Finite Group Databasebeta

← C29×#22372 #20317272

Subgroups — C29×#22372 #20317272

Order 7424.

716 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2395C211yesmaximal, characteristic
2C29×#1955C211yesmaximal, characteristic
3C29×#1940C211yesmaximal, characteristic, complemented
4C29×#1924C211yesmaximal, characteristic, complemented
5C29×#1923C211yesmaximal, characteristic, complemented
6C29×#1923C211yesmaximal, characteristic, complemented
7C29×#1923C211yesmaximal, characteristic, complemented
8C29×#1917C211yesmaximal, characteristic, complemented
9C29×#1916C211yesmaximal, characteristic, complemented
10C29×#1869C211yesmaximal, characteristic
11C29×#1850C211yesmaximal, characteristic, complemented
12C29×#1798C211yesmaximal, characteristic, complemented
13C29×#1770C211yesmaximal, characteristic, complemented
14C29×#1752C211yesmaximal, characteristic, complemented
15C29×#1750C211yesmaximal, characteristic, complemented
16C23×C8×C29C2211yescharacteristic
17C2×C4×D4×C29C2211yescharacteristic
18C2×C29×#117C2211yescharacteristic
19C2×C29×C4⋊C8C2211yescharacteristic
20C2×C29×C4⋊C8C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×C22⋊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×#97C2211yescharacteristic
32C2×C29×#97C2211yescharacteristic
33C2×C29×#97C2211yescharacteristic
34C2×C4×C8×C29C2211yescharacteristic
35C2×C4×C8×C29C2211yescharacteristic
36C29×#400C411yescharacteristic
37C29×#399C411yescharacteristic
38C29×#398C411yescharacteristic
39C29×#397C411yescharacteristic
40C29×#397C411yescharacteristic
41C29×#397C411yescharacteristic
42C29×#394C411yescharacteristic
43C29×#394C411yescharacteristic
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×C29C2311yescharacteristic
61C23×C4×C29C2311yescharacteristic
62C22×C8×C29—22no—
63C22×C8×C29—41no—
64C22×C8×C29—41no—
65C22×C8×C29C2311yescharacteristic
66C22×C8×C29C2311yescharacteristic
67C22×C8×C29C2311yescharacteristic
68C22×C8×C29C2311yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C22×C8×C29C2311yescharacteristic
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C4×D4×C29—41no—
74C4×D4×C29—41no—
75C29×#117—41no—
76C29×#117—41no—
77C2×C4⋊C4×C29C2×C411yescharacteristic
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×C4⋊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×C22⋊C4×C29C2×C411yescharacteristic
92C2×C22⋊C4×C29C2×C411yescharacteristic
93C2×C22⋊C4×C29C2×C411yescharacteristic
94C2×C42×C29C2311yescharacteristic
95C2×C42×C29C2311yescharacteristic
96C2×C42×C29C2311yescharacteristic
97C2×C42×C29C2311yescharacteristic
98C2×C42×C29C2311yescharacteristic
99C29×C4⋊C8—22no—
100C29×C4⋊C8—41no—
101C29×C4⋊C8—41no—
102C29×C4⋊C8—41no—
103C29×C4⋊C8—41no—
104C29×C22⋊C8—22no—
105C29×C22⋊C8—22no—
106C29×C22⋊C8—22no—
107C29×C22⋊C8—41no—
108C29×C22⋊C8—41no—
109C29×C22⋊C8—41no—
110C29×C22⋊C8—41no—
111C29×#97—41no—
112C29×#97—41no—
113C29×#97—41no—
114C4×C8×C29—22no—
115C4×C8×C29—41no—
116C29×#95C2×C411yescharacteristic
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
126C24×C29C22×C411yescharacteristic
127C24×C29C22×C411yescharacteristic
128C2×D4×C29—22no—
129C2×D4×C29—41no—
130C2×D4×C29—41no—
131C22×C4×C29—21no—
132C22×C4×C29—21no—
133C22×C4×C29—21no—
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×C29C22×C411yescharacteristic
144C22×C4×C29C22×C411yescharacteristic
145C22×C4×C29C22×C411yescharacteristic
146C22×C4×C29C22×C411yescharacteristic
147C22×C4×C29C22×C411yescharacteristic
