Finite Group Databasebeta

← C29×#22367 #20317267

Subgroups — C29×#22367 #20317267

Order 7424.

774 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C29×#123C211yesmaximal, characteristic
2C29×#1954C211yesmaximal, characteristic
3C29×#1940C211yesmaximal, characteristic, complemented
4C29×#1924C211yesmaximal, characteristic, complemented
5C29×#1924C211yesmaximal, characteristic, complemented
6C29×#1924C211yesmaximal, characteristic, complemented
7C29×#1924C211yesmaximal, characteristic, complemented
8C29×#1917C211yesmaximal, characteristic, complemented
9C29×#1916C211yesmaximal, characteristic, complemented
10C29×#1869C211yesmaximal, characteristic
11C29×#1850C211yesmaximal, characteristic, complemented
12C29×#1797C211yesmaximal, characteristic, complemented
13C29×#1771C211yesmaximal, characteristic, complemented
14C29×#1752C211yesmaximal, characteristic, complemented
15C29×#1749C211yesmaximal, characteristic, complemented
16C23×C8×C29C2211yescharacteristic
17C2×C29×#123C411yescharacteristic
18C2×C4×D4×C29C2211yescharacteristic
19C22×C42×C29C2211yescharacteristic
20C2×C29×C4⋊C8C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×C4⋊C8C2211yescharacteristic
25C2×C29×C22⋊C8C2211yescharacteristic
26C2×C29×C22⋊C8C2211yescharacteristic
27C2×C29×C22⋊C8C2211yescharacteristic
28C2×C29×C22⋊C8C2211yescharacteristic
29C2×C29×C22⋊C8C2211yescharacteristic
30C2×C29×C22⋊C8C2211yescharacteristic
31C2×C29×C22⋊C8C2211yescharacteristic
32C2×C29×#97C2211yescharacteristic
33C2×C29×#97C2211yescharacteristic
34C2×C29×#97C2211yescharacteristic
35C2×C29×#97C2211yescharacteristic
36C2×C4×C8×C29C2211yescharacteristic
37C29×#388C411yescharacteristic
38C29×#388C411yescharacteristic
39C29×#387C411yescharacteristic
40C29×#387C411yescharacteristic
41C29×#386C411yescharacteristic
42C29×#385C411yescharacteristic
43C29×#381C411yescharacteristic
44C4×C4⋊C4×C29C2211yescharacteristic
45C4×C4⋊C4×C29C2211yescharacteristic
46C4×C22⋊C4×C29C2211yescharacteristic
47C4×C22⋊C4×C29C2211yescharacteristic
48C4×C22⋊C4×C29C2211yescharacteristic
49C29×#336C2211yescharacteristic
50C29×#336C2211yescharacteristic
51C29×#336C2211yescharacteristic
52C29×#336C2211yescharacteristic
53C29×#336C2211yescharacteristic
54C29×#336C2211yescharacteristic
55C29×#336C2211yescharacteristic
56C29×#336C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×D4×C29C2×C411yescharacteristic
60C23×C4×C29C2×C411yescharacteristic
61C23×C4×C29C2×C411yescharacteristic
62C23×C4×C29C2311yescharacteristic
63C23×C4×C29C2311yescharacteristic
64C22×C8×C29—22no—
65C22×C8×C29—41no—
66C22×C8×C29—41no—
67C22×C8×C29C2311yescharacteristic
68C22×C8×C29C2311yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C22×C8×C29C2311yescharacteristic
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C29×#123—24no—
76C4×D4×C29—41no—
77C4×D4×C29—41no—
78C2×C4⋊C4×C29C2×C411yescharacteristic
79C2×C4⋊C4×C29C2×C411yescharacteristic
80C2×C4⋊C4×C29C2×C411yescharacteristic
81C2×C4⋊C4×C29C2×C411yescharacteristic
82C2×C4⋊C4×C29C2×C411yescharacteristic
83C2×C22⋊C4×C29C2×C411yescharacteristic
