Finite Group Databasebeta

← C29×#22334 #20317234

Subgroups — C29×#22334 #20317234

Order 7424.

806 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2392C211yesmaximal, characteristic
2C29×#1955C211yesmaximal, characteristic, complemented
3C29×#1954C211yesmaximal, characteristic, complemented
4C29×#1924C211yesmaximal, characteristic, complemented
5C29×#1924C211yesmaximal, characteristic, complemented
6C29×#1917C211yesmaximal, characteristic, complemented
7C29×#1916C211yesmaximal, characteristic, complemented
8C29×#1870C211yesmaximal, characteristic, complemented
9C29×#1870C211yesmaximal, characteristic, complemented
10C29×#1869C211yesmaximal, characteristic, complemented
11C29×#1869C211yesmaximal, characteristic, complemented
12C29×#1818C211yesmaximal, characteristic, complemented
13C29×#1753C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C29C211yesmaximal, characteristic, complemented
15C29×#1750C211yesmaximal, characteristic, complemented
16C22×M16×C29C2211yescharacteristic
17C23×C8×C29C2211yescharacteristic
18C2×C4×D4×C29C2211yescharacteristic
19C2×C4×D4×C29C2211yescharacteristic
20C2×C4×D4×C29C2211yescharacteristic
21C2×C29×#117C2211yescharacteristic
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×C22⋊C8C2211yescharacteristic
32C2×C29×C22⋊C8C2211yescharacteristic
33C2×C29×C22⋊C8C2211yescharacteristic
34C2×C29×#97C2211yescharacteristic
35C2×C29×#97C2211yescharacteristic
36C2×C4×C8×C29C2211yescharacteristic
37C2×C4×C8×C29C2211yescharacteristic
38C29×#398C411yescharacteristic
39C29×#397C411yescharacteristic
40C29×#396C411yescharacteristic
41C29×#396C411yescharacteristic
42C29×#394C411yescharacteristic
43C29×#394C411yescharacteristic
44C29×#394C411yescharacteristic
45C29×#392C411yescharacteristic
46C4×C4⋊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
60C22×D4×C29C2×C411yescharacteristic
61C22×D4×C29C2×C411yescharacteristic
62C23×C4×C29C2311yescharacteristic
63C23×C4×C29C2311yescharacteristic
64C23×C4×C29C2311yescharacteristic
65C2×M16×C29—22no—
66C2×M16×C29—41no—
67C2×M16×C29—41no—
68C22×C8×C29—22no—
69C22×C8×C29—41no—
70C22×C8×C29—41no—
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C22×C8×C29C2311yescharacteristic
77C22×C8×C29C2311yescharacteristic
78C22×C8×C29C2311yescharacteristic
79C4×D4×C29—41no—
80C4×D4×C29—41no—
81C4×D4×C29—41no—
82C4×D4×C29—41no—
83C4×D4×C29—41no—
84C4×D4×C29—41no—
85C29×#117—41no—
86C29×#117—41no—
87C2×C4⋊C4×C29C2×C411yescharacteristic
88C2×C4⋊C4×C29C2×C411yescharacteristic
89C2×C4⋊C4×C29C2×C411yescharacteristic
90C2×C4⋊C4×C29C2×C411yescharacteristic
91C2×C4⋊C4×C29C2×C411yescharacteristic
92C2×C4⋊C4×C29C2×C411yescharacteristic
93C2×C4⋊C4×C29C2×C411yescharacteristic
94C2×C22⋊C4×C29C2×C411yescharacteristic
95C2×C22⋊C4×C29C2×C411yescharacteristic
96C2×C22⋊C4×C29C2×C411yescharacteristic
97C2×C22⋊C4×C29C2×C411yescharacteristic
98C2×C22⋊C4×C29C2×C411yescharacteristic
99C2×C22⋊C4×C29C2×C411yescharacteristic
100C2×C22⋊C4×C29C2×C411yescharacteristic
101C2×C22⋊C4×C29C2×C411yescharacteristic
102C2×C22⋊C4×C29C2×C411yescharacteristic
103C2×C22⋊C4×C29C2×C411yescharacteristic
104C2×C22⋊C4×C29C2×C411yescharacteristic
105C2×C22⋊C4×C29C2×C411yescharacteristic
106C2×C42×C29C2311yescharacteristic
107C2×C42×C29C2311yescharacteristic
108C2×C42×C29C2311yescharacteristic
109C2×C42×C29C2311yescharacteristic
110C29×C4⋊C8—41no—
111C29×C4⋊C8—41no—
112C29×C22⋊C8—22no—
113C29×C22⋊C8—22no—
114C29×C22⋊C8—22no—
115C29×C22⋊C8—22no—
116C29×C22⋊C8—41no—
117C29×C22⋊C8—41no—
118C29×C22⋊C8—41no—
119C29×C22⋊C8—41no—
120C29×C22⋊C8—41no—
121C29×C22⋊C8—41no—
122C29×#97—41no—
123C29×#97—41no—
124C4×C8×C29—41no—
125C4×C8×C29—41no—
126C29×#95C2×C411yescharacteristic
127C29×#95C2×C411yescharacteristic
128C29×#95C2×C411yescharacteristic
129C29×#95C2×C411yescharacteristic
130C29×#95C2×C411yescharacteristic
131C29×#95C2×C411yescharacteristic
132C24×C29C22×C411yescharacteristic
133C24×C29C22×C411yescharacteristic
134C24×C29C22×C411yescharacteristic
135C2×D4×C29—22no—
136C2×D4×C29—22no—
137C2×D4×C29—22no—
138C2×D4×C29—41no—
139C2×D4×C29—41no—
140C2×D4×C29—41no—
141C2×D4×C29—41no—
142C2×D4×C29—41no—
143C2×D4×C29—41no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—21no—
150C22×C4×C29—21no—
151C22×C4×C29—21no—
152C22×C4×C29—21no—
153C22×C4×C29—21no—
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×C29C22×C411yescharacteristic
163C22×C4×C29C22×C411yescharacteristic
164C22×C4×C29C22×C411yescharacteristic
165C22×C4×C29C22×C411yescharacteristic
166C22×C4×C29C22×C411yescharacteristic
167C22×C4×C29C22×C411yescharacteristic
168C22×C4×C29C22×C411yescharacteristic
169C22