Finite Group Databasebeta

← C29×#36698 #20331598

Subgroups — C29×#36698 #20331598

Order 7424.

1484 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2844C211yesmaximal, characteristic, complemented
2C29×#2838C214yesmaximal, complemented
3C29×#2836C214yesmaximal, complemented
4C29×#2833C212yesmaximal, complemented
5C29×#2830C212yesmaximal
6C29×#2822C211yesmaximal, characteristic, complemented
7C29×#2820C212yesmaximal
8C29×#2401C214yesmaximal, complemented
9C29×#2399C212yesmaximal, complemented
10C29×#2396C214yesmaximal, complemented
11C29×#2395C212yesmaximal
12C4×C29×#125C212yesmaximal, complemented
13C4×C29×#124C211yesmaximal, characteristic
14C2×C29×#125C2212yes—
15C2×C29×#124C2211yescharacteristic
16C2×C4×Q8×C29C2211yescharacteristic
17C2×C4×Q8×C29C2212yes—
18C2×C4×D4×C29C2211yescharacteristic
19C2×C29×#117C2212yes—
20C29×#401C2214yes—
21C29×#400C2214yes—
22C29×#400C2214yes—
23C29×#400C2214yes—
24C29×#400C2212yes—
25C29×#400C2214yes—
26C29×#399C2214yes—
27C29×#399C2212yes—
28C29×#398C2212yes—
29C29×#398C2212yes—
30C29×#398C2214yes—
31C29×#398C2214yes—
32C29×#398C2212yes—
33C29×#398C2214yes—
34C29×#397C2214yes—
35C29×#397C2214yes—
36C29×#397C2214yes—
37C29×#397C2212yes—
38C29×#397C2214yes—
39C29×#396C2214yes—
40C29×#396C2214yes—
41C29×#396C2214yes—
42C29×#395C2214yes—
43C29×#395C2212yes—
44C29×#395C2212yes—
45C29×#395C2214yes—
46C29×#394C2214yes—
47C29×#393C2214yes—
48C29×#391C2211yescharacteristic
49C29×#390C2211yescharacteristic
50C29×#389C2212yes—
51C29×#389C2212yes—
52C29×#388C2214yes—
53C29×#387C2214yes—
54C29×#387C2214yes—
55C29×#382C2211yescharacteristic
56C29×#382C2212yes—
57C4×C4⋊C4×C29C2214yes—
58C4×C4⋊C4×C29C2212yes—
59C4×C4⋊C4×C29C2214yes—
60C4×C4⋊C4×C29C2212yes—
61C4×C4⋊C4×C29C2214yes—
62C4×C22⋊C4×C29C2214yes—
63C4×C22⋊C4×C29C2214yes—
64C4×C22⋊C4×C29C2212yes—
65C29×#376C2212yes—
66C43×C29C2211yescharacteristic
67C22×Q8×C29C2311yescharacteristic
68C22×Q8×C29C2312yes—
69C22×D4×C29C2311yescharacteristic
70C23×C4×C29C2312yes—
71C29×#125—28no—
72C29×#124—24no—
73C4×Q8×C29—44no—
74C4×Q8×C29—42no—
75C4×D4×C29—42no—
76C29×#117—44no—
77C2×C4⋊C4×C29C2314yes—
78C2×C4⋊C4×C29C2314yes—
79C2×C4⋊C4×C29C2312yes—
80C2×C4⋊C4×C29C2312yes—
81C2×C4⋊C4×C29C2312yes—
82C2×C4⋊C4×C29C2312yes—
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29C2312yes—
86C2×C4⋊C4×C29C2314yes—
87C2×C4⋊C4×C29C2312yes—
88C2×C4⋊C4×C29C2312yes—
89C2×C4⋊C4×C29C2312yes—
90C2×C4⋊C4×C29C2314yes—
91C2×C4⋊C4×C29C2314yes—
92C2×C4⋊C4×C29C2314yes—
93C2×C4⋊C4×C29C2314yes—
94C2×C22⋊C4×C29C2314yes—
95C2×C22⋊C4×C29C2314yes—
96C2×C22⋊C4×C29C2312yes—
97C2×C22⋊C4×C29C2314yes—
98C2×C22⋊C4×C29C2314yes—
99C2×C22⋊C4×C29C2314yes—
100C2×C22⋊C4×C29C2314yes—
101C2×C42×C29C2314yes—
102C2×C42×C29C2311yescharacteristic
103C2×C42×C29C2312yes—
104C2×C42×C29C2312yes—
105C2×C42×C29C2314yes—
106C2×C42×C29C2311yescharacteristic
107C2×C42×C29C2312yes—
108C2×C42×C29C2311yescharacteristic
109C29×#95C2314yes—
110C29×#95C2312yes—
