Finite Group Databasebeta

← C29×#14052 #20308952

Subgroups — C29×#14052 #20308952

Order 7424.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×C22⋊Q8C211yesmaximal, characteristic
2C2×C29×#391C211yesmaximal, characteristic, complemented
3C2×C29×#385C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C29C211yesmaximal, characteristic
5C22×C29×#95C211yesmaximal, characteristic
6C29×#1446C211yesmaximal, characteristic, complemented
7C29×#1445C211yesmaximal, characteristic, complemented
8C29×#1441C211yesmaximal, characteristic, complemented
9C29×#1441C211yesmaximal, characteristic, complemented
10C29×#1436C211yesmaximal, characteristic, complemented
11C29×#1436C211yesmaximal, characteristic, complemented
12C29×C4⋊#95C211yesmaximal, characteristic, complemented
13C29×C22⋊#95C211yesmaximal, characteristic
14C29×C22⋊#95C211yesmaximal, characteristic
15C29×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C24×C4×C29C2211yescharacteristic
19C24×C4×C29C2211yescharacteristic
20C2×C29×C22⋊Q8—24no—
21C2×C29×C22⋊Q8—24no—
22C2×C29×C22⋊Q8C418yescomplemented
23C22×C4⋊C4×C29C2211yescharacteristic
24C22×C4⋊C4×C29C2211yescharacteristic
25C22×C4⋊C4×C29C2211yescharacteristic
26C22×C4⋊C4×C29C2211yescharacteristic
27C22×C4⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C22⋊C4×C29C2211yescharacteristic
30C22×C22⋊C4×C29C2211yescharacteristic
31C22×C22⋊C4×C29C2211yescharacteristic
32C22×C42×C29C2211yescharacteristic
33C22×C42×C29C2211yescharacteristic
34C29×#391—24no—
35C29×#385—24no—
36C4×C22⋊C4×C29—24no—
37C2×C29×#95—24no—
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
54C2×C29×#95C2211yescharacteristic
55C2×C29×#95C2211yescharacteristic
56C2×C29×#95C2211yescharacteristic
57C2×C29×#95C2211yescharacteristic
58C25×C29C2311yescharacteristic
59C22×Q8×C29—22no—
60C22×Q8×C29—22no—
61C22×Q8×C29—22no—
62C22×Q8×C29—22no—
63C22×Q8×C29—41no—
64C22×Q8×C29—41no—
65C22×Q8×C29C2×C414yescomplemented
66C23×C4×C29—22no—
67C23×C4×C29—22no—
68C23×C4×C29—22no—
69C23×C4×C29—22no—
70C23×C4×C29—22no—
71C23×C4×C29—22no—
72C23×C4×C29—22no—
73C23×C4×C29—22no—
74C23×C4×C29—22no—
75C23×C4×C29—22no—
76C23×C4×C29—22no—
77C23×C4×C29—22no—
78C23×C4×C29—22no—
79C23×C4×C29—41no—
80C23×C4×C29—41no—
81C23×C4×C29—41no—
82C23×C4×C29—41no—
83C23×C4×C29—41no—
84C23×C4×C29—41no—
85C23×C4×C29C2×C414yes—
86C23×C4×C29Q814yescomplemented
87C23×C4×C29C2311yescharacteristic
88C23×C4×C29C2311yescharacteristic
89C23×C4×C29C2311yescharacteristic
90C23×C4×C29C2311yescharacteristic
91C23×C4×C29C2311yescharacteristic
92C23×C4×C29C2311yescharacteristic
93C23×C4×C29C2311yescharacteristic
94C23×C4×C29C2311yescharacteristic
95C23×C4×C29C2311yescharacteristic
96C23×C4×C29C2311yescharacteristic
97C23×C4×C29C2311yescharacteristic
98C23×C4×C29C2311yescharacteristic
99C23×C4×C29C2311yescharacteristic
100C23×C4×C29C2311yescharacteristic
101C29×C22⋊Q8—232no—
102C2×C4⋊C4×C29—22no—
103C2×C4⋊C4×C29—22no—
