Finite Group Databasebeta

← C29×#14488 #20309388

Subgroups — C29×#14488 #20309388

Order 7424.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#388C211yesmaximal, characteristic
2C2×C29×#388C211yesmaximal, characteristic
3C2×C29×#385C211yesmaximal, characteristic
4C29×#1444C211yesmaximal, characteristic, complemented
5C29×#1442C211yesmaximal, characteristic, complemented
6C29×#1442C211yesmaximal, characteristic, complemented
7C29×#1441C211yesmaximal, characteristic, complemented
8C29×#1439C211yesmaximal, characteristic
9C29×#1439C211yesmaximal, characteristic
10C29×#1436C211yesmaximal, characteristic, complemented
11C29×C4⋊#95C211yesmaximal, characteristic, complemented
12C29×C4⋊#95C211yesmaximal, characteristic, complemented
13C29×#1434C211yesmaximal, characteristic, complemented
14C29×C22⋊#95C211yesmaximal, characteristic
15C29×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C29C2211yescharacteristic
17C22×C4⋊C4×C29C2211yescharacteristic
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C4⋊C4×C29C2211yescharacteristic
23C22×C22⋊C4×C29C2211yescharacteristic
24C22×C22⋊C4×C29C2211yescharacteristic
25C22×C22⋊C4×C29C2211yescharacteristic
26C22×C22⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C42×C29C2211yescharacteristic
30C22×C42×C29C2211yescharacteristic
31C29×#388—24no—
32C29×#388C418yescomplemented
33C29×#385—24no—
34C2×C29×#95C2211yescharacteristic
35C2×C29×#95C2211yescharacteristic
36C2×C29×#95C2211yescharacteristic
37C2×C29×#95C2211yescharacteristic
38C2×C29×#95C2211yescharacteristic
39C2×C29×#95C2211yescharacteristic
40C2×C29×#95C2211yescharacteristic
41C2×C29×#95C2211yescharacteristic
42C2×C29×#95C2211yescharacteristic
43C2×C29×#95C2211yescharacteristic
44C2×C29×#95C2211yescharacteristic
45C2×C29×#95C2211yescharacteristic
46C2×C29×#95C2211yescharacteristic
47C2×C29×#95C2211yescharacteristic
48C2×C29×#95C2211yescharacteristic
49C2×C29×#95C2211yescharacteristic
50C2×C29×#95C2211yescharacteristic
51C2×C29×#95C2211yescharacteristic
52C2×C29×#95C2211yescharacteristic
53C2×C29×#95C2211yescharacteristic
54C25×C29C2311yescharacteristic
55C23×C4×C29—22no—
56C23×C4×C29—22no—
57C23×C4×C29—22no—
58C23×C4×C29—41no—
59C23×C4×C29—41no—
60C23×C4×C29—41no—
61C23×C4×C29—41no—
62C23×C4×C29C2311yescharacteristic
63C23×C4×C29C2311yescharacteristic
64C23×C4×C29C2311yescharacteristic
65C23×C4×C29C2311yescharacteristic
66C23×C4×C29C2311yescharacteristic
67C23×C4×C29C2311yescharacteristic
68C23×C4×C29C2311yescharacteristic
69C23×C4×C29C2311yescharacteristic
70C23×C4×C29C2311yescharacteristic
71C23×C4×C29C2311yescharacteristic
72C23×C4×C29C2311yescharacteristic
73C23×C4×C29C2311yescharacteristic
74C23×C4×C29C2311yescharacteristic
75C23×C4×C29C2311yescharacteristic
76C2×C4⋊C4×C29—22no—
77C2×C4⋊C4×C29—22no—
78C2×C4⋊C4×C29—22no—
79C2×C4⋊C4×C29—22no—
80C2×C4⋊C4×C29—22no—
81C2×C4⋊C4×C29—22no—
82C2×C4⋊C4×C29—22no—
83C2×C4⋊C4×C29—41no—
84C2×C4⋊C4×C29—41no—
85C2×C4⋊C4×C29—41no—
86C2×C4⋊C4×C29—41no—
87C2×C4⋊C4×C29—41no—
88C2×C4⋊C4×C29—41no—
89C2×C4⋊C4×C29—41no—
90C2×C4⋊C4×C29—41no—
91C2×C4⋊C4×C29—41no—
92C2×C4⋊C4×C29—41no—
93C2×C4⋊C4×C29C2×C414yescomplemented