111C29×#95C2312yes—
112C29×#95C2314yes—
113C29×#95C2314yes—
114C29×#95C2314yes—
115C29×#95C2314yes—
116C29×#95C2312yes—
117C29×#95C2312yes—
118C29×#95C2314yes—
119C29×#95C2314yes—
120C29×#95C2314yes—
121C29×#95C2314yes—
122C29×#95C2314yes—
123C29×#95C2314yes—
124C29×#95C2314yes—
125C29×#95C2314yes—
126C24×C29C2412yes—
127C2×Q8×C29—22no—
128C2×Q8×C29—41no—
129C2×Q8×C29—42no—
130C2×Q8×C29—41no—
131C2×Q8×C29—44no—
132C2×D4×C29—22no—
133C2×D4×C29—41no—
134C2×D4×C29—41no—
135C22×C4×C29—24no—
136C22×C4×C29—28no—
137C22×C4×C29C2411yescharacteristic
138C22×C4×C29C2412yes—
139C22×C4×C29C2414yes—
140C22×C4×C29C2412yes—
141C22×C4×C29C2414yes—
142C22×C4×C29C2412yes—
143C22×C4×C29C2414yes—
144C22×C4×C29C2414yes—
145C22×C4×C29C2412yes—
146C22×C4×C29C2412yes—
147C22×C4×C29C2411yescharacteristic
148C22×C4×C29C2411yescharacteristic
149C4⋊C4×C29—28no—
150C4⋊C4×C29—24no—
151C4⋊C4×C29—24no—
152C4⋊C4×C29—28no—
153C4⋊C4×C29—42no—
154C4⋊C4×C29—42no—
155C4⋊C4×C29—44no—
156C4⋊C4×C29—44no—
157C4⋊C4×C29—44no—
158C4⋊C4×C29—44no—
159C4⋊C4×C29—42no—
160C4⋊C4×C29—42no—
161C4⋊C4×C29—41no—
162C4⋊C4×C29—41no—
163C4⋊C4×C29—42no—
164C4⋊C4×C29—42no—
165C4⋊C4×C29—44no—
166C22⋊C4×C29—28no—
167C22⋊C4×C29—44no—
168C22⋊C4×C29—44no—
169C22⋊C4×C29—44no—
170C22⋊C4×C29—44no—
171C22⋊C4×C29—44no—
172C22⋊C4×C29—42no—
173C42×C29—28no—
174C42×C29—22no—
175C42×C29—24no—
176C42×C29—24no—
177C42×C29—28no—
178C42×C29—42no—
179C42×C29—41no—
180C42×C29#4114yes—
181#36698C2911yesmaximal, characteristic, direct product factor, Sylow
182C23×C29—22no—
183C23×C29—22no—
184C23×C29—24no—
185C23×C29—24no—
186C23×C29—22no—
187C23×C29C2511yescharacteristic
188Q8×C29—44no—
189Q8×C29—48no—
190D4×C29—44no—
191C2×C4×C29—21no—
192C2×C4×C29—22no—
193C2×C4×C29—22no—
194C2×C4×C29—21no—
195C2×C4×C29—22no—
196C2×C4×C29—24no—
197C2×C4×C29—24no—
198C2×C4×C29—21no—
199C2×C4×C29—24no—
200C2×C4×C29—24no—
201C2×C4×C29—22no—
202C2×C4×C29—22no—
203C2×C4×C29—22no—
204C2×C4×C29—24no—
205C2×C4×C29—22no—
206C2×C4×C29—24no—
207C2×C4×C29—24no—
208C2×C4×C29—22no—
209C2×C4×C29—22no—
210C2×C4×C29—22no—
211C2×C4×C29—24no—
212C2×C4×C29—24no—
213C2×C4×C29—24no—
214C2×C4×C29—24no—
215C2×C4×C29—24no—
216C2×C4×C29—24no—
217C2×C4×C29—22no—
218C2×C4×C29—24no—
219C2×C4×C29—48no—
220C2×C4×C29C2×#4114yes—
221C2×C4×C29C2×#4112yes—
222C2×C4×C29H(5,𝔽2)12yes—
223C2×C4×C292−1+414yes—
224#2844C2×C2911yescharacteristic, complemented
225#2838C2×C2914yescomplemented
226#2836C2×C2914yescomplemented
227#2833C2×C2912yescomplemented
228#2830C2×C2912yes—
229#2822C2×C2911yescharacteristic, complemented
230#2820C2×C2912yes—
231#2401C2×C2914yescomplemented
232#2399C2×C2912yescomplemented
233#2396C2×C2914yescomplemented
234#2395C2×C2912yes—
235C4×#125C2×C2912yescomplemented
236C4×#124C2×C2911yescharacteristic
237C22×C29—42no—
238C22×C29—44no—
239C22×C29—42no—
240C22×C29—42no—
241C22×C29—44no—
242C22×C29C22×#4111yescharacteristic
243C22×C29C2×H(5,𝔽2)11yescharacteristic
