Finite Group Databasebeta

← C29×#14362 #20309262

Subgroups — C29×#14362 #20309262

Order 7424.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1050 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×#389C211yesmaximal, characteristic, complemented
4C2×C29×#387C211yesmaximal, characteristic, complemented
5C2×C29×#380C211yesmaximal, characteristic
6C29×#1446C211yesmaximal, characteristic, complemented
7C29×#1441C211yesmaximal, characteristic, complemented
8C29×#1441C211yesmaximal, characteristic, complemented
9C29×#1441C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic
11C29×#1439C211yesmaximal, characteristic
12C29×#1437C211yesmaximal, characteristic
13C29×#1437C211yesmaximal, characteristic
14C29×#1436C211yesmaximal, characteristic, complemented
15C29×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C29C2211yescharacteristic
17C24×C4×C29C2211yescharacteristic
18C2×C29×C22⋊Q8—24no—
19C2×C29×C22⋊Q8—24no—
20C2×C29×C22⋊Q8C418yescomplemented
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C4⋊C4×C29C2211yescharacteristic
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×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C42×C29C2211yescharacteristic
35C22×C42×C29C2211yescharacteristic
36C29×#391—24no—
37C29×#389—24no—
38C29×#387—24no—
39C29×#380—24no—
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×C414yes—
66C23×C4×C29—22no—
67C23×C4×C29—22no—
68C23×C4×C29—22no—
69C23×C4×C29—22no—
70C23×C4×C29—41no—
71C23×C4×C29—41no—
72C23×C4×C29C2×C414yes—
73C23×C4×C29C2311yescharacteristic
74C23×C4×C29C2311yescharacteristic
75C23×C4×C29C2311yescharacteristic
76C23×C4×C29C2311yescharacteristic
77C23×C4×C29C2311yescharacteristic
78C23×C4×C29C2311yescharacteristic
79C23×C4×C29C2311yescharacteristic
80C23×C4×C29C2311yescharacteristic
81C23×C4×C29C2311yescharacteristic
82C23×C4×C29C2311yescharacteristic
83C23×C4×C29C2311yescharacteristic
84C23×C4×C29C2311yescharacteristic
85C23×C4×C29C2311yescharacteristic
86C23×C4×C29C2311yescharacteristic
87C29×C22⋊Q8—232no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—22no—
91C2×C4⋊C4×C29—22no—
92C2×C4⋊C4×C29—22no—
93C2×C4⋊C4×C29—22no—
94C2×C4⋊C4×C29—22no—
95C2×C4⋊C4×C29—22no—
96C2×C4⋊C4×C29—22no—
97C2×C4⋊C4×C29—22no—
98C2×C4⋊C4×C29—22no—
99C2×C4⋊C4×C29—41no—
100C2×C4⋊C4×C29—41no—
101C2×C4⋊C4×C29—41no—
102C2×C4⋊C4×C29—41no—
103C2×C4⋊C4×C29—41no—
104C2×C4⋊C4×C29C2×C414yes—
105C2×C4⋊C4×C29C2×C414yes—
106C2×C4⋊C4×C29C2×C414yes—
107C2×C4⋊C4×C29D414yes—
108C2×C4⋊C4×C29D414yes—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—22no—
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—41no—
119C2×C22⋊C4×C29—41no—
120C2×C22⋊C4×C29—41no—
121C2×C22⋊C4×C29—41no—
122C2×C22⋊C4×C29—41no—
123C2×C22⋊C4×C29—41no—
124C2×C22⋊C4×C29C2×C414yes—
125C2×C22⋊C4×C29C2×C414yes—
126C2×C22⋊C4×C29Q814yescomplemented
127C2×C42×C29—22no—
128C2×C42×C29—22no—
129C2×C42×C29—22no—
130C2×C42×C29—41no—
131C2×C42×C29—41no—
132C2×C42×C29—41no—
133C29×#95—22no—
134C29×#95—22no—
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—41no—
145C29×#95—41no—
146C29×#95—41no—
147C29×#95—41no—
148C29×#95—41no—
149C29×#95—41no—
150C29×#95D414yes—
151C24×C29—21no—
152C24×C29—21no—
153C24×C29—21no—
154C24×C29—21no—
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×Q812yes—
165C24×C29#4112yes—
166C24×C29C2411yescharacteristic
167C2×Q8×C29—28no—
168C2×Q8×C29—28no—