94C2×C22⋊C4×C29—22no—
95C2×C22⋊C4×C29—22no—
96C2×C22⋊C4×C29—22no—
97C2×C22⋊C4×C29—22no—
98C2×C22⋊C4×C29—22no—
99C2×C22⋊C4×C29—41no—
100C2×C22⋊C4×C29—41no—
101C2×C22⋊C4×C29—41no—
102C2×C22⋊C4×C29—41no—
103C2×C22⋊C4×C29—41no—
104C2×C22⋊C4×C29—41no—
105C2×C22⋊C4×C29—41no—
106C2×C22⋊C4×C29—41no—
107C2×C22⋊C4×C29C2×C414yes—
108C2×C22⋊C4×C29C2×C414yes—
109C2×C22⋊C4×C29C2×C414yes—
110C2×C22⋊C4×C29D414yes—
111C2×C22⋊C4×C29Q814yes—
112C2×C42×C29—22no—
113C2×C42×C29—22no—
114C2×C42×C29—41no—
115C2×C42×C29—41no—
116C2×C42×C29—41no—
117C2×C42×C29C2×C414yescomplemented
118C29×#95—22no—
119C29×#95—22no—
120C29×#95—22no—
121C29×#95—22no—
122C29×#95—22no—
123C29×#95—22no—
124C29×#95—22no—
125C29×#95—41no—
126C29×#95—41no—
127C29×#95—41no—
128C29×#95—41no—
129C29×#95—41no—
130C29×#95—41no—
131C29×#95—41no—
132C29×#95—41no—
133C29×#95—41no—
134C29×#95—41no—
135C29×#95—41no—
136C29×#95C2×C414yescomplemented
137C29×#95C2×C414yescomplemented
138C24×C29—21no—
139C24×C29—21no—
140C24×C29—21no—
141C24×C29—21no—
142C24×C29—21no—
143C24×C29—21no—
144C24×C29—21no—
145C24×C29—21no—
146C24×C29—21no—
147C24×C29—21no—
148C24×C29—21no—
149C24×C29—21no—
150C24×C29C22×C412yes—
151C24×C29C2×D412yes—
152C24×C29C2×Q812yes—
153C24×C29C2411yescharacteristic
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—21no—
177C22×C4×C29—21no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—21no—
182C22×C4×C29—21no—
183C22×C4×C29—21no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—21no—
187C22×C4×C29—21no—
188C22×C4×C29—21no—
189C22×C4×C29—21no—
190C22×C4×C29—21no—
191C22×C4×C29—21no—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—21no—
195C22×C4×C29—21no—
196C22×C4×C29—21no—
197C22×C4×C29—21no—
198C22×C4×C29—21no—
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—21no—
206C22×C4×C29—21no—
207C22×C4×C29—21no—
208C22×C4×C29—21no—
209C22×C4×C29—21no—
210C22×C4×C29—21no—
211C22×C4×C29—21no—
212C22×C4×C29—21no—
213C22×C4×C29—21no—
214C22×C4×C29—21no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—21no—
227C22×C4×C29—21no—
228C22×C4×C29—21no—
229C22×C4×C29—21no—
230C22×C4×C29—21no—
231C22×C4×C29—21no—
232C22×C4×C29—21no—
233C22×C4×C29—21no—
234C22×C4×C29—21no—
235C22×C4×C29—21no—
236C22×C4×C29—21no—
237C22×C4×C29—21no—
238C22×C4×C29—44no—
239C22×C4×C29—44no—
240C22×C4×C29—44no—
241C22×C4×C29—44no—
242C22×C4×C29—44no—
243C22×C4×C29—44no—
244C22×C4×C29—44no—
245C22×C4×C29C22×C412yes—
246C22×C4×C29C22×C412yes—
247C22×C4×C29C22×C412yes—
248C22×C4×C29C22×C412yes—
249C22×C4×C29C22×C412yes—
250C22×C4×C29C22×C412yes—
251C22×C4×C29C2×D412yes—
252C22×C4×C29C2×D412yes—
253C22×C4×C29C2×Q812yes—
254C22×C4×C29C2×Q812yes—
255C22×C4×C29#4112yes—
256C22×C4×C29#4112yes—
257C22×C4×C29#4112yes—
258C22×C4×C29#4112yes—
259C4⋊C4×C29—44no—
260C4⋊C4×C29—44no—
261C4⋊C4×C29—44no—
262C4⋊C4×C29—44no—
263C4⋊C4×C29—44no—
264C4⋊C4×C29—44no—
265C22⋊C4×C29—44no—
266C22⋊C4×C29—44no—
267C22⋊C4×C29—44no—
268C22⋊C4×C29—44no—
269C22⋊C4×C29—44no—
270C22⋊C4×C29C4⋊C4116yescomplemented
271C42×C29—44no—
272C42×C29—44no—
273#14488C2911yesmaximal, characteristic, direct product factor, Sylow
274C23×C29—22no—
275C23×C29—22no—
276C23×C29—22no—
