Finite Group Databasebeta

← C29×#25490 #20320390

Subgroups — C29×#25490 #20320390

Order 7424.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3165C211yesmaximal, characteristic, complemented
2C29×#3077C211yesmaximal, characteristic
3C2×C29×#476C211yesmaximal, characteristic
4C29×#2962C211yesmaximal, characteristic, complemented
5C29×#2090C212yesmaximal, complemented
6C29×#2063C212yesmaximal
7C29×#1997C211yesmaximal, characteristic, complemented
8C29×#1951C212yesmaximal, complemented
9C29×#1950C211yesmaximal, characteristic, complemented
10C29×#1931C212yesmaximal
11C4×C29×#100C211yesmaximal, characteristic
12C29×#533C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C29C2211yescharacteristic
15C29×#501—22no—
16C29×#500—21no—
17C29×#498—21no—
18C29×#478—22no—
19C29×#476—21no—
20C29×#476—21no—
21C29×#476—22no—
22C29×#476—21no—
23C29×#474—21no—
24C29×#446—21no—
25C29×#446—22no—
26C8×Q8×C29—21no—
27C2×C29×#108C2212yes—
28C29×#428C2212yes—
29C29×#428C2212yes—
30C29×#428C2212yes—
31C2×C29×#106C2212yes—
32C29×#424C2212yes—
33C29×#423C2211yescharacteristic
34C2×C29×C4⋊C8C2211yescharacteristic
35C29×#418C2212yes—
36C2×C29×#102C2212yes—
37C2×C29×#100C2211yescharacteristic
38C2×C29×#100C2211yescharacteristic
39C29×#405C2212yes—
40C4×M16×C29C2211yescharacteristic
41C4×M16×C29C2211yescharacteristic
42C29×#343C2212yes—
43C29×#343C2211yescharacteristic
44C29×#343C2212yes—
45C29×#343C2211yescharacteristic
46C29×#341C2212yes—
47C22×Q8×C29—21no—
48C22×D4×C29C2311yescharacteristic
49C23×C4×C29—21no—
50C2×M16×C29C2312yes—
51C2×M16×C29C2311yescharacteristic
52C2×M16×C29C2311yescharacteristic
53C2×M16×C29C2311yescharacteristic
54C2×M16×C29C2311yescharacteristic
55C22×C8×C29C2312yes—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8D411yescharacteristic
61C29×C4⋊Q8D411yescharacteristic
62C29×#125D412yes—
63C29×C22⋊Q8—21no—
64C29×C22⋊Q8—21no—
65C4×Q8×C29—21no—
66C4×Q8×C29—21no—
67C4×D4×C29—21no—
68C4×D4×C29—21no—
69C4×D4×C29—21no—
70C4×D4×C29—21no—
71C29×#117C2312yes—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29C2311yescharacteristic
74C2×C4⋊C4×C29C2312yes—
75C2×C22⋊C4×C29—21no—
76C2×C42×C29C2311yescharacteristic
77C29×#108—24no—
78C29×#107—22no—
79C29×#107—22no—
80C29×#107—22no—
81C29×#106—22no—
82C29×#106—22no—
83C29×#106—22no—
84C29×#106—22no—
85C29×#106—22no—
86C29×C4⋊C8—22no—
87C29×C4⋊C8—22no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8D411yescharacteristic
91C29×C4⋊C8D411yescharacteristic
92C29×C4⋊C8D412yes—
93C29×#102—22no—
94C29×#102—22no—
95C29×#102—22no—
96C29×#102—22no—
97C29×#100—22no—
98C29×#100Q814yescomplemented
99C29×#97—22no—
100C29×#97—21no—
101C29×#97—21no—
102C4×C8×C29—22no—
103C4×C8×C29—21no—
104C4×C8×C29—21no—
105C24×C29—21no—
106C2×Q8×C29—21no—
107C2×Q8×C29—21no—
108C2×Q8×C29—41no—
109C2×Q8×C29—41no—
110C2×Q8×C29—82no—
111C2×D4×C29—21no—
112C2×D4×C29—21no—
113C2×D4×C29—21no—
114C2×D4×C29—21no—
115C2×D4×C29—21no—
116C2×D4×C29C2×Q812yes—
117C22×C4×C29—21no—
118C22×C4×C29—22no—
119C22×C4×C29—41no—
120C22×C4×C29—41no—
121C22×C4×C29—82no—
122C22×C4×C29#4111yescharacteristic
123C22×C4×C29#4111yescharacteristic
124C22×C4×C29C2411yescharacteristic
125M16×C29—21no—
126M16×C29—21no—
127M16×C29—21no—
128M16×C29—21no—
129M16×C29—22no—
130M16×C29—21no—
131M16×C29—22no—
132M16×C29C2×Q812yes—
133M16×C29C2×Q812yes—
134M16×C29#4112yes—
135C2×C8×C29—21no—
136C2×C8×C29—21no—
137C2×C8×C29—21no—
138C2×C8×C29—22no—
139C2×C8×C29—22no—
140C2×C8×C29—21no—
141C2×C8×C29—22no—
142C2×C8×C29C2×D412yes—
143C2×C8×C29C2×D412yes—
144C4⋊C4×C29—22no—