148C22×C4×C29C22×C411yescharacteristic
149C22×C4×C29C22×C411yescharacteristic
150C22×C4×C29C22×C411yescharacteristic
151C22×C4×C29C22×C411yescharacteristic
152C22×C4×C29C22×C411yescharacteristic
153C22×C4×C29C22×C411yescharacteristic
154C22×C4×C29C22×C411yescharacteristic
155C22×C4×C29C2411yescharacteristic
156C2×C8×C29—21no—
157C2×C8×C29—21no—
158C2×C8×C29—21no—
159C2×C8×C29—21no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
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—44no—
179C2×C8×C29#4112yes—
180C2×C8×C29#4112yes—
181C4⋊C4×C29—22no—
182C4⋊C4×C29—41no—
183C4⋊C4×C29—41no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29—41no—
188C22⋊C4×C29—22no—
189C22⋊C4×C29—22no—
190C22⋊C4×C29—22no—
191C22⋊C4×C29—22no—
192C22⋊C4×C29—41no—
193C22⋊C4×C29—41no—
194C22⋊C4×C29—41no—
195C22⋊C4×C29—41no—
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C42×C29—21no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—21no—
207C42×C29—21no—
208#22372C2911yesmaximal, characteristic, direct product factor, Sylow
209C23×C29—21no—
210C23×C29—21no—
211C23×C29—21no—
212C23×C29—21no—
213C23×C29—21no—
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#13112yes—
223C23×C29C23×C411yescharacteristic
224D4×C29—44no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
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—41no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—41no—
267C2×C4×C29—41no—
268C2×C4×C29#13112yes—
269C2×C4×C29C2×#4111yescharacteristic
270C2×C4×C29C2×#4111yescharacteristic
271C2×C4×C29H(5,𝔽2)11yescharacteristic
272C2×C4×C29H(5,𝔽2)11yescharacteristic
273C2×C4×C29H(5,𝔽2)11yescharacteristic
274C2×C4×C292−1+411yescharacteristic
275C8×C29—22no—
276C8×C29—22no—
277C8×C29—41no—
278C8×C29—41no—
279C8×C29—41no—
280C8×C29—41no—
281C8×C29—41no—
282C8×C29—41no—
283#2395C2×C2911yescharacteristic
284#1955C2×C2911yescharacteristic
285#1940C2×C2911yescharacteristic, complemented
286#1924C2×C2911yescharacteristic, complemented
287#1923C2×C2911yescharacteristic, complemented
288#1923C2×C2911yescharacteristic, complemented
289#1923C2×C2911yescharacteristic, complemented
290#1917C2×C2911yescharacteristic, complemented
291#1916C2×C2911yescharacteristic, complemented
292#1869C2×C2911yescharacteristic
293#1850C2×C2911yescharacteristic, complemented
294#1798C2×C2911yescharacteristic, complemented
295#1770C2×C2911yescharacteristic, complemented
296#1752C2×C2911yescharacteristic, complemented
297#1750C2×C2911yescharacteristic, complemented
298C22×C29—22no—
299C22×C29—22no—
300C22×C29—22no—
301C22×C29—41no—
302C22×C29—41no—
303C22×C29—41no—
304C22×C29—41no—
305C22×C29—41no—
306C22×C29—41no—
307C22×C29—41no—
308C22×C29—41no—
309C22×C29—41no—
310C22×C29—41no—
311C22×C29—41no—
312C22×C29C4×#4111yescharacteristic
313C22×C29#51811yescharacteristic
314C22×C29#52011yescharacteristic
315C22×C29C2×#13111yescharacteristic
316C22×C29C2×#13111yescharacteristic
317C22×C29#56811yescharacteristic
318C22×C29#56811yescharacteristic
319C4×C29—22no—
320C4×C29—41no—
321C4×C29—41no—
322C4×C29—41no—
323C4×C29—41no—
324C4×C29—41no—
325C4×C29—41no—
326C4×C29—41no—
327C4×C29—41no—
328C4×C29—41no—
329C4×C29—41no—
330C4×C29—41no—
331C4×C29#53811yescharacteristic
332C4×C29#53911yescharacteristic
333C4×C29#54011yescharacteristic
334C4×C29#54211yescharacteristic
335C23×C8C22×C2911yescharacteristic
336C2×C4×D4C22×C2911yescharacteristic
337C2×#117C22×C2911yescharacteristic