169C2×Q8×C29—44no—
170C2×Q8×C29—44no—
171C2×Q8×C29—44no—
172C2×Q8×C29—44no—
173C2×Q8×C29—44no—
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—28no—
227C22×C4×C29—28no—
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—21no—
246C22×C4×C29—21no—
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—44no—
257C22×C4×C29—44no—
258C22×C4×C29—44no—
259C22×C4×C29—44no—
260C22×C4×C29—44no—
261C22×C4×C29C22×C412yes—
262C22×C4×C29C22×C412yes—
263C22×C4×C29C22×C412yes—
264C22×C4×C29C22×C412yes—
265C22×C4×C29C22×C412yes—
266C22×C4×C29C22×C412yes—
267C22×C4×C29C2×D412yes—
268C22×C4×C29C2×D412yes—
269C22×C4×C29C2×D412yes—
270C22×C4×C29C2×D412yes—
271C22×C4×C29C2×D412yes—
272C22×C4×C29C2×D412yes—
273C22×C4×C29C2×D412yes—
274C22×C4×C29C2×D412yes—
275C22×C4×C29C2×D412yes—
276C22×C4×C29C2×Q812yes—
277C22×C4×C29C2×Q812yes—
278C22×C4×C29#4112yes—
279C4⋊C4×C29—28no—
280C4⋊C4×C29—28no—
281C4⋊C4×C29—44no—
282C4⋊C4×C29—44no—
283C4⋊C4×C29—44no—
284C4⋊C4×C29—44no—
285C4⋊C4×C29C22⋊C4116yescomplemented
286C22⋊C4×C29—28no—
287C22⋊C4×C29—28no—
288C22⋊C4×C29—44no—
289C22⋊C4×C29—44no—
290C22⋊C4×C29—44no—
291C22⋊C4×C29—44no—
292C42×C29—44no—
293C42×C29—44no—
294#14362C2911yesmaximal, characteristic, direct product factor, Sylow
295C23×C29—22no—
296C23×C29—22no—
297C23×C29—22no—
298C23×C29—22no—
299C23×C29—22no—
300C23×C29—22no—
301C23×C29—22no—
302C23×C29—22no—
303C23×C29—22no—
304C23×C29—22no—
305C23×C29—22no—
306C23×C29—22no—
307C23×C29—22no—
308C23×C29—22no—
309C23×C29—22no—
310C23×C29—22no—
311C23×C29—22no—
312C23×C29—22no—
313C23×C29—41no—
314C23×C29—41no—
315C23×C29—41no—
316C23×C29—41no—
317C23×C29—41no—
318C23×C29—41no—
319C23×C29—41no—
320C23×C29—41no—
321C23×C29—41no—
322C23×C29—41no—
323C23×C29—41no—
324C23×C29—41no—
325C23×C29—41no—
326C23×C29—41no—
327C23×C29—41no—
328C23×C29—41no—
329C23×C29C4×Q814yes—
330C23×C29C23×C411yescharacteristic
331C23×C29C22×D411yescharacteristic
332C23×C29C22×D411yescharacteristic
333C23×C29C22×D411yescharacteristic
334C23×C29C22×Q811yescharacteristic
335C23×C29C2×#4111yescharacteristic
336C23×C29C2×#4111yescharacteristic
337C23×C29H(5,𝔽2)11yescharacteristic
338C23×C29H(5,𝔽2)11yescharacteristic
339C23×C29H(5,𝔽2)11yescharacteristic
340C23×C29H(5,𝔽2)11yescharacteristic
341C23×C292−1+411yescharacteristic
342C23×C292−1+411yescharacteristic
343C23×C292−1+411yescharacteristic
344C23×C292−1+411yescharacteristic
345Q8×C29—416no—
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—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—416no—
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×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×C29C2×C22⋊C414yes—
442C2×C4×C29C2×C22⋊C414yes—
443C2×C4×C29C2×C22⋊C414yes—
444C2×C4×C29C4×D414yes—
445C22×C22⋊Q8C2×C2911yescharacteristic
446C2×#391C2×C2911yescharacteristic, complemented
447C2×#389C2×C2911yescharacteristic, complemented
448C2×#387C2×C2911yescharacteristic, complemented
449C2×#380C2×C2911yescharacteristic
450#1446C2×C2911yescharacteristic, complemented
451#1441C2×C2911yescharacteristic, complemented
452#1441C2×C2911yescharacteristic, complemented
453#1441C2×C2911yescharacteristic, complemented
454#1439C2×C2911yescharacteristic
455#1439C2×C2911yescharacteristic
456#1437C2×C2911yescharacteristic
457#1437C2×C2911yescharacteristic
458#1436C2×C2911yescharacteristic, complemented
459C22⋊#95C2×C2911yescharacteristic