145C4⋊C4×C29—22no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—22no—
151C4⋊C4×C29—22no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29C2×D412yes—
155C4⋊C4×C29C2×D412yes—
156C22⋊C4×C29—22no—
157C22⋊C4×C29—41no—
158C22⋊C4×C29—41no—
159C42×C29—22no—
160C42×C29C2×D411yescharacteristic
161C42×C29C2×D411yescharacteristic
162C42×C29C2×D411yescharacteristic
163C42×C29C2×D411yescharacteristic
164#25490C2911yesmaximal, characteristic, direct product factor, Sylow
165C23×C29—22no—
166C23×C29—41no—
167C23×C29—41no—
168C23×C29—81no—
169C23×C29—81no—
170C23×C29C2×#4111yescharacteristic
171Q8×C29—42no—
172Q8×C29—81no—
173Q8×C29—82no—
174Q8×C29—82no—
175D4×C29—22no—
176D4×C29—22no—
177D4×C29—41no—
178D4×C29—41no—
179C2×C4×C29—22no—
180C2×C4×C29—22no—
181C2×C4×C29—22no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—42no—
185C2×C4×C29—82no—
186C2×C4×C29—82no—
187C2×C4×C29—81no—
188C2×C4×C29—82no—
189C2×C4×C29#12111yescharacteristic
190C2×C4×C29#12111yescharacteristic
191C2×C4×C29#12111yescharacteristic
192C2×C4×C29#12111yescharacteristic
193C2×C4×C29C22×D411yescharacteristic
194C2×C4×C29C22×D411yescharacteristic
195C2×C4×C29C22×Q811yescharacteristic
196C2×C4×C29C2×#4111yescharacteristic
197C2×C4×C292−1+411yescharacteristic
198C2×C4×C292−1+411yescharacteristic
199C8×C29—22no—
200C8×C29—22no—
201C8×C29—22no—
202C8×C29—22no—
203C8×C29—22no—
204C8×C29—41no—
205C8×C29—42no—
206#3165C2×C2911yescharacteristic, complemented
207#3077C2×C2911yescharacteristic
208C2×#476C2×C2911yescharacteristic
209#2962C2×C2911yescharacteristic, complemented
210#2090C2×C2912yescomplemented
211#2063C2×C2912yes—
212#1997C2×C2911yescharacteristic, complemented
213#1951C2×C2912yescomplemented
214#1950C2×C2911yescharacteristic, complemented
215#1931C2×C2912yes—
216C4×#100C2×C2911yescharacteristic
217C22×C29—21no—
218C22×C29—21no—
219C22×C29—42no—
220C22×C29—82no—
221C22×C29—82no—
222C22×C29—81no—
223C22×C29—81no—
224C22×C29C2×#12111yescharacteristic
225C22×C29#53311yescharacteristic
226C22×C29#54111yescharacteristic
227C4×C29—21no—
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—42no—
231C4×C29—42no—
232C4×C29—81no—
233C4×C29—82no—
234C4×C29#47112yes—
235C4×C29#54711yescharacteristic
236C4×C29#54811yescharacteristic
237C4×C29D4×Q811yescharacteristic
238C4×C29D4×Q811yescharacteristic
239#533C22×C2911yescharacteristic
240C2×C4⋊Q8C22×C2911yescharacteristic
241C2×C4×D4C22×C2911yescharacteristic
242#501—22no—
243#500—21no—
244#498—21no—
245#478—22no—
246#476—21no—
247#476—21no—
248#476—22no—
249#476—21no—
250#474—21no—
251#446—22no—
252#446—21no—
253C8×Q8—21no—
254C2×#108C22×C2912yes—
255#428C22×C2912yes—
256#428C22×C2912yes—
257#428C22×C2912yes—
258C2×#106C22×C2912yes—
259#424C22×C2912yes—
260#423C22×C2911yescharacteristic
261C2×C4⋊C8C22×C2911yescharacteristic
262#418C22×C2912yes—
263C2×#102C22×C2912yes—
264C2×#100C22×C2911yescharacteristic
265C2×#100C22×C2911yescharacteristic
266#405C22×C2912yes—
267C4×M16C22×C2911yescharacteristic
268C4×M16C22×C2911yescharacteristic
269#343C22×C2912yes—
270#343C22×C2911yescharacteristic
271#343C22×C2912yes—
272#343C22×C2911yescharacteristic
273#341C22×C2912yes—
274C2×C29—21no—
275C2×C29—21no—
276C2×C29—82no—
277C2×C29#242911yescharacteristic
278C2×C29C2×#47111yescharacteristic
279C2×C29#306811yescharacteristic
280C22×Q8—21no—
281C22×D4C23×C2911yescharacteristic
282C23×C4—21no—
283C2×M16C23×C2912yes—
284C2×M16C23×C2911yescharacteristic
285C2×M16C23×C2911yescharacteristic
286C2×M16C23×C2911yescharacteristic
287C2×M16C23×C2911yescharacteristic