84C2×C22⋊C4×C29C2×C411yescharacteristic
85C2×C22⋊C4×C29C2×C411yescharacteristic
86C2×C22⋊C4×C29C2×C411yescharacteristic
87C2×C22⋊C4×C29C2×C411yescharacteristic
88C2×C22⋊C4×C29C2×C411yescharacteristic
89C2×C22⋊C4×C29C2×C411yescharacteristic
90C2×C22⋊C4×C29C2×C411yescharacteristic
91C2×C42×C29—41no—
92C2×C42×C29—41no—
93C2×C42×C29C2×C411yescharacteristic
94C2×C42×C29C2×C411yescharacteristic
95C2×C42×C29C2311yescharacteristic
96C2×C42×C29C2311yescharacteristic
97C2×C42×C29C2311yescharacteristic
98C2×C42×C29C2311yescharacteristic
99C2×C42×C29C2311yescharacteristic
100C29×C4⋊C8—22no—
101C29×C4⋊C8—41no—
102C29×C4⋊C8—41no—
103C29×C4⋊C8—41no—
104C29×C4⋊C8—41no—
105C29×C22⋊C8—22no—
106C29×C22⋊C8—22no—
107C29×C22⋊C8—22no—
108C29×C22⋊C8—41no—
109C29×C22⋊C8—41no—
110C29×C22⋊C8—41no—
111C29×C22⋊C8—41no—
112C29×#97—22no—
113C29×#97—41no—
114C29×#97—41no—
115C29×#97—41no—
116C4×C8×C29—41no—
117C29×#95C2×C411yescharacteristic
118C29×#95C2×C411yescharacteristic
119C29×#95C2×C411yescharacteristic
120C29×#95C2×C411yescharacteristic
121C29×#95C2×C411yescharacteristic
122C29×#95C2×C411yescharacteristic
123C29×#95C2×C411yescharacteristic
124C29×#95C2×C411yescharacteristic
125C29×#95C2×C411yescharacteristic
126C29×#95C2×C411yescharacteristic
127C24×C29C22×C411yescharacteristic
128C24×C29C22×C411yescharacteristic
129C2×D4×C29—41no—
130C2×D4×C29—41no—
131C2×D4×C29M1614yes—
132C22×C4×C29—22no—
133C22×C4×C29—22no—
134C22×C4×C29—21no—
135C22×C4×C29—21no—
136C22×C4×C29—21no—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—41no—
147C22×C4×C29—41no—
148C22×C4×C29—41no—
149C22×C4×C29—41no—
150C22×C4×C29C22×C411yescharacteristic
151C22×C4×C29C22×C411yescharacteristic
152C22×C4×C29C22×C411yescharacteristic
153C22×C4×C29C22×C411yescharacteristic
154C22×C4×C29C22×C411yescharacteristic
155C22×C4×C29C22×C411yescharacteristic
156C22×C4×C29C22×C411yescharacteristic
157C22×C4×C29C22×C411yescharacteristic
158C22×C4×C29C22×C411yescharacteristic
159C22×C4×C29C22×C411yescharacteristic
160C22×C4×C29C22×C411yescharacteristic
161C22×C4×C29C22×C411yescharacteristic
162C22×C4×C29C2411yescharacteristic
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—44no—
186C2×C8×C29#4112yes—
187C2×C8×C29#4112yes—
188C4⋊C4×C29—22no—
189C4⋊C4×C29—22no—
190C4⋊C4×C29—22no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C22⋊C4×C29—22no—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—22no—
196C22⋊C4×C29—22no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—21no—
207C42×C29—21no—
208C42×C29—21no—
209C42×C29—21no—
210C42×C29—21no—
211C42×C29—41no—
212C42×C29—41no—
213#22367C2911yesmaximal, characteristic, direct product factor, Sylow
214C23×C29—21no—
215C23×C29—21no—
216C23×C29—21no—
217C23×C29—21no—
218C23×C29—21no—
219C23×C29—21no—
220C23×C29—21no—
221C23×C29—21no—
222C23×C29—21no—
223C23×C29—21no—
224C23×C29—21no—
225C23×C29—21no—
226C23×C29C2×M1612yes—
227C23×C29C2×M1612yes—
228C23×C29C23×C411yescharacteristic
229D4×C29—44no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—44no—
265C2×C4×C29—44no—