277C23×C29—22no—
278C23×C29—22no—
279C23×C29—22no—
280C23×C29—22no—
281C23×C29—22no—
282C23×C29—22no—
283C23×C29—22no—
284C23×C29—22no—
285C23×C29—22no—
286C23×C29—22no—
287C23×C29—22no—
288C23×C29—22no—
289C23×C29—22no—
290C23×C29—22no—
291C23×C29—22no—
292C23×C29—41no—
293C23×C29—41no—
294C23×C29—41no—
295C23×C29—41no—
296C23×C29—41no—
297C23×C29—41no—
298C23×C29—41no—
299C23×C29—41no—
300C23×C29—41no—
301C23×C29—41no—
302C23×C29—41no—
303C23×C29—41no—
304C23×C29—41no—
305C23×C29—41no—
306C23×C29—41no—
307C23×C29—41no—
308C23×C29C2×C4⋊C414yes—
309C23×C29C23×C411yescharacteristic
310C23×C29C22×D411yescharacteristic
311C23×C29C22×Q811yescharacteristic
312C23×C29C2×#4111yescharacteristic
313C23×C29C2×#4111yescharacteristic
314C23×C29C2×#4111yescharacteristic
315C23×C29C2×#4111yescharacteristic
316C23×C29H(5,𝔽2)11yescharacteristic
317C23×C29H(5,𝔽2)11yescharacteristic
318C23×C29H(5,𝔽2)11yescharacteristic
319C23×C29H(5,𝔽2)11yescharacteristic
320C23×C29H(5,𝔽2)11yescharacteristic
321C23×C29H(5,𝔽2)11yescharacteristic
322C23×C292−1+411yescharacteristic
323C23×C292−1+411yescharacteristic
324C2×C4×C29—22no—
325C2×C4×C29—22no—
326C2×C4×C29—22no—
327C2×C4×C29—22no—
328C2×C4×C29—22no—
329C2×C4×C29—22no—
330C2×C4×C29—22no—
331C2×C4×C29—22no—
332C2×C4×C29—22no—
333C2×C4×C29—22no—
334C2×C4×C29—22no—
335C2×C4×C29—22no—
336C2×C4×C29—22no—
337C2×C4×C29—22no—
338C2×C4×C29—22no—
339C2×C4×C29—22no—
340C2×C4×C29—22no—
341C2×C4×C29—22no—
342C2×C4×C29—22no—
343C2×C4×C29—22no—
344C2×C4×C29—22no—
345C2×C4×C29—22no—
346C2×C4×C29—22no—
347C2×C4×C29—22no—
348C2×C4×C29—22no—
349C2×C4×C29—22no—
350C2×C4×C29—22no—
351C2×C4×C29—22no—
352C2×C4×C29—22no—
353C2×C4×C29—22no—
354C2×C4×C29—22no—
355C2×C4×C29—22no—
356C2×C4×C29—22no—
357C2×C4×C29—22no—
358C2×C4×C29—22no—
359C2×C4×C29—22no—
360C2×C4×C29—416no—
361C2×C4×C29—41no—
362C2×C4×C29—41no—
363C2×C4×C29—41no—
364C2×C4×C29—41no—
365C2×C4×C29—41no—
366C2×C4×C29—41no—
367C2×C4×C29—41no—
368C2×C4×C29—41no—
369C2×C4×C29—41no—
370C2×C4×C29—41no—
371C2×C4×C29—41no—
372C2×C4×C29—41no—
373C2×C4×C29—41no—
374C2×C4×C29—41no—
375C2×C4×C29—41no—
376C2×C4×C29—41no—
377C2×C4×C29—41no—
378C2×C4×C29—41no—
379C2×C4×C29—41no—
380C2×C4×C29—41no—
381C2×C4×C29—41no—
382C2×C4×C29—41no—
383C2×C4×C29—41no—
384C2×C4×C29—41no—
385C2×C4×C29—41no—
386C2×C4×C29—41no—
387C2×C4×C29—41no—
388C2×C4×C29—41no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—41no—
393C2×C4×C29—41no—
394C2×C4×C29—41no—
395C2×C4×C29—41no—
396C2×C4×C29—41no—
397C2×C4×C29—41no—
398C2×C4×C29—41no—
399C2×C4×C29—41no—
400C2×C4×C29—41no—
401C2×C4×C29—41no—
402C2×C4×C29—41no—
403C2×C4×C29—41no—
404C2×C4×C29—41no—
405C2×C4×C29—41no—
406C2×C4×C29—41no—
407C2×C4×C29—41no—
408C2×C4×C29—41no—
409C2×C4×C29—41no—
410C2×C4×C29—41no—
411C2×C4×C29—41no—
412C2×C4×C29—41no—
413C2×C4×C29—41no—
414C2×C4×C29—41no—
415C2×C4×C29—41no—
416C2×C4×C29—41no—
417C2×C4×C29—41no—
418C2×C4×C29—41no—
419C2×C4×C29—41no—
420C2×C4×C29—41no—
421C2×C4×C29C2×C4⋊C414yes—
422C2×C4×C29C2×C4⋊C414yes—
423C2×#388C2×C2911yescharacteristic
424C2×#388C2×C2911yescharacteristic
425C2×#385C2×C2911yescharacteristic
426#1444C2×C2911yescharacteristic, complemented