288C22×C8C23×C2912yes—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8D4×C2911yescharacteristic
294C4⋊Q8D4×C2911yescharacteristic
295#125D4×C2912yes—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304#117C23×C2912yes—
305C2×C4⋊C4—21no—
306C2×C4⋊C4C23×C2911yescharacteristic
307C2×C4⋊C4C23×C2912yes—
308C2×C22⋊C4—21no—
309C2×C42C23×C2911yescharacteristic
310#108—24no—
311#107—22no—
312#107—22no—
313#107—22no—
314#106—22no—
315#106—22no—
316#106—22no—
317#106—22no—
318#106—22no—
319C4⋊C8—22no—
320C4⋊C8—22no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8D4×C2911yescharacteristic
324C4⋊C8D4×C2911yescharacteristic
325C4⋊C8D4×C2912yes—
326#102—22no—
327#102—22no—
328#102—22no—
329#102—22no—
330#100—22no—
331#100Q8×C2914yescomplemented
332#97—22no—
333#97—21no—
334#97—21no—
335C4×C8—22no—
336C4×C8—21no—
337C4×C8—21no—
338C29#2549011yescharacteristic, direct product factor, Sylow
339C24—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4C2×Q8×C2912yes—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—82no—
356C22×C4#41×C2911yescharacteristic
357C22×C4#41×C2911yescharacteristic
358C22×C4C24×C2911yescharacteristic
359M16—21no—
360M16—21no—
361M16—21no—
362M16—21no—
363M16—22no—
364M16—21no—
365M16—22no—
366M16C2×Q8×C2912yes—
367M16C2×Q8×C2912yes—
368M16#41×C2912yes—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8C2×D4×C2912yes—
377C2×C8C2×D4×C2912yes—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4C2×D4×C2912yes—
389C4⋊C4C2×D4×C2912yes—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C42—22no—
394C42C2×D4×C2911yescharacteristic
395C42C2×D4×C2911yescharacteristic
396C42C2×D4×C2911yescharacteristic
397C42C2×D4×C2911yescharacteristic
398C23—22no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23C2×#41×C2911yescharacteristic
404Q8—42no—
405Q8—81no—
406Q8—82no—
407Q8—82no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—81no—
421C2×C4—82no—
422C2×C4C29×#12111yescharacteristic
423C2×C4C29×#12111yescharacteristic
424C2×C4C29×#12111yescharacteristic
425C2×C4C29×#12111yescharacteristic
426C2×C4C22×D4×C2911yescharacteristic
427C2×C4C22×D4×C2911yescharacteristic
428C2×C4C22×Q8×C2911yescharacteristic
429C2×C4C2×#41×C2911yescharacteristic
430C2×C4C29×2−1+411yescharacteristic
431C2×C4C29×2−1+411yescharacteristic
432C8—22no—
433C8—22no—
434C8—22no—
435C8—22no—
436C8—22no—
437C8—41no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—82no—
443C22—82no—
444C22—81no—
445C22—81no—
446C22C2×C29×#12111yescharacteristic
447C22C29×#53311yescharacteristic
448C22C29×#54111yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—81no—
455C4—82no—
456C4C29×#47112yes—
457C4C29×#54711yescharacteristic
458C4C29×#54811yescharacteristic
459C4D4×Q8×C2911yescharacteristic
460C4D4×Q8×C2911yescharacteristic
461C2—21no—
462C2—21no—
463C2—82no—
464C2C29×#242911yescharacteristic
465C2C2×C29×#47111yescharacteristic
466C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×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. C29×#3165C2semidirect
4. C29×#2962C2semidirect
5. C29×#2090C2semidirect
7. C29×#1997C2semidirect
8. C29×#1951C2semidirect
9. C29×#1950C2semidirect
98. C29×#100Q8semidirect
164. #25490C29direct (N × H)
206. #3165C2×C29semidirect
209. #2962C2×C29semidirect
210. #2090C2×C29semidirect
212. #1997C2×C29semidirect
213. #1951C2×C29semidirect
214. #1950C2×C29semidirect
331. #100Q8×C29semidirect
338. C29#25490direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31652
C29×#30772
C2×C29×#4762
C29×#29622
C29×#20902
C29×#20632
C29×#19972
C29×#19512
C29×#19502
C29×#19312
C4×C29×#1002
#2549029