104C2×C4⋊C4×C29—22no—
105C2×C4⋊C4×C29—22no—
106C2×C4⋊C4×C29—22no—
107C2×C4⋊C4×C29—22no—
108C2×C4⋊C4×C29—22no—
109C2×C4⋊C4×C29—22no—
110C2×C4⋊C4×C29—22no—
111C2×C4⋊C4×C29—22no—
112C2×C4⋊C4×C29—41no—
113C2×C4⋊C4×C29—41no—
114C2×C4⋊C4×C29C2×C414yescomplemented
115C2×C4⋊C4×C29C2×C414yescomplemented
116C2×C4⋊C4×C29C2×C414yescomplemented
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—22no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29—22no—
121C2×C22⋊C4×C29—22no—
122C2×C22⋊C4×C29—22no—
123C2×C22⋊C4×C29—22no—
124C2×C22⋊C4×C29C2×C414yes—
125C2×C22⋊C4×C29C2×C414yes—
126C2×C22⋊C4×C29D414yes—
127C2×C22⋊C4×C29D414yes—
128C2×C22⋊C4×C29Q814yescomplemented
129C2×C42×C29—22no—
130C2×C42×C29—22no—
131C2×C42×C29—22no—
132C2×C42×C29—22no—
133C2×C42×C29—41no—
134C2×C42×C29—41no—
135C29×#95—22no—
136C29×#95—22no—
137C29×#95—22no—
138C29×#95—22no—
139C29×#95—22no—
140C29×#95—22no—
141C29×#95—22no—
142C29×#95—22no—
143C29×#95—22no—
144C29×#95—22no—
145C29×#95—22no—
146C29×#95—22no—
147C29×#95—22no—
148C29×#95—41no—
149C29×#95—41no—
150C29×#95—41no—
151C29×#95—41no—
152C29×#95—41no—
153C29×#95—41no—
154C29×#95D414yes—
155C24×C29—21no—
156C24×C29—21no—
157C24×C29—21no—
158C24×C29—21no—
159C24×C29—21no—
160C24×C29—21no—
161C24×C29—21no—
162C24×C29—21no—
163C24×C29C22×C412yes—
164C24×C29C2×D412yes—
165C24×C29C2×D412yes—
166C24×C29C2×Q812yes—
167C24×C29C2×Q812yes—
168C24×C29#4112yes—
169C24×C29#4112yes—
170C24×C29C2411yescharacteristic
171C2×Q8×C29—28no—
172C2×Q8×C29—28no—
173C2×Q8×C29—44no—
174C2×Q8×C29—44no—
175C2×Q8×C29—44no—
176C2×Q8×C29—44no—
177C2×Q8×C29—44no—
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—28no—
195C22×C4×C29—28no—
196C22×C4×C29—28no—
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—21no—
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29—21no—
245C22×C4×C29—28no—
246C22×C4×C29—28no—
247C22×C4×C29—21no—
248C22×C4×C29—21no—
249C22×C4×C29—21no—
250C22×C4×C29—21no—
251C22×C4×C29—21no—
252C22×C4×C29—21no—
253C22×C4×C29—21no—
254C22×C4×C29—21no—
255C22×C4×C29—21no—
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—21no—
259C22×C4×C29—21no—
260C22×C4×C29—21no—
261C22×C4×C29—44no—
262C22×C4×C29—44no—
263C22×C4×C29—44no—
264C22×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×C29—44no—
271C22×C4×C29—44no—
272C22×C4×C29—44no—
273C22×C4×C29—44no—
274C22×C4×C29—44no—
275C22×C4×C29—44no—
276C22×C4×C29—44no—
277C22×C4×C29C22×C412yes—
278C22×C4×C29C22×C412yes—
279C22×C4×C29C22×C412yes—
280C22×C4×C29C22×C412yes—
281C22×C4×C29C22×C412yes—
282C22×C4×C29C22×C412yes—
283C22×C4×C29C2×D412yes—
284C22×C4×C29C2×D412yes—
285C22×C4×C29C2×D412yes—
286C22×C4×C29C2×D412yes—
287C22×C4×C29C2×D412yes—
288C22×C4×C29C2×D412yes—
289C22×C4×C29C2×D412yes—
290C22×C4×C29C2×Q812yes—
291C22×C4×C29C2×Q812yes—
292C22×C4×C29C2×Q812yes—
293C22×C4×C29C2×Q812yes—
294C22×C4×C29#4112yes—
295C22×C4×C29#4112yes—
296C22×C4×C29#4112yes—
297C4⋊C4×C29—28no—