460C22×C29—24no—
461C22×C29—24no—
462C22×C29—24no—
463C22×C29—42no—
464C22×C29—42no—
465C22×C29—42no—
466C22×C29—42no—
467C22×C29—42no—
468C22×C29—42no—
469C22×C29—42no—
470C22×C29—42no—
471C22×C29—42no—
472C22×C29—42no—
473C22×C29—42no—
474C22×C29—42no—
475C22×C29C22×C22⋊C411yescharacteristic
476C22×C29C2×C4×D411yescharacteristic
477C22×C29C2×C4×Q811yescharacteristic
478C22×C29#51811yescharacteristic
479C22×C29#51911yescharacteristic
480C22×C29#52011yescharacteristic
481C22×C29#52011yescharacteristic
482C22×C29#53511yescharacteristic
483C22×C29#53611yescharacteristic
484C22×C29#53611yescharacteristic
485C22×C29#53711yescharacteristic
486C22×C29#53711yescharacteristic
487C22×C29#53711yescharacteristic
488C22×C29#53811yescharacteristic
489C22×C29#53911yescharacteristic
490C22×C29#54111yescharacteristic
491C22×C29#54211yescharacteristic
492C22×C29#54311yescharacteristic
493C22×C29#54411yescharacteristic
494C22×C29D4211yescharacteristic
495C22×C29D4211yescharacteristic
496C22×C29#54611yescharacteristic
497C22×C29#54611yescharacteristic
498C22×C29#54611yescharacteristic
499C22×C29#54811yescharacteristic
500C22×C29#54811yescharacteristic
501C22×C29D4×Q811yescharacteristic
502C22×C29D4×Q811yescharacteristic
503C22×C29D4×Q811yescharacteristic
504C22×C29#55211yescharacteristic
505C22×C29#55411yescharacteristic
506C22×C29#56211yescharacteristic
507C22×C29#56211yescharacteristic
508C22×C29#56311yescharacteristic
509C22×C29#56311yescharacteristic
510C4×C29—24no—
511C4×C29—24no—
512C4×C29—24no—
513C4×C29—24no—
514C4×C29—42no—
515C4×C29—42no—
516C4×C29—42no—
517C4×C29—42no—
518C4×C29—42no—
519C4×C29—42no—
520C4×C29—81no—
521C4×C29—81no—
522C4×C29—81no—
523C4×C29—81no—
524C23×Q8C22×C2911yescharacteristic
525C24×C4C22×C2911yescharacteristic
526C2×C22⋊Q8—24no—
527C2×C22⋊Q8—24no—
528C2×C22⋊Q8C4×C2918yescomplemented
529C22×C4⋊C4C22×C2911yescharacteristic
530C22×C4⋊C4C22×C2911yescharacteristic
531C22×C4⋊C4C22×C2911yescharacteristic
532C22×C4⋊C4C22×C2911yescharacteristic
533C22×C4⋊C4C22×C2911yescharacteristic
534C22×C4⋊C4C22×C2911yescharacteristic
535C22×C4⋊C4C22×C2911yescharacteristic
536C22×C22⋊C4C22×C2911yescharacteristic
537C22×C22⋊C4C22×C2911yescharacteristic
538C22×C22⋊C4C22×C2911yescharacteristic
539C22×C22⋊C4C22×C2911yescharacteristic
540C22×C22⋊C4C22×C2911yescharacteristic
541C22×C22⋊C4C22×C2911yescharacteristic
542C22×C42C22×C2911yescharacteristic
543C22×C42C22×C2911yescharacteristic
544#391—24no—
545#389—24no—
546#387—24no—
547#380—24no—
548C2×#95C22×C2911yescharacteristic
549C2×#95C22×C2911yescharacteristic
550C2×#95C22×C2911yescharacteristic
551C2×#95C22×C2911yescharacteristic
552C2×#95C22×C2911yescharacteristic
553C2×#95C22×C2911yescharacteristic
554C2×#95C22×C2911yescharacteristic
555C2×#95C22×C2911yescharacteristic
556C2×#95C22×C2911yescharacteristic
557C2×#95C22×C2911yescharacteristic
558C2×#95C22×C2911yescharacteristic
559C2×#95C22×C2911yescharacteristic
560C2×#95C22×C2911yescharacteristic
561C2×#95C22×C2911yescharacteristic
562C2×#95C22×C2911yescharacteristic
563C2×#95C22×C2911yescharacteristic
564C2×#95C22×C2911yescharacteristic
565C2×#95C22×C2911yescharacteristic
566C2×C29—44no—
567C2×C29#231111yescharacteristic
568C2×C29#232311yescharacteristic
569C2×C29#232911yescharacteristic
570C2×C29D4×C22⋊C411yescharacteristic
571C2×C29Q8×C22⋊C411yescharacteristic