244C22×C29C2×2−1+412yes—
245C22×C29#58511yescharacteristic
246C22×C29#58512yes—
247C4×C29—22no—
248C4×C29—24no—
249C4×C29—44no—
250C4×C29—42no—
251C4×C29—44no—
252C4×C29—42no—
253C4×C29—41no—
254C4×C29—44no—
255C4×C29—42no—
256C4×C29—42no—
257C4×C29—44no—
258C4×C29#56314yes—
259C2×#125C22×C2912yes—
260C2×#124C22×C2911yescharacteristic
261C2×C4×Q8C22×C2912yes—
262C2×C4×Q8C22×C2911yescharacteristic
263C2×C4×D4C22×C2911yescharacteristic
264C2×#117C22×C2912yes—
265#401C22×C2914yes—
266#400C22×C2914yes—
267#400C22×C2914yes—
268#400C22×C2914yes—
269#400C22×C2912yes—
270#400C22×C2914yes—
271#399C22×C2914yes—
272#399C22×C2912yes—
273#398C22×C2912yes—
274#398C22×C2912yes—
275#398C22×C2914yes—
276#398C22×C2914yes—
277#398C22×C2912yes—
278#398C22×C2914yes—
279#397C22×C2914yes—
280#397C22×C2914yes—
281#397C22×C2914yes—
282#397C22×C2912yes—
283#397C22×C2914yes—
284#396C22×C2914yes—
285#396C22×C2914yes—
286#396C22×C2914yes—
287#395C22×C2914yes—
288#395C22×C2912yes—
289#395C22×C2912yes—
290#395C22×C2914yes—
291#394C22×C2914yes—
292#393C22×C2914yes—
293#391C22×C2911yescharacteristic
294#390C22×C2911yescharacteristic
295#389C22×C2912yes—
296#389C22×C2912yes—
297#388C22×C2914yes—
298#387C22×C2914yes—
299#387C22×C2914yes—
300#382C22×C2912yes—
301#382C22×C2911yescharacteristic
302C4×C4⋊C4C22×C2914yes—
303C4×C4⋊C4C22×C2912yes—
304C4×C4⋊C4C22×C2914yes—
305C4×C4⋊C4C22×C2912yes—
306C4×C4⋊C4C22×C2914yes—
307C4×C22⋊C4C22×C2914yes—
308C4×C22⋊C4C22×C2912yes—
309C4×C22⋊C4C22×C2914yes—
310#376C22×C2912yes—
311C43C22×C2911yescharacteristic
312C2×C29—82no—
313C2×C29#346011yescharacteristic
314C2×C29#346112yes—
315C2×C29C2×#56311yescharacteristic
316C2×C29#352911yescharacteristic
317C2×C29#353112yes—
318C22×Q8C23×C2911yescharacteristic
319C22×Q8C23×C2912yes—
320C22×D4C23×C2911yescharacteristic
321C23×C4C23×C2912yes—
322#125—28no—
323#124—24no—
324C4×Q8—44no—
325C4×Q8—42no—
326C4×D4—42no—
327#117—44no—
328C2×C4⋊C4C23×C2914yes—
329C2×C4⋊C4C23×C2914yes—
330C2×C4⋊C4C23×C2912yes—
331C2×C4⋊C4C23×C2912yes—
332C2×C4⋊C4C23×C2912yes—
333C2×C4⋊C4C23×C2912yes—
334C2×C4⋊C4C23×C2911yescharacteristic
335C2×C4⋊C4C23×C2911yescharacteristic
336C2×C4⋊C4C23×C2912yes—
337C2×C4⋊C4C23×C2914yes—
338C2×C4⋊C4C23×C2912yes—
339C2×C4⋊C4C23×C2912yes—
340C2×C4⋊C4C23×C2912yes—
341C2×C4⋊C4C23×C2914yes—
342C2×C4⋊C4C23×C2914yes—
343C2×C4⋊C4C23×C2914yes—
344C2×C4⋊C4C23×C2914yes—
345C2×C22⋊C4C23×C2914yes—
346C2×C22⋊C4C23×C2914yes—
347C2×C22⋊C4C23×C2912yes—
348C2×C22⋊C4C23×C2914yes—
349C2×C22⋊C4C23×C2914yes—
350C2×C22⋊C4C23×C2914yes—
351C2×C22⋊C4C23×C2914yes—
352C2×C42C23×C2914yes—
353C2×C42C23×C2911yescharacteristic
354C2×C42C23×C2912yes—
355C2×C42C23×C2912yes—
356C2×C42C23×C2914yes—
357C2×C42C23×C2911yescharacteristic
358C2×C42C23×C2912yes—
359C2×C42C23×C2911yescharacteristic
360#95C23×C2914yes—
361#95C23×C2912yes—
362#95C23×C2912yes—
363#95C23×C2914yes—
364#95C23×C2914yes—
365#95C23×C2914yes—
366#95C23×C2914yes—
367#95C23×C2912yes—