427#1442C2×C2911yescharacteristic, complemented
428#1442C2×C2911yescharacteristic, complemented
429#1441C2×C2911yescharacteristic, complemented
430#1439C2×C2911yescharacteristic
431#1439C2×C2911yescharacteristic
432#1436C2×C2911yescharacteristic, complemented
433C4⋊#95C2×C2911yescharacteristic, complemented
434C4⋊#95C2×C2911yescharacteristic, complemented
435#1434C2×C2911yescharacteristic, complemented
436C22⋊#95C2×C2911yescharacteristic
437C22⋊#95C2×C2911yescharacteristic
438C22×C29—24no—
439C22×C29—24no—
440C22×C29—24no—
441C22×C29—42no—
442C22×C29—42no—
443C22×C29—42no—
444C22×C29—42no—
445C22×C29—42no—
446C22×C29—42no—
447C22×C29—42no—
448C22×C29—42no—
449C22×C29—42no—
450C22×C29—42no—
451C22×C29—42no—
452C22×C29—42no—
453C22×C29C22×C4⋊C411yescharacteristic
454C22×C29C4×#4111yescharacteristic
455C22×C29C4×#4111yescharacteristic
456C22×C29#51811yescharacteristic
457C22×C29#51811yescharacteristic
458C22×C29#52011yescharacteristic
459C22×C29#52011yescharacteristic
460C22×C29#53511yescharacteristic
461C22×C29#53611yescharacteristic
462C22×C29#53811yescharacteristic
463C22×C29#53811yescharacteristic
464C22×C29#53811yescharacteristic
465C22×C29#53911yescharacteristic
466C22×C29#54011yescharacteristic
467C22×C29#54211yescharacteristic
468C22×C29#54211yescharacteristic
469C22×C29#54211yescharacteristic
470C22×C29#54411yescharacteristic
471C22×C29#54411yescharacteristic
472C22×C29#54611yescharacteristic
473C22×C29#54611yescharacteristic
474C22×C29#54611yescharacteristic
475C22×C29#54611yescharacteristic
476C22×C29#55111yescharacteristic
477C22×C29#55211yescharacteristic
478C22×C29#55311yescharacteristic
479C22×C29#55411yescharacteristic
480C22×C29#55411yescharacteristic
481C22×C29#55411yescharacteristic
482C22×C29#55411yescharacteristic
483C22×C29#55611yescharacteristic
484C22×C29#56011yescharacteristic
485C22×C29#56011yescharacteristic
486C22×C29#56211yescharacteristic
487C22×C29#56211yescharacteristic
488C4×C29—24no—
489C4×C29—24no—
490C4×C29—42no—
491C4×C29—42no—
492C4×C29—42no—
493C4×C29—42no—
494C4×C29—42no—
495C4×C29—42no—
496C4×C29—42no—
497C4×C29—42no—
498C4×C29—81no—
499C4×C29—81no—
500C4×C29—81no—
501C4×C29—81no—
502C24×C4C22×C2911yescharacteristic
503C22×C4⋊C4C22×C2911yescharacteristic
504C22×C4⋊C4C22×C2911yescharacteristic
505C22×C4⋊C4C22×C2911yescharacteristic
506C22×C4⋊C4C22×C2911yescharacteristic
507C22×C4⋊C4C22×C2911yescharacteristic
508C22×C4⋊C4C22×C2911yescharacteristic
509C22×C22⋊C4C22×C2911yescharacteristic
510C22×C22⋊C4C22×C2911yescharacteristic
511C22×C22⋊C4C22×C2911yescharacteristic
512C22×C22⋊C4C22×C2911yescharacteristic
513C22×C22⋊C4C22×C2911yescharacteristic
514C22×C22⋊C4C22×C2911yescharacteristic
515C22×C42C22×C2911yescharacteristic
516C22×C42C22×C2911yescharacteristic
517#388—24no—
518#388C4×C2918yescomplemented
519#385—24no—
520C2×#95C22×C2911yescharacteristic
521C2×#95C22×C2911yescharacteristic
522C2×#95C22×C2911yescharacteristic
523C2×#95C22×C2911yescharacteristic
524C2×#95C22×C2911yescharacteristic
525C2×#95C22×C2911yescharacteristic
526C2×#95C22×C2911yescharacteristic
527C2×#95C22×C2911yescharacteristic
528C2×#95C22×C2911yescharacteristic