298C4⋊C4×C29—28no—
299C4⋊C4×C29—28no—
300C4⋊C4×C29—44no—
301C4⋊C4×C29—44no—
302C22⋊C4×C29—28no—
303C22⋊C4×C29—28no—
304C22⋊C4×C29—44no—
305C22⋊C4×C29C22⋊C4116yes—
306C42×C29—44no—
307C42×C29—44no—
308#14052C2911yesmaximal, characteristic, direct product factor, Sylow
309C23×C29—22no—
310C23×C29—22no—
311C23×C29—22no—
312C23×C29—22no—
313C23×C29—22no—
314C23×C29—22no—
315C23×C29—22no—
316C23×C29—22no—
317C23×C29—22no—
318C23×C29—22no—
319C23×C29—22no—
320C23×C29—22no—
321C23×C29—22no—
322C23×C29—22no—
323C23×C29—22no—
324C23×C29—22no—
325C23×C29—22no—
326C23×C29—22no—
327C23×C29—22no—
328C23×C29—22no—
329C23×C29—22no—
330C23×C29—22no—
331C23×C29—22no—
332C23×C29—22no—
333C23×C29—22no—
334C23×C29—22no—
335C23×C29—22no—
336C23×C29—22no—
337C23×C29C2×C22⋊C414yes—
338C23×C29C4×Q814yes—
339C23×C29C4×Q814yes—
340C23×C29C22⋊Q814yes—
341C23×C29C22⋊Q814yes—
342C23×C29#12414yes—
343C23×C29C4⋊Q814yes—
344C23×C29C23×C411yescharacteristic
345C23×C29C22×D411yescharacteristic
346C23×C29C22×D411yescharacteristic
347C23×C29C22×D411yescharacteristic
348C23×C29C22×Q811yescharacteristic
349C23×C29C22×Q811yescharacteristic
350C23×C29C2×#4111yescharacteristic
351C23×C29C2×#4111yescharacteristic
352C23×C29C2×#4111yescharacteristic
353C23×C29C2×#4111yescharacteristic
354C23×C29C2×#4111yescharacteristic
355C23×C29H(5,𝔽2)11yescharacteristic
356C23×C29H(5,𝔽2)11yescharacteristic
357C23×C29H(5,𝔽2)11yescharacteristic
358C23×C292−1+411yescharacteristic
359Q8×C29—416no—
360C2×C4×C29—22no—
361C2×C4×C29—22no—
362C2×C4×C29—22no—
363C2×C4×C29—22no—
364C2×C4×C29—22no—
365C2×C4×C29—22no—
366C2×C4×C29—22no—
367C2×C4×C29—22no—
368C2×C4×C29—22no—
369C2×C4×C29—22no—
370C2×C4×C29—22no—
371C2×C4×C29—22no—
372C2×C4×C29—22no—
373C2×C4×C29—22no—
374C2×C4×C29—22no—
375C2×C4×C29—22no—
376C2×C4×C29—22no—
377C2×C4×C29—22no—
378C2×C4×C29—22no—
379C2×C4×C29—22no—
380C2×C4×C29—22no—
381C2×C4×C29—22no—
382C2×C4×C29—22no—
383C2×C4×C29—22no—
384C2×C4×C29—22no—
385C2×C4×C29—22no—
386C2×C4×C29—22no—
387C2×C4×C29—22no—
388C2×C4×C29—22no—
389C2×C4×C29—22no—
390C2×C4×C29—22no—
391C2×C4×C29—22no—
392C2×C4×C29—22no—
393C2×C4×C29—22no—
394C2×C4×C29—22no—
395C2×C4×C29—22no—
396C2×C4×C29—22no—
397C2×C4×C29—22no—
398C2×C4×C29—22no—
399C2×C4×C29—22no—
400C2×C4×C29—22no—
401C2×C4×C29—22no—
402C2×C4×C29—22no—
403C2×C4×C29—22no—
404C2×C4×C29—22no—
405C2×C4×C29—22no—
406C2×C4×C29—22no—
407C2×C4×C29—22no—
408C2×C4×C29—416no—
409C2×C4×C29—416no—
410C2×C4×C29—416no—
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×C29—41no—
422C2×C4×C29—41no—
423C2×C4×C29—41no—
424C2×C4×C29—41no—
425C2×C4×C29—41no—
426C2×C4×C29—41no—
427C2×C4×C29—41no—
428C2×C4×C29—41no—
429C2×C4×C29—41no—
430C2×C4×C29—41no—
431C2×C4×C29—41no—
432C2×C4×C29—41no—
433C2×C4×C29—41no—
434C2×C4×C29—41no—
435C2×C4×C29—41no—
436C2×C4×C29—41no—
437C2×C4×C29—41no—
438C2×C4×C29—41no—
439C2×C4×C29—41no—
440C2×C4×C29—41no—
441C2×C4×C29—41no—
442C2×C4×C29—41no—