266C2×C4×C29—41no—
267C2×C4×C29—41no—
268C2×C4×C29—41no—
269C2×C4×C29—41no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29—41no—
273C2×C4×C29—41no—
274C2×C4×C29C2×M1612yes—
275C2×C4×C29#13112yes—
276C2×C4×C29C2×#4111yescharacteristic
277C2×C4×C29C2×#4111yescharacteristic
278C2×C4×C29H(5,𝔽2)11yescharacteristic
279C2×C4×C29H(5,𝔽2)11yescharacteristic
280C2×C4×C29H(5,𝔽2)11yescharacteristic
281C2×C4×C292−1+411yescharacteristic
282C8×C29—22no—
283C8×C29—22no—
284C8×C29—41no—
285C8×C29—41no—
286C8×C29—41no—
287C8×C29—41no—
288C8×C29—41no—
289C8×C29—41no—
290C4×#123C2×C2911yescharacteristic
291#1954C2×C2911yescharacteristic
292#1940C2×C2911yescharacteristic, complemented
293#1924C2×C2911yescharacteristic, complemented
294#1924C2×C2911yescharacteristic, complemented
295#1924C2×C2911yescharacteristic, complemented
296#1924C2×C2911yescharacteristic, complemented
297#1917C2×C2911yescharacteristic, complemented
298#1916C2×C2911yescharacteristic, complemented
299#1869C2×C2911yescharacteristic
300#1850C2×C2911yescharacteristic, complemented
301#1797C2×C2911yescharacteristic, complemented
302#1771C2×C2911yescharacteristic, complemented
303#1752C2×C2911yescharacteristic, complemented
304#1749C2×C2911yescharacteristic, complemented
305C22×C29—22no—
306C22×C29—22no—
307C22×C29—22no—
308C22×C29—22no—
309C22×C29—22no—
310C22×C29—22no—
311C22×C29—41no—
312C22×C29—41no—
313C22×C29—41no—
314C22×C29—41no—
315C22×C29—41no—
316C22×C29—41no—
317C22×C29—41no—
318C22×C29—41no—
319C22×C29C4×#4111yescharacteristic
320C22×C29#51811yescharacteristic
321C22×C29#52011yescharacteristic
322C22×C29C22×M1611yescharacteristic
323C22×C29C2×#13111yescharacteristic
324C22×C29#56811yescharacteristic
325C22×C29#56811yescharacteristic
326C4×C29—22no—
327C4×C29—22no—
328C4×C29—41no—
329C4×C29—41no—
330C4×C29—41no—
331C4×C29—41no—
332C4×C29—41no—
333C4×C29—41no—
334C4×C29—41no—
335C4×C29—41no—
336C4×C29—41no—
337C4×C29—41no—
338C4×C29#53811yescharacteristic
339C4×C29#53911yescharacteristic
340C4×C29#54011yescharacteristic
341C4×C29#54211yescharacteristic
342C23×C8C22×C2911yescharacteristic
343C2×#123C4×C2911yescharacteristic
344C2×C4×D4C22×C2911yescharacteristic
345C22×C42C22×C2911yescharacteristic
346C2×C4⋊C8C22×C2911yescharacteristic
347C2×C4⋊C8C22×C2911yescharacteristic
348C2×C4⋊C8C22×C2911yescharacteristic
349C2×C4⋊C8C22×C2911yescharacteristic
350C2×C4⋊C8C22×C2911yescharacteristic
351C2×C22⋊C8C22×C2911yescharacteristic
352C2×C22⋊C8C22×C2911yescharacteristic
353C2×C22⋊C8C22×C2911yescharacteristic
354C2×C22⋊C8C22×C2911yescharacteristic
355C2×C22⋊C8C22×C2911yescharacteristic
356C2×C22⋊C8C22×C2911yescharacteristic
357C2×C22⋊C8C22×C2911yescharacteristic
358C2×#97C22×C2911yescharacteristic
359C2×#97C22×C2911yescharacteristic
360C2×#97C22×C2911yescharacteristic
361C2×#97C22×C2911yescharacteristic
362C2×C4×C8C22×C2911yescharacteristic
363#388C4×C2911yescharacteristic
364#388C4×C2911yescharacteristic
365#387C4×C2911yescharacteristic
366#387C4×C2911yescharacteristic
367#386C4×C2911yescharacteristic
368#385C4×C2911yescharacteristic