529C2×#95C22×C2911yescharacteristic
530C2×#95C22×C2911yescharacteristic
531C2×#95C22×C2911yescharacteristic
532C2×#95C22×C2911yescharacteristic
533C2×#95C22×C2911yescharacteristic
534C2×#95C22×C2911yescharacteristic
535C2×#95C22×C2911yescharacteristic
536C2×#95C22×C2911yescharacteristic
537C2×#95C22×C2911yescharacteristic
538C2×#95C22×C2911yescharacteristic
539C2×#95C22×C2911yescharacteristic
540C2×C29—44no—
541C2×C29#231711yescharacteristic
542C2×C29#233511yescharacteristic
543C2×C29#233711yescharacteristic
544C2×C29#234911yescharacteristic
545C2×C29#234911yescharacteristic
546C2×C29#237311yescharacteristic
547C2×C29#237711yescharacteristic
548C2×C29#268511yescharacteristic
549C2×C29#268711yescharacteristic
550C2×C29#270011yescharacteristic
551C2×C29#270311yescharacteristic
552C2×C29#274211yescharacteristic
553C2×C29#276811yescharacteristic
554C2×C29#278811yescharacteristic
555C2×C29#279011yescharacteristic
556C25C23×C2911yescharacteristic
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4C23×C2911yescharacteristic
565C23×C4C23×C2911yescharacteristic
566C23×C4C23×C2911yescharacteristic
567C23×C4C23×C2911yescharacteristic
568C23×C4C23×C2911yescharacteristic
569C23×C4C23×C2911yescharacteristic
570C23×C4C23×C2911yescharacteristic
571C23×C4C23×C2911yescharacteristic
572C23×C4C23×C2911yescharacteristic
573C23×C4C23×C2911yescharacteristic
574C23×C4C23×C2911yescharacteristic
575C23×C4C23×C2911yescharacteristic
576C23×C4C23×C2911yescharacteristic
577C23×C4C23×C2911yescharacteristic
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4C2×C4×C2914yescomplemented
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4C2×C4×C2914yes—
610C2×C22⋊C4C2×C4×C2914yes—
611C2×C22⋊C4C2×C4×C2914yes—
612C2×C22⋊C4D4×C2914yes—
613C2×C22⋊C4Q8×C2914yes—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42C2×C4×C2914yescomplemented
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95C2×C4×C2914yescomplemented
639#95C2×C4×C2914yescomplemented
640C29#1448811yescharacteristic, direct product factor, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C2912yes—
654C24C2×D4×C2912yes—
655C24C2×Q8×C2912yes—
656C24C24×C2911yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4C22×C4×C2912yes—
749C22×C4C22×C4×C2912yes—
750C22×C4C22×C4×C2912yes—
751C22×C4C22×C4×C2912yes—
752C22×C4C22×C4×C2912yes—
753C22×C4C22×C4×C2912yes—
754C22×C4C2×D4×C2912yes—
755C22×C4C2×D4×C2912yes—
756C22×C4C2×Q8×C2912yes—
757C22×C4C2×Q8×C2912yes—
758C22×C4#41×C2912yes—
759C22×C4#41×C2912yes—
760C22×C4#41×C2912yes—
761C22×C4#41×C2912yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4C4⋊C4×C29116yescomplemented
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C2914yes—
811C23C23×C4×C2911yescharacteristic
812C23C22×D4×C2911yescharacteristic
813C23C22×Q8×C2911yescharacteristic
814C23C2×#41×C2911yescharacteristic
815C23C2×#41×C2911yescharacteristic
816C23C2×#41×C2911yescharacteristic
817C23C2×#41×C2911yescharacteristic
818C23C29×H(5,𝔽2)11yescharacteristic
819C23C29×H(5,𝔽2)11yescharacteristic
820C23C29×H(5,𝔽2)11yescharacteristic
821C23C29×H(5,𝔽2)11yescharacteristic
822C23C29×H(5,𝔽2)11yescharacteristic