368#95C23×C2912yes—
369#95C23×C2914yes—
370#95C23×C2914yes—
371#95C23×C2914yes—
372#95C23×C2914yes—
373#95C23×C2914yes—
374#95C23×C2914yes—
375#95C23×C2914yes—
376#95C23×C2914yes—
377C29#3669811yescharacteristic, direct product factor, Sylow
378C24C24×C2912yes—
379C2×Q8—22no—
380C2×Q8—41no—
381C2×Q8—42no—
382C2×Q8—41no—
383C2×Q8—44no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C22×C4—24no—
388C22×C4—28no—
389C22×C4C24×C2912yes—
390C22×C4C24×C2912yes—
391C22×C4C24×C2914yes—
392C22×C4C24×C2914yes—
393C22×C4C24×C2912yes—
394C22×C4C24×C2914yes—
395C22×C4C24×C2912yes—
396C22×C4C24×C2911yescharacteristic
397C22×C4C24×C2914yes—
398C22×C4C24×C2912yes—
399C22×C4C24×C2911yescharacteristic
400C22×C4C24×C2911yescharacteristic
401C4⋊C4—28no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—28no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—44no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—44no—
415C4⋊C4—44no—
416C4⋊C4—44no—
417C4⋊C4—44no—
418C22⋊C4—28no—
419C22⋊C4—44no—
420C22⋊C4—42no—
421C22⋊C4—44no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C22⋊C4—44no—
425C42—28no—
426C42—22no—
427C42—24no—
428C42—24no—
429C42—28no—
430C42—42no—
431C42—41no—
432C42#41×C2914yes—
433C23—22no—
434C23—22no—
435C23—24no—
436C23—24no—
437C23—22no—
438C23C25×C2911yescharacteristic
439Q8—44no—
440Q8—48no—
441D4—44no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—48no—
471C2×C4C2×#41×C2914yes—
472C2×C4C2×#41×C2912yes—
473C2×C4C29×H(5,𝔽2)12yes—
474C2×C4C29×2−1+414yes—
475C22—42no—
476C22—44no—
477C22—42no—
478C22—42no—
479C22—44no—
480C22C22×#41×C2911yescharacteristic
481C22C2×C29×H(5,𝔽2)11yescharacteristic
482C22C2×C29×2−1+412yes—
483C22C29×#58511yescharacteristic
484C22C29×#58512yes—
485C4—22no—
486C4—24no—
487C4—42no—
488C4—44no—
489C4—44no—
490C4—42no—
491C4—44no—
492C4—42no—
493C4—41no—
494C4—42no—
495C4—44no—
496C4C29×#56314yes—
497C2—82no—
498C2C29×#346011yescharacteristic
499C2C29×#346112yes—
500C2C2×C29×#56311yescharacteristic
501C2C29×#352911yescharacteristic
502C2C29×#353112yes—
subgroupG/H
centerC22×C4×C29C24
commutator, Frattini, cosocleC23C25×C29
socleC23×C29C25
prime radicalC22×D4×C29C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2844C2semidirect
2. C29×#2838C2semidirect
3. C29×#2836C2semidirect
4. C29×#2833C2semidirect
6. C29×#2822C2semidirect
8. C29×#2401C2semidirect
9. C29×#2399C2semidirect
10. C29×#2396C2semidirect
12. C4×C29×#125C2semidirect
181. #36698C29direct (N × H)
224. #2844C2×C29semidirect
225. #2838C2×C29semidirect
226. #2836C2×C29semidirect
227. #2833C2×C29semidirect
229. #2822C2×C29semidirect
231. #2401C2×C29semidirect
232. #2399C2×C29semidirect
233. #2396C2×C29semidirect
235. C4×#125C2×C29semidirect
377. C29#36698direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#28442
C29×#28382
C29×#28362
C29×#28332
C29×#28302
C29×#28222
C29×#28202
C29×#24012
C29×#23992
C29×#23962
C29×#23952
C4×C29×#1252
C4×C29×#1242
#3669829