369#381C4×C2911yescharacteristic
370C4×C4⋊C4C22×C2911yescharacteristic
371C4×C4⋊C4C22×C2911yescharacteristic
372C4×C22⋊C4C22×C2911yescharacteristic
373C4×C22⋊C4C22×C2911yescharacteristic
374C4×C22⋊C4C22×C2911yescharacteristic
375#336C22×C2911yescharacteristic
376#336C22×C2911yescharacteristic
377#336C22×C2911yescharacteristic
378#336C22×C2911yescharacteristic
379#336C22×C2911yescharacteristic
380#336C22×C2911yescharacteristic
381#336C22×C2911yescharacteristic
382#336C22×C2911yescharacteristic
383#336C22×C2911yescharacteristic
384#336C22×C2911yescharacteristic
385C2×C29—42no—
386C2×C29—42no—
387C2×C29#233511yescharacteristic
388C2×C29#296911yescharacteristic
389C2×C29#297011yescharacteristic
390C2×C29#297311yescharacteristic
391C2×C29#297611yescharacteristic
392C2×C29#299011yescharacteristic
393C2×C29#299511yescharacteristic
394C22×D4C2×C4×C2911yescharacteristic
395C23×C4C2×C4×C2911yescharacteristic
396C23×C4C2×C4×C2911yescharacteristic
397C23×C4C23×C2911yescharacteristic
398C23×C4C23×C2911yescharacteristic
399C22×C8—22no—
400C22×C8—41no—
401C22×C8—41no—
402C22×C8C23×C2911yescharacteristic
403C22×C8C23×C2911yescharacteristic
404C22×C8C23×C2911yescharacteristic
405C22×C8C23×C2911yescharacteristic
406C22×C8C23×C2911yescharacteristic
407C22×C8C23×C2911yescharacteristic
408C22×C8C23×C2911yescharacteristic
409C22×C8C23×C2911yescharacteristic
410#123—24no—
411C4×D4—41no—
412C4×D4—41no—
413C2×C4⋊C4C2×C4×C2911yescharacteristic
414C2×C4⋊C4C2×C4×C2911yescharacteristic
415C2×C4⋊C4C2×C4×C2911yescharacteristic
416C2×C4⋊C4C2×C4×C2911yescharacteristic
417C2×C4⋊C4C2×C4×C2911yescharacteristic
418C2×C22⋊C4C2×C4×C2911yescharacteristic
419C2×C22⋊C4C2×C4×C2911yescharacteristic
420C2×C22⋊C4C2×C4×C2911yescharacteristic
421C2×C22⋊C4C2×C4×C2911yescharacteristic
422C2×C22⋊C4C2×C4×C2911yescharacteristic
423C2×C22⋊C4C2×C4×C2911yescharacteristic
424C2×C22⋊C4C2×C4×C2911yescharacteristic
425C2×C22⋊C4C2×C4×C2911yescharacteristic
426C2×C42—41no—
427C2×C42—41no—
428C2×C42C2×C4×C2911yescharacteristic
429C2×C42C2×C4×C2911yescharacteristic
430C2×C42C23×C2911yescharacteristic
431C2×C42C23×C2911yescharacteristic
432C2×C42C23×C2911yescharacteristic
433C2×C42C23×C2911yescharacteristic
434C2×C42C23×C2911yescharacteristic
435C4⋊C8—22no—
436C4⋊C8—41no—
437C4⋊C8—41no—
438C4⋊C8—41no—
439C4⋊C8—41no—
440C22⋊C8—22no—
441C22⋊C8—22no—
442C22⋊C8—22no—
443C22⋊C8—41no—
444C22⋊C8—41no—
445C22⋊C8—41no—
446C22⋊C8—41no—
447#97—22no—
448#97—41no—
449#97—41no—
450#97—41no—
451C4×C8—41no—
452#95C2×C4×C2911yescharacteristic
453#95C2×C4×C2911yescharacteristic
454#95C2×C4×C2911yescharacteristic
455#95C2×C4×C2911yescharacteristic
456#95C2×C4×C2911yescharacteristic
457#95C2×C4×C2911yescharacteristic
458#95C2×C4×C2911yescharacteristic
459#95C2×C4×C2911yescharacteristic
460#95C2×C4×C2911yescharacteristic
461#95C2×C4×C2911yescharacteristic
462C29#2236711yescharacteristic, direct product factor, Sylow
463C24C22×C4×C2911yescharacteristic
464C24C22×C4×C2911yescharacteristic
465C2×D4—41no—
466C2×D4—41no—