443C2×C4×C29—41no—
444C2×C4×C29—41no—
445C2×C4×C29—41no—
446C2×C4×C29—41no—
447C2×C4×C29—41no—
448C2×C4×C29—41no—
449C2×C4×C29—41no—
450C2×C4×C29—41no—
451C2×C4×C29—41no—
452C2×C4×C29—41no—
453C2×C4×C29—41no—
454C2×C4×C29—41no—
455C2×C4×C29—41no—
456C2×C4×C29—41no—
457C2×C4×C29C2×C22⋊C414yes—
458C2×C4×C29C2×C22⋊C414yes—
459C2×C4×C29C4×D414yes—
460C2×C4×C29C22⋊Q814yescomplemented
461C22×C22⋊Q8C2×C2911yescharacteristic
462C2×#391C2×C2911yescharacteristic, complemented
463C2×#385C2×C2911yescharacteristic
464C2×C4×C22⋊C4C2×C2911yescharacteristic
465C22×#95C2×C2911yescharacteristic
466#1446C2×C2911yescharacteristic, complemented
467#1445C2×C2911yescharacteristic, complemented
468#1441C2×C2911yescharacteristic, complemented
469#1441C2×C2911yescharacteristic, complemented
470#1436C2×C2911yescharacteristic, complemented
471#1436C2×C2911yescharacteristic, complemented
472C4⋊#95C2×C2911yescharacteristic, complemented
473C22⋊#95C2×C2911yescharacteristic
474C22⋊#95C2×C2911yescharacteristic
475C22⋊#95C2×C2911yescharacteristic
476C22×C29—24no—
477C22×C29—24no—
478C22×C29—24no—
479C22×C29—24no—
480C22×C29—24no—
481C22×C29—24no—
482C22×C29—24no—
483C22×C29—24no—
484C22×C29—24no—
485C22×C29—24no—
486C22×C29—24no—
487C22×C29—24no—
488C22×C29—24no—
489C22×C29—24no—
490C22×C29#39118yescomplemented
491C22×C29C22×C22⋊C411yescharacteristic
492C22×C29C2×C4×D411yescharacteristic
493C22×C29C2×C4×Q811yescharacteristic
494C22×C29C2×C4×Q811yescharacteristic
495C22×C29C4×#4111yescharacteristic
496C22×C29#51811yescharacteristic
497C22×C29#52011yescharacteristic
498C22×C29C2×C22⋊Q811yescharacteristic
499C22×C29C2×C22⋊Q811yescharacteristic
500C22×C29C2×C22⋊Q811yescharacteristic
501C22×C29#52511yescharacteristic
502C22×C29C2×#12411yescharacteristic
503C22×C29#52911yescharacteristic
504C22×C29C2×C4⋊Q811yescharacteristic
505C22×C29#53311yescharacteristic
506C22×C29#53811yescharacteristic
507C22×C29#53911yescharacteristic
508C22×C29#54311yescharacteristic
509C22×C29#54411yescharacteristic
510C22×C29D4211yescharacteristic
511C22×C29D4211yescharacteristic
512C22×C29#54611yescharacteristic
513C22×C29#54611yescharacteristic
514C22×C29#54611yescharacteristic
515C22×C29#54611yescharacteristic
516C22×C29#54611yescharacteristic
517C22×C29#54711yescharacteristic
518C22×C29#54711yescharacteristic
519C22×C29D4×Q811yescharacteristic
520C22×C29#55111yescharacteristic
521C22×C29#55111yescharacteristic
522C22×C29#55211yescharacteristic
523C22×C29#55411yescharacteristic
524C22×C29#55411yescharacteristic
525C22×C29#55411yescharacteristic
526C4×C29—24no—
527C4×C29—24no—
528C4×C29—24no—
529C4×C29—24no—
530C4×C29—42no—
531C4×C29—42no—
532C4×C29—42no—
533C4×C29—42no—
534C4×C29—42no—
535C4×C29—42no—
536C4×C29—42no—
537C4×C29—42no—
538C4×C29—81no—
539C4×C29—81no—
540C23×Q8C22×C2911yescharacteristic
541C24×C4C22×C2911yescharacteristic
542C24×C4C22×C2911yescharacteristic
543C24×C4C22×C2911yescharacteristic
