C2911yescharacteristic
212#3079C2×C2911yescharacteristic
213#2875C2×C2911yescharacteristic
214#1998C2×C2911yescharacteristic, complemented
215#1997C2×C2911yescharacteristic, complemented
216#1952C2×C2912yescomplemented
217#1951C2×C2912yescomplemented
218#1849C2×C2911yescharacteristic, complemented
219#1816C2×C2912yes—
220#1815C2×C2912yes—
221C22×C29—21no—
222C22×C29—21no—
223C22×C29—22no—
224C22×C29—41no—
225C22×C29—41no—
226C22×C29C2×#12111yescharacteristic
227C22×C29#53312yes—
228C4×C29—22no—
229C4×C29—21no—
230C4×C29—21no—
231C4×C29—21no—
232C4×C29—21no—
233C4×C29—41no—
234C4×C29—41no—
235C4×C29—81no—
236C4×C29—82no—
237C4×C29—81no—
238C4×C29C2×C22⋊Q812yes—
239C4×C29C2×C4⋊Q811yescharacteristic
240C4×C29#53211yescharacteristic
241C2×#131C22×C2912yes—
242C2×C4⋊Q8C22×C2911yescharacteristic
243C2×#125C22×C2911yescharacteristic
244C4×#41C22×C2911yescharacteristic
245#501—21no—
246#501—21no—
247#501—22no—
248#479—21no—
249#479—21no—
250#478—21no—
251#478—21no—
252#477—21no—
253#476—21no—
254#475—21no—
255#474—21no—
256C2×#108C22×C2912yes—
257C2×#108C22×C2912yes—
258#428C22×C2912yes—
259#428C22×C2911yescharacteristic
260#428C22×C2911yescharacteristic
261C2×#107C22×C2912yes—
262C2×#106C22×C2912yes—
263#423C22×C2911yescharacteristic
264#423C22×C2911yescharacteristic
265#417C22×C2912yes—
266#417C22×C2911yescharacteristic
267#417C22×C2911yescharacteristic
268#405—22no—
269#405C22×C2912yes—
270C4×M16—21no—
271C4×M16C22×C2911yescharacteristic
272C2×#97—21no—
273C2×#97C22×C2911yescharacteristic
274#343C22×C2912yes—
275#343C22×C2912yes—
276#343C22×C2912yes—
277#343C22×C2912yes—
278C2×C29—22no—
279C2×C29—42no—
280C2×C29#285711yescharacteristic
281C2×C29#306811yescharacteristic
282C2×C29#306911yescharacteristic
283C2×#41C23×C2911yescharacteristic
284C22×Q8—21no—
285#131—24no—
286#131Q8×C2918yescomplemented
287C2×M16—22no—
288C2×M16C23×C2912yes—
289C2×M16C23×C2911yescharacteristic
290C2×M16C23×C2911yescharacteristic
291C2×M16C23×C2912yes—
292C22×C8—22no—
293C22×C8C23×C2912yes—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298#125—21no—
299#125—21no—
300#125—21no—
301#125—21no—
302C4×Q8D4×C2911yescharacteristic
303C4×Q8D4×C2911yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C4×D4D4×C2911yescharacteristic
307C4×D4D4×C2911yescharacteristic
308#117—21no—
309#117C23×C2911yescharacteristic
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4C23×C2911yescharacteristic
314C2×C4⋊C4C23×C2911yescharacteristic
315C2×C4⋊C4C23×C2912yes—
316C2×C42—21no—
317C2×C42C23×C2911yescharacteristic
318#108—24no—
319#108—24no—
320#107—22no—
321#107—22no—
322#107—22no—
323#107—21no—
324#107—21no—
325#106—22no—
326#106—22no—
327#106—22no—
328#106—21no—
329#106—21no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334#103—22no—
335#103—21no—
336#103—21no—
337#102—22no—
338#102—21no—
339#102—21no—
340#97—22no—
341#97—21no—
342#97D4×C2911yescharacteristic
343#97D4×C2911yescharacteristic
344#97D4×C2912yes—
345C4×C8—22no—
346C4×C8—21no—
347C29#3322311yescharacteristic, direct product factor, Sylow
348#41—22no—
349#41C2×Q8×C2914yes—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—82no—
353C2×Q8C2×D4×C2911yescharacteristic
354C2×D4—21no—
355C2×D4C2×D4×C2911yescharacteristic
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4#41×C2911yescharacteristic
363C22×C4#41×C2911yescharacteristic
364C22×C4C24×C2911yescharacteristic
365M16—22no—
366M16—28no—
367M16—22no—
368M16—22no—
369M16—22no—
370M16—22no—
371M16C2×Q8×C2914yes—
372C2×C8—22no—
373C2×C8—28no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8C2×D4×C2912yes—
378C2×C8C2×D4×C2912yes—
379C2×C8C2×Q8×C2914yes—
380C2×C8#41×C2914yes—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4C2×D4×C2911yescharacteristic
396C4⋊C4C2×D4×C2911yescharacteristic
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42C2×D4×C2911yescharacteristic
404C42C2×D4×C2911yescharacteristic
405C42C2×D4×C2911yescharacteristic
406C42C2×D4×C2911yescharacteristic
407C23—21no—
408C23C2×#41×C2911yescharacteristic
409Q8—21no—
410Q8—82no—
411Q8—82no—
412Q8C29×C4⋊Q812yes—
413D4—24no—
414D4—21no—
415D4C29×C4⋊Q812yes—
416C2×C4—21no—
417C2×C4—24no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—82no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4C29×#12111yescharacteristic
431C2×C4C29×#12111yescharacteristic
432C2×C4C29×#12111yescharacteristic
433C2×C4C29×#12111yescharacteristic
434C2×C4C22×D4×C2911yescharacteristic
435C2×C4C22×D4×C2911yescharacteristic
436C2×C4C22×Q8×C2912yes—
437C2×C4C2×#41×C2912yes—
438C8—24no—
439C8—42no—
440C8—41no—
441C8—41no—
442C8C29×C22⋊Q814yes—
443C8C29×C22⋊Q814yes—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—41no—
448C22—41no—
449C22C2×C29×#12111yescharacteristic
450C22C29×#53312yes—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—22no—
456C4—41no—
457C4—41no—
458C4—82no—
459C4—81no—
460C4—81no—
461C4C2×C29×C22⋊Q812yes—
462C4C2×C29×C4⋊Q811yescharacteristic
463C4C29×#53211yescharacteristic
464C2—22no—
465C2—42no—
466C2C29×#285711yescharacteristic
467C2C29×#306811yescharacteristic
468C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×#41×C29C23
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×#1998C2semidirect
6. C29×#1997C2semidirect
7. C29×#1952C2semidirect
8. C29×#1951C2semidirect
9. C29×#1849C2semidirect
52. C29×#131Q8semidirect
172. #33223C29direct (N × H)
210. C2×#501C2×C29semidirect
214. #1998C2×C29semidirect
215. #1997C2×C29semidirect
216. #1952C2×C29semidirect
217. #1951C2×C29semidirect
218. #1849C2×C29semidirect
286. #131Q8×C29semidirect
347. C29#33223direct (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×#30802
C29×#30792
C29×#28752
C29×#19982
C29×#19972
C29×#19522
C29×#19512
C29×#18492
C29×#18162
C29×#18152
#3322329