823C23C29×H(5,𝔽2)11yescharacteristic
824C23C29×2−1+411yescharacteristic
825C23C29×2−1+411yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—416no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4C2×C4⋊C4×C2914yes—
924C2×C4C2×C4⋊C4×C2914yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C2911yescharacteristic
941C22C4×#41×C2911yescharacteristic
942C22C4×#41×C2911yescharacteristic
943C22C29×#51811yescharacteristic
944C22C29×#51811yescharacteristic
945C22C29×#52011yescharacteristic
946C22C29×#52011yescharacteristic
947C22C29×#53511yescharacteristic
948C22C29×#53611yescharacteristic
949C22C29×#53811yescharacteristic
950C22C29×#53811yescharacteristic
951C22C29×#53811yescharacteristic
952C22C29×#53911yescharacteristic
953C22C29×#54011yescharacteristic
954C22C29×#54211yescharacteristic
955C22C29×#54211yescharacteristic
956C22C29×#54211yescharacteristic
957C22C29×#54411yescharacteristic
958C22C29×#54411yescharacteristic
959C22C29×#54611yescharacteristic
960C22C29×#54611yescharacteristic
961C22C29×#54611yescharacteristic
962C22C29×#54611yescharacteristic
963C22C29×#55111yescharacteristic
964C22C29×#55211yescharacteristic
965C22C29×#55311yescharacteristic
966C22C29×#55411yescharacteristic
967C22C29×#55411yescharacteristic
968C22C29×#55411yescharacteristic
969C22C29×#55411yescharacteristic
970C22C29×#55611yescharacteristic
971C22C29×#56011yescharacteristic
972C22C29×#56011yescharacteristic
973C22C29×#56211yescharacteristic
974C22C29×#56211yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C29×#231711yescharacteristic
991C2C29×#233511yescharacteristic
992C2C29×#233711yescharacteristic
993C2C29×#234911yescharacteristic
994C2C29×#234911yescharacteristic
995C2C29×#237311yescharacteristic
996C2C29×#237711yescharacteristic
997C2C29×#268511yescharacteristic
998C2C29×#268711yescharacteristic
999C2C29×#270011yescharacteristic
1000C2C29×#270311yescharacteristic
1001C2C29×#274211yescharacteristic
1002C2C29×#276811yescharacteristic
1003C2C29×#278811yescharacteristic
1004C2C29×#279011yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC25×C29C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
4. C29×#1444C2semidirect
5. C29×#1442C2semidirect
6. C29×#1442C2semidirect
7. C29×#1441C2semidirect
10. C29×#1436C2semidirect
11. C29×C4⋊#95C2semidirect
12. C29×C4⋊#95C2semidirect
13. C29×#1434C2semidirect
32. C29×#388C4semidirect
93. C2×C4⋊C4×C29C2×C4semidirect
117. C2×C42×C29C2×C4semidirect
136. C29×#95C2×C4semidirect
137. C29×#95C2×C4semidirect
270. C22⋊C4×C29C4⋊C4semidirect
273. #14488C29direct (N × H)
426. #1444C2×C29semidirect
427. #1442C2×C29semidirect
428. #1442C2×C29semidirect
429. #1441C2×C29semidirect
432. #1436C2×C29semidirect
433. C4⋊#95C2×C29semidirect
434. C4⋊#95C2×C29semidirect
435. #1434C2×C29semidirect
518. #388C4×C29semidirect
595. C2×C4⋊C4C2×C4×C29semidirect
619. C2×C42C2×C4×C29semidirect
638. #95C2×C4×C29semidirect
639. #95C2×C4×C29semidirect
640. C29#14488direct (N × H)
773. C22⋊C4C4⋊C4×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#3882
C2×C29×#3852
C29×#14442
C29×#14422
C29×#14412
C29×#14392
C29×#14362
C29×C4⋊#952
C29×#14342
C29×C22⋊#952
#1448829