338C2×C4⋊C8C22×C2911yescharacteristic
339C2×C4⋊C8C22×C2911yescharacteristic
340C2×C4⋊C8C22×C2911yescharacteristic
341C2×C4⋊C8C22×C2911yescharacteristic
342C2×C4⋊C8C22×C2911yescharacteristic
343C2×C22⋊C8C22×C2911yescharacteristic
344C2×C22⋊C8C22×C2911yescharacteristic
345C2×C22⋊C8C22×C2911yescharacteristic
346C2×C22⋊C8C22×C2911yescharacteristic
347C2×C22⋊C8C22×C2911yescharacteristic
348C2×C22⋊C8C22×C2911yescharacteristic
349C2×C22⋊C8C22×C2911yescharacteristic
350C2×#97C22×C2911yescharacteristic
351C2×#97C22×C2911yescharacteristic
352C2×#97C22×C2911yescharacteristic
353C2×C4×C8C22×C2911yescharacteristic
354C2×C4×C8C22×C2911yescharacteristic
355#400C4×C2911yescharacteristic
356#399C4×C2911yescharacteristic
357#398C4×C2911yescharacteristic
358#397C4×C2911yescharacteristic
359#397C4×C2911yescharacteristic
360#397C4×C2911yescharacteristic
361#394C4×C2911yescharacteristic
362#394C4×C2911yescharacteristic
363C4×C4⋊C4C22×C2911yescharacteristic
364C4×C4⋊C4C22×C2911yescharacteristic
365C4×C22⋊C4C22×C2911yescharacteristic
366C4×C22⋊C4C22×C2911yescharacteristic
367C4×C22⋊C4C22×C2911yescharacteristic
368#336C22×C2911yescharacteristic
369#336C22×C2911yescharacteristic
370#336C22×C2911yescharacteristic
371#336C22×C2911yescharacteristic
372#336C22×C2911yescharacteristic
373#336C22×C2911yescharacteristic
374#336C22×C2911yescharacteristic
375#336C22×C2911yescharacteristic
376#336C22×C2911yescharacteristic
377#336C22×C2911yescharacteristic
378C2×C29—42no—
379C2×C29—81no—
380C2×C29#233511yescharacteristic
381C2×C29#296811yescharacteristic
382C2×C29#296811yescharacteristic
383C2×C29#297611yescharacteristic
384C2×C29#298111yescharacteristic
385C2×C29#299411yescharacteristic
386C2×C29#299511yescharacteristic
387C22×D4C2×C4×C2911yescharacteristic
388C23×C4C23×C2911yescharacteristic
389C23×C4C23×C2911yescharacteristic
390C22×C8—22no—
391C22×C8—41no—
392C22×C8—41no—
393C22×C8C23×C2911yescharacteristic
394C22×C8C23×C2911yescharacteristic
395C22×C8C23×C2911yescharacteristic
396C22×C8C23×C2911yescharacteristic
397C22×C8C23×C2911yescharacteristic
398C22×C8C23×C2911yescharacteristic
399C22×C8C23×C2911yescharacteristic
400C22×C8C23×C2911yescharacteristic
401C4×D4—41no—
402C4×D4—41no—
403#117—41no—
404#117—41no—
405C2×C4⋊C4C2×C4×C2911yescharacteristic
406C2×C4⋊C4C2×C4×C2911yescharacteristic
407C2×C4⋊C4C2×C4×C2911yescharacteristic
408C2×C4⋊C4C2×C4×C2911yescharacteristic
409C2×C4⋊C4C2×C4×C2911yescharacteristic
410C2×C4⋊C4C2×C4×C2911yescharacteristic
411C2×C4⋊C4C2×C4×C2911yescharacteristic
412C2×C22⋊C4C2×C4×C2911yescharacteristic
413C2×C22⋊C4C2×C4×C2911yescharacteristic
414C2×C22⋊C4C2×C4×C2911yescharacteristic
415C2×C22⋊C4C2×C4×C2911yescharacteristic
416C2×C22⋊C4C2×C4×C2911yescharacteristic
417C2×C22⋊C4C2×C4×C2911yescharacteristic
418C2×C22⋊C4C2×C4×C2911yescharacteristic
419C2×C22⋊C4C2×C4×C2911yescharacteristic
420C2×C22⋊C4C2×C4×C2911yescharacteristic
421C2×C22⋊C4C2×C4×C2911yescharacteristic
422C2×C42C23×C2911yescharacteristic
423C2×C42C23×C2911yescharacteristic
424C2×C42C23×C2911yescharacteristic
425C2×C42C23×C2911yescharacteristic
426C2×C42C23×C2911yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—41no—
429C4⋊C8—41no—
430C4⋊C8—41no—
431C4⋊C8—41no—
432C22⋊C8—22no—
433C22⋊C8—22no—
434C22⋊C8—22no—
435C22⋊C8—41no—
436C22⋊C8—41no—
437C22⋊C8—41no—
438C22⋊C8—41no—
439#97—41no—
440#97—41no—
441#97—41no—
442C4×C8—22no—
443C4×C8—41no—
444#95C2×C4×C2911yescharacteristic