467C2×D4M16×C2914yes—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4C22×C4×C2911yescharacteristic
487C22×C4C22×C4×C2911yescharacteristic
488C22×C4C22×C4×C2911yescharacteristic
489C22×C4C22×C4×C2911yescharacteristic
490C22×C4C22×C4×C2911yescharacteristic
491C22×C4C22×C4×C2911yescharacteristic
492C22×C4C22×C4×C2911yescharacteristic
493C22×C4C22×C4×C2911yescharacteristic
494C22×C4C22×C4×C2911yescharacteristic
495C22×C4C22×C4×C2911yescharacteristic
496C22×C4C22×C4×C2911yescharacteristic
497C22×C4C22×C4×C2911yescharacteristic
498C22×C4C24×C2911yescharacteristic
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—44no—
522C2×C8#41×C2912yes—
523C2×C8#41×C2912yes—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—41no—
548C42—41no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23C2×M16×C2912yes—
562C23C2×M16×C2912yes—
563C23C23×C4×C2911yescharacteristic
564D4—44no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4C2×M16×C2912yes—
610C2×C4C29×#13112yes—
611C2×C4C2×#41×C2911yescharacteristic
612C2×C4C2×#41×C2911yescharacteristic
613C2×C4C29×H(5,𝔽2)11yescharacteristic
614C2×C4C29×H(5,𝔽2)11yescharacteristic
615C2×C4C29×H(5,𝔽2)11yescharacteristic
616C2×C4C29×2−1+411yescharacteristic
617C8—22no—
618C8—22no—
619C8—41no—
620C8—41no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C4×#41×C2911yescharacteristic
640C22C29×#51811yescharacteristic
641C22C29×#52011yescharacteristic
642C22C22×M16×C2911yescharacteristic
643C22C2×C29×#13111yescharacteristic
644C22C29×#56811yescharacteristic
645C22C29×#56811yescharacteristic
646C4—22no—
647C4—22no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4C29×#53811yescharacteristic
659C4C29×#53911yescharacteristic
660C4C29×#54011yescharacteristic
661C4C29×#54211yescharacteristic
662C2—42no—
663C2—42no—
664C2C29×#233511yescharacteristic
665C2C29×#296911yescharacteristic
666C2C29×#297011yescharacteristic
667C2C29×#297311yescharacteristic
668C2C29×#297611yescharacteristic
669C2C29×#299011yescharacteristic
670C2C29×#299511yescharacteristic
subgroupG/H
centerC22×C4×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC22×C4C24×C29
socleC23×C29C23×C4
prime radicalC22×D4×C29C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1940C2semidirect
4. C29×#1924C2semidirect
5. C29×#1924C2semidirect
6. C29×#1924C2semidirect
7. C29×#1924C2semidirect
8. C29×#1917C2semidirect
9. C29×#1916C2semidirect
11. C29×#1850C2semidirect
12. C29×#1797C2semidirect
13. C29×#1771C2semidirect
14. C29×#1752C2semidirect
15. C29×#1749C2semidirect
213. #22367C29direct (N × H)
292. #1940C2×C29semidirect
293. #1924C2×C29semidirect
294. #1924C2×C29semidirect
295. #1924C2×C29semidirect
296. #1924C2×C29semidirect
297. #1917C2×C29semidirect
298. #1916C2×C29semidirect
300. #1850C2×C29semidirect
301. #1797C2×C29semidirect
302. #1771C2×C29semidirect
303. #1752C2×C29semidirect
304. #1749C2×C29semidirect
462. C29#22367direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C29×#1232
C29×#19542
C29×#19402
C29×#19242
C29×#19172
C29×#19162
C29×#18692
C29×#18502
C29×#17972
C29×#17712
C29×#17522
C29×#17492
#2236729