544C2×C22⋊Q8—24no—
545C2×C22⋊Q8—24no—
546C2×C22⋊Q8C4×C2918yescomplemented
547C22×C4⋊C4C22×C2911yescharacteristic
548C22×C4⋊C4C22×C2911yescharacteristic
549C22×C4⋊C4C22×C2911yescharacteristic
550C22×C4⋊C4C22×C2911yescharacteristic
551C22×C4⋊C4C22×C2911yescharacteristic
552C22×C22⋊C4C22×C2911yescharacteristic
553C22×C22⋊C4C22×C2911yescharacteristic
554C22×C22⋊C4C22×C2911yescharacteristic
555C22×C22⋊C4C22×C2911yescharacteristic
556C22×C42C22×C2911yescharacteristic
557C22×C42C22×C2911yescharacteristic
558#391—24no—
559#385—24no—
560C4×C22⋊C4—24no—
561C2×#95—24no—
562C2×#95C22×C2911yescharacteristic
563C2×#95C22×C2911yescharacteristic
564C2×#95C22×C2911yescharacteristic
565C2×#95C22×C2911yescharacteristic
566C2×#95C22×C2911yescharacteristic
567C2×#95C22×C2911yescharacteristic
568C2×#95C22×C2911yescharacteristic
569C2×#95C22×C2911yescharacteristic
570C2×#95C22×C2911yescharacteristic
571C2×#95C22×C2911yescharacteristic
572C2×#95C22×C2911yescharacteristic
573C2×#95C22×C2911yescharacteristic
574C2×#95C22×C2911yescharacteristic
575C2×#95C22×C2911yescharacteristic
576C2×#95C22×C2911yescharacteristic
577C2×#95C22×C2911yescharacteristic
578C2×#95C22×C2911yescharacteristic
579C2×#95C22×C2911yescharacteristic
580C2×#95C22×C2911yescharacteristic
581C2×#95C22×C2911yescharacteristic
582C2×C29—28no—
583C2×C29C2×#39111yescharacteristic
584C2×C29C4×C22⋊Q811yescharacteristic
585C2×C29#232911yescharacteristic
586C2×C29D4×C22⋊C411yescharacteristic
587C2×C29#233911yescharacteristic
588C2×C29#236011yescharacteristic
589C2×C29#236811yescharacteristic
590C2×C29#243711yescharacteristic
591C2×C29#243811yescharacteristic
592C2×C29#244011yescharacteristic
593C2×C29#244911yescharacteristic
594C2×C29#245011yescharacteristic
595C2×C29#247211yescharacteristic
596C2×C29#248811yescharacteristic
597C2×C29#254911yescharacteristic
598C25C23×C2911yescharacteristic
599C22×Q8—22no—
600C22×Q8—22no—
601C22×Q8—22no—
602C22×Q8—22no—
603C22×Q8—41no—
604C22×Q8—41no—
605C22×Q8C2×C4×C2914yescomplemented
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—22no—
616C23×C4—22no—
617C23×C4—22no—
618C23×C4—22no—
619C23×C4—41no—
620C23×C4—41no—
621C23×C4—41no—
622C23×C4—41no—
623C23×C4—41no—
624C23×C4—41no—
625C23×C4C2×C4×C2914yes—
626C23×C4Q8×C2914yescomplemented
627C23×C4C23×C2911yescharacteristic
628C23×C4C23×C2911yescharacteristic
629C23×C4C23×C2911yescharacteristic
630C23×C4C23×C2911yescharacteristic
631C23×C4C23×C2911yescharacteristic
632C23×C4C23×C2911yescharacteristic
633C23×C4C23×C2911yescharacteristic
634C23×C4C23×C2911yescharacteristic
635C23×C4C23×C2911yescharacteristic
636C23×C4C23×C2911yescharacteristic
637C23×C4C23×C2911yescharacteristic
638C23×C4C23×C2911yescharacteristic
639C23×C4C23×C2911yescharacteristic
640C23×C4C23×C2911yescharacteristic
641C22⋊Q8—232no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4C2×C4×C2914yescomplemented
655C2×C4⋊C4C2×C4×C2914yescomplemented