445#95C2×C4×C2911yescharacteristic
446#95C2×C4×C2911yescharacteristic
447#95C2×C4×C2911yescharacteristic
448#95C2×C4×C2911yescharacteristic
449#95C2×C4×C2911yescharacteristic
450#95C2×C4×C2911yescharacteristic
451#95C2×C4×C2911yescharacteristic
452#95C2×C4×C2911yescharacteristic
453#95C2×C4×C2911yescharacteristic
454C29#2237211yescharacteristic, direct product factor, Sylow
455C24C22×C4×C2911yescharacteristic
456C24C22×C4×C2911yescharacteristic
457C2×D4—22no—
458C2×D4—41no—
459C2×D4—41no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4C22×C4×C2911yescharacteristic
473C22×C4C22×C4×C2911yescharacteristic
474C22×C4C22×C4×C2911yescharacteristic
475C22×C4C22×C4×C2911yescharacteristic
476C22×C4C22×C4×C2911yescharacteristic
477C22×C4C22×C4×C2911yescharacteristic
478C22×C4C22×C4×C2911yescharacteristic
479C22×C4C22×C4×C2911yescharacteristic
480C22×C4C22×C4×C2911yescharacteristic
481C22×C4C22×C4×C2911yescharacteristic
482C22×C4C22×C4×C2911yescharacteristic
483C22×C4C22×C4×C2911yescharacteristic
484C22×C4C24×C2911yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
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—44no—
508C2×C8#41×C2912yes—
509C2×C8#41×C2912yes—
510C4⋊C4—22no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23C29×#13112yes—
551C23C23×C4×C2911yescharacteristic
552D4—44no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
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—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4C29×#13112yes—
597C2×C4C2×#41×C2911yescharacteristic
598C2×C4C2×#41×C2911yescharacteristic
599C2×C4C29×H(5,𝔽2)11yescharacteristic
600C2×C4C29×H(5,𝔽2)11yescharacteristic
601C2×C4C29×H(5,𝔽2)11yescharacteristic
602C2×C4C29×2−1+411yescharacteristic
603C8—22no—
604C8—22no—
605C8—41no—
606C8—41no—
607C8—41no—
608C8—41no—
609C8—41no—
610C8—41no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22C4×#41×C2911yescharacteristic
626C22C29×#51811yescharacteristic
627C22C29×#52011yescharacteristic
628C22C2×C29×#13111yescharacteristic
629C22C2×C29×#13111yescharacteristic
630C22C29×#56811yescharacteristic
631C22C29×#56811yescharacteristic
632C4—22no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4C29×#53811yescharacteristic
645C4C29×#53911yescharacteristic
646C4C29×#54011yescharacteristic
647C4C29×#54211yescharacteristic
648C2—42no—
649C2—81no—
650C2C29×#233511yescharacteristic
651C2C29×#296811yescharacteristic
652C2C29×#296811yescharacteristic
653C2C29×#297611yescharacteristic
654C2C29×#298111yescharacteristic
655C2C29×#299411yescharacteristic
656C2C29×#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×#1923C2semidirect
6. C29×#1923C2semidirect
7. C29×#1923C2semidirect
8. C29×#1917C2semidirect
9. C29×#1916C2semidirect
11. C29×#1850C2semidirect
12. C29×#1798C2semidirect
13. C29×#1770C2semidirect
14. C29×#1752C2semidirect
15. C29×#1750C2semidirect
208. #22372C29direct (N × H)
285. #1940C2×C29semidirect
286. #1924C2×C29semidirect
287. #1923C2×C29semidirect
288. #1923C2×C29semidirect
289. #1923C2×C29semidirect
290. #1917C2×C29semidirect
291. #1916C2×C29semidirect
293. #1850C2×C29semidirect
294. #1798C2×C29semidirect
295. #1770C2×C29semidirect
296. #1752C2×C29semidirect
297. #1750C2×C29semidirect
454. C29#22372direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23952
C29×#19552
C29×#19402
C29×#19242
C29×#19232
C29×#19172
C29×#19162
C29×#18692
C29×#18502
C29×#17982
C29×#17702
C29×#17522
C29×#17502
#2237229