572C2×C29#236011yescharacteristic
573C2×C29#237811yescharacteristic
574C2×C29#267611yescharacteristic
575C2×C29#267711yescharacteristic
576C2×C29#268111yescharacteristic
577C2×C29#268311yescharacteristic
578C2×C29#269011yescharacteristic
579C2×C29#269211yescharacteristic
580C2×C29#270211yescharacteristic
581C2×C29#270411yescharacteristic
582C25C23×C2911yescharacteristic
583C22×Q8—22no—
584C22×Q8—22no—
585C22×Q8—22no—
586C22×Q8—22no—
587C22×Q8—41no—
588C22×Q8—41no—
589C22×Q8C2×C4×C2914yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—22no—
594C23×C4—41no—
595C23×C4—41no—
596C23×C4C2×C4×C2914yes—
597C23×C4C23×C2911yescharacteristic
598C23×C4C23×C2911yescharacteristic
599C23×C4C23×C2911yescharacteristic
600C23×C4C23×C2911yescharacteristic
601C23×C4C23×C2911yescharacteristic
602C23×C4C23×C2911yescharacteristic
603C23×C4C23×C2911yescharacteristic
604C23×C4C23×C2911yescharacteristic
605C23×C4C23×C2911yescharacteristic
606C23×C4C23×C2911yescharacteristic
607C23×C4C23×C2911yescharacteristic
608C23×C4C23×C2911yescharacteristic
609C23×C4C23×C2911yescharacteristic
610C23×C4C23×C2911yescharacteristic
611C22⋊Q8—232no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4C2×C4×C2914yes—
629C2×C4⋊C4C2×C4×C2914yes—
630C2×C4⋊C4C2×C4×C2914yes—
631C2×C4⋊C4D4×C2914yes—
632C2×C4⋊C4D4×C2914yes—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—41no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4C2×C4×C2914yes—
649C2×C22⋊C4C2×C4×C2914yes—
650C2×C22⋊C4Q8×C2914yescomplemented
651C2×C42—22no—
652C2×C42—22no—
653C2×C42—22no—
654C2×C42—41no—
655C2×C42—41no—
656C2×C42—41no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—41no—
669#95—41no—
670#95—41no—
671#95—41no—
672#95—41no—
673#95—41no—
674#95D4×C2914yes—
675C29#1436211yescharacteristic, direct product factor, Sylow
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24C22×C4×C2912yes—
689C24C2×Q8×C2912yes—
690C24#41×C2912yes—
691C24C24×C2911yescharacteristic
692C2×Q8—28no—
693C2×Q8—28no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
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—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—28no—
752C22×C4—28no—
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—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4C22×C4×C2912yes—
787C22×C4C22×C4×C2912yes—
788C22×C4C22×C4×C2912yes—
789C22×C4C22×C4×C2912yes—
790C22×C4C22×C4×C2912yes—
791C22×C4C22×C4×C2912yes—
792C22×C4C2×D4×C2912yes—
793C22×C4C2×D4×C2912yes—
794C22×C4C2×D4×C2912yes—
795C22×C4C2×D4×C2912yes—
796C22×C4C2×D4×C2912yes—
797C22×C4C2×D4×C2912yes—
798C22×C4C2×D4×C2912yes—
799C22×C4C2×D4×C2912yes—
800C22×C4C2×D4×C2912yes—
801C22×C4C2×Q8×C2912yes—
802C22×C4C2×Q8×C2912yes—
803C22×C4#41×C2912yes—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4C22⋊C4×C29116yescomplemented
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C42—44no—
818C42—44no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23C4×Q8×C2914yes—
854C23C23×C4×C2911yescharacteristic
855C23C22×D4×C2911yescharacteristic
856C23C22×D4×C2911yescharacteristic
857C23C22×D4×C2911yescharacteristic
858C23C22×Q8×C2911yescharacteristic
859C23C2×#41×C2911yescharacteristic
860C23C2×#41×C2911yescharacteristic
861C23C29×H(5,𝔽2)11yescharacteristic
862C23C29×H(5,𝔽2)11yescharacteristic
863C23C29×H(5,𝔽2)11yescharacteristic
864C23C29×H(5,𝔽2)11yescharacteristic
865C23C29×2−1+411yescharacteristic