656C2×C4⋊C4C2×C4×C2914yescomplemented
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4C2×C4×C2914yes—
665C2×C22⋊C4C2×C4×C2914yes—
666C2×C22⋊C4D4×C2914yes—
667C2×C22⋊C4D4×C2914yes—
668C2×C22⋊C4Q8×C2914yescomplemented
669C2×C42—22no—
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—22no—
673C2×C42—41no—
674C2×C42—41no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95D4×C2914yes—
695C29#1405211yescharacteristic, direct product factor, Sylow
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24C22×C4×C2912yes—
705C24C2×D4×C2912yes—
706C24C2×D4×C2912yes—
707C24C2×Q8×C2912yes—
708C24C2×Q8×C2912yes—
709C24#41×C2912yes—
710C24#41×C2912yes—
711C24C24×C2911yescharacteristic
712C2×Q8—28no—
713C2×Q8—28no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—44no—
718C2×Q8—44no—
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—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4C22×C4×C2912yes—
819C22×C4C22×C4×C2912yes—
820C22×C4C22×C4×C2912yes—
821C22×C4C22×C4×C2912yes—
822C22×C4C22×C4×C2912yes—
823C22×C4C22×C4×C2912yes—
824C22×C4C2×D4×C2912yes—
825C22×C4C2×D4×C2912yes—
826C22×C4C2×D4×C2912yes—
827C22×C4C2×D4×C2912yes—
828C22×C4C2×D4×C2912yes—
829C22×C4C2×D4×C2912yes—
830C22×C4C2×D4×C2912yes—
831C22×C4C2×Q8×C2912yes—
832C22×C4C2×Q8×C2912yes—
833C22×C4C2×Q8×C2912yes—
834C22×C4C2×Q8×C2912yes—
835C22×C4#41×C2912yes—
836C22×C4#41×C2912yes—
837C22×C4#41×C2912yes—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—44no—
846C22⋊C4C22⋊C4×C29116yes—
847C42—44no—
848C42—44no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C2×C22⋊C4×C2914yes—
878C23C4×Q8×C2914yes—
879C23C4×Q8×C2914yes—
880C23C29×C22⋊Q814yes—
881C23C29×C22⋊Q814yes—
882C23C29×#12414yes—
883C23C29×C4⋊Q814yes—
884C23C23×C4×C2911yescharacteristic
885C23C22×D4×C2911yescharacteristic
886C23C22×D4×C2911yescharacteristic
887C23C22×D4×C2911yescharacteristic
888C23C22×Q8×C2911yescharacteristic
889C23C22×Q8×C2911yescharacteristic
890C23C2×#41×C2911yescharacteristic
891C23C2×#41×C2911yescharacteristic
892C23C2×#41×C2911yescharacteristic
893C23C2×#41×C2911yescharacteristic
894C23C2×#41×C2911yescharacteristic
895C23C29×H(5,𝔽2)11yescharacteristic
896C23C29×H(5,𝔽2)11yescharacteristic
897C23C29×H(5,𝔽2)11yescharacteristic
898C23C29×2−1+411yescharacteristic
899Q8—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—416no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4C2×C22⋊C4×C2914yes—
998C2×C4C2×C22⋊C4×C2914yes—
999C2×C4C4×D4×C2914yes—
1000C2×C4C29×C22⋊Q814yescomplemented
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22C29×#39118yescomplemented
1016C22C22×C22⋊C4×C2911yescharacteristic
1017C22C2×C4×D4×C2911yescharacteristic
1018C22C2×C4×Q8×C2911yescharacteristic
1019C22C2×C4×Q8×C2911yescharacteristic
1020C22C4×#41×C2911yescharacteristic
1021C22C29×#51811yescharacteristic
1022C22C29×#52011yescharacteristic
1023C22C2×C29×C22⋊Q811yescharacteristic
1024C22C2×C29×C22⋊Q811yescharacteristic