866C23C29×2−1+411yescharacteristic
867C23C29×2−1+411yescharacteristic
868C23C29×2−1+411yescharacteristic
869Q8—416no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
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—416no—
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×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
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×C4C2×C22⋊C4×C2914yes—
966C2×C4C2×C22⋊C4×C2914yes—
967C2×C4C2×C22⋊C4×C2914yes—
968C2×C4C4×D4×C2914yes—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C22×C22⋊C4×C2911yescharacteristic
985C22C2×C4×D4×C2911yescharacteristic
986C22C2×C4×Q8×C2911yescharacteristic
987C22C29×#51811yescharacteristic
988C22C29×#51911yescharacteristic
989C22C29×#52011yescharacteristic
990C22C29×#52011yescharacteristic
991C22C29×#53511yescharacteristic
992C22C29×#53611yescharacteristic
993C22C29×#53611yescharacteristic
994C22C29×#53711yescharacteristic
995C22C29×#53711yescharacteristic
996C22C29×#53711yescharacteristic
997C22C29×#53811yescharacteristic
998C22C29×#53911yescharacteristic
999C22C29×#54111yescharacteristic
1000C22C29×#54211yescharacteristic
1001C22C29×#54311yescharacteristic
1002C22C29×#54411yescharacteristic
1003C22D42×C2911yescharacteristic
1004C22D42×C2911yescharacteristic
1005C22C29×#54611yescharacteristic
1006C22C29×#54611yescharacteristic
1007C22C29×#54611yescharacteristic
1008C22C29×#54811yescharacteristic
1009C22C29×#54811yescharacteristic
1010C22D4×Q8×C2911yescharacteristic
1011C22D4×Q8×C2911yescharacteristic
1012C22D4×Q8×C2911yescharacteristic
1013C22C29×#55211yescharacteristic
1014C22C29×#55411yescharacteristic
1015C22C29×#56211yescharacteristic
1016C22C29×#56211yescharacteristic
1017C22C29×#56311yescharacteristic
1018C22C29×#56311yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—24no—
1022C4—24no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—81no—
1030C4—81no—
1031C4—81no—
1032C4—81no—
1033C2—44no—
1034C2C29×#231111yescharacteristic
1035C2C29×#232311yescharacteristic
1036C2C29×#232911yescharacteristic
1037C2D4×C22⋊C4×C2911yescharacteristic
1038C2Q8×C22⋊C4×C2911yescharacteristic
1039C2C29×#236011yescharacteristic
1040C2C29×#237811yescharacteristic
1041C2C29×#267611yescharacteristic
1042C2C29×#267711yescharacteristic
1043C2C29×#268111yescharacteristic
1044C2C29×#268311yescharacteristic
1045C2C29×#269011yescharacteristic
1046C2C29×#269211yescharacteristic
1047C2C29×#270211yescharacteristic
1048C2C29×#270411yescharacteristic
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
3. C2×C29×#389C2semidirect
4. C2×C29×#387C2semidirect
6. C29×#1446C2semidirect
7. C29×#1441C2semidirect
8. C29×#1441C2semidirect
9. C29×#1441C2semidirect
14. C29×#1436C2semidirect
20. C2×C29×C22⋊Q8C4semidirect
126. C2×C22⋊C4×C29Q8semidirect
285. C4⋊C4×C29C22⋊C4semidirect
294. #14362C29direct (N × H)
446. C2×#391C2×C29semidirect
447. C2×#389C2×C29semidirect
448. C2×#387C2×C29semidirect
450. #1446C2×C29semidirect
451. #1441C2×C29semidirect
452. #1441C2×C29semidirect
453. #1441C2×C29semidirect
458. #1436C2×C29semidirect
528. C2×C22⋊Q8C4×C29semidirect
650. C2×C22⋊C4Q8×C29semidirect
675. C29#14362direct (N × H)
810. C4⋊C4C22⋊C4×C29semidirect

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×#3892
C2×C29×#3872
C2×C29×#3802
C29×#14462
C29×#14412
C29×#14392
C29×#14372
C29×#14362
C29×C22⋊#952
#1436229