1025C22C2×C29×C22⋊Q811yescharacteristic
1026C22C29×#52511yescharacteristic
1027C22C2×C29×#12411yescharacteristic
1028C22C29×#52911yescharacteristic
1029C22C2×C29×C4⋊Q811yescharacteristic
1030C22C29×#53311yescharacteristic
1031C22C29×#53811yescharacteristic
1032C22C29×#53911yescharacteristic
1033C22C29×#54311yescharacteristic
1034C22C29×#54411yescharacteristic
1035C22D42×C2911yescharacteristic
1036C22D42×C2911yescharacteristic
1037C22C29×#54611yescharacteristic
1038C22C29×#54611yescharacteristic
1039C22C29×#54611yescharacteristic
1040C22C29×#54611yescharacteristic
1041C22C29×#54611yescharacteristic
1042C22C29×#54711yescharacteristic
1043C22C29×#54711yescharacteristic
1044C22D4×Q8×C2911yescharacteristic
1045C22C29×#55111yescharacteristic
1046C22C29×#55111yescharacteristic
1047C22C29×#55211yescharacteristic
1048C22C29×#55411yescharacteristic
1049C22C29×#55411yescharacteristic
1050C22C29×#55411yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—24no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—81no—
1065C2—28no—
1066C2C2×C29×#39111yescharacteristic
1067C2C4×C29×C22⋊Q811yescharacteristic
1068C2C29×#232911yescharacteristic
1069C2D4×C22⋊C4×C2911yescharacteristic
1070C2C29×#233911yescharacteristic
1071C2C29×#236011yescharacteristic
1072C2C29×#236811yescharacteristic
1073C2C29×#243711yescharacteristic
1074C2C29×#243811yescharacteristic
1075C2C29×#244011yescharacteristic
1076C2C29×#244911yescharacteristic
1077C2C29×#245011yescharacteristic
1078C2C29×#247211yescharacteristic
1079C2C29×#248811yescharacteristic
1080C2C29×#254911yescharacteristic
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
2. C2×C29×#391C2semidirect
6. C29×#1446C2semidirect
7. C29×#1445C2semidirect
8. C29×#1441C2semidirect
9. C29×#1441C2semidirect
10. C29×#1436C2semidirect
11. C29×#1436C2semidirect
12. C29×C4⋊#95C2semidirect
22. C2×C29×C22⋊Q8C4semidirect
65. C22×Q8×C29C2×C4semidirect
86. C23×C4×C29Q8semidirect
114. C2×C4⋊C4×C29C2×C4semidirect
115. C2×C4⋊C4×C29C2×C4semidirect
116. C2×C4⋊C4×C29C2×C4semidirect
128. C2×C22⋊C4×C29Q8semidirect
308. #14052C29direct (N × H)
460. C2×C4×C29C22⋊Q8semidirect
462. C2×#391C2×C29semidirect
466. #1446C2×C29semidirect
467. #1445C2×C29semidirect
468. #1441C2×C29semidirect
469. #1441C2×C29semidirect
470. #1436C2×C29semidirect
471. #1436C2×C29semidirect
472. C4⋊#95C2×C29semidirect
490. C22×C29#391semidirect
546. C2×C22⋊Q8C4×C29semidirect
605. C22×Q8C2×C4×C29semidirect
626. C23×C4Q8×C29semidirect
654. C2×C4⋊C4C2×C4×C29semidirect
655. C2×C4⋊C4C2×C4×C29semidirect
656. C2×C4⋊C4C2×C4×C29semidirect
668. C2×C22⋊C4Q8×C29semidirect
695. C29#14052direct (N × H)
1000. C2×C4C29×C22⋊Q8semidirect
1015. C22C29×#391semidirect

Maximal subgroups

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

subgroupindex
C22×C29×C22⋊Q82
C2×C29×#3912
C2×C29×#3852
C2×C4×C22⋊C4×C292
C22×C29×#952
C29×#14462
C29×#14452
C29×#14412
C29×#14362
C29×C4⋊#952
C29×C22⋊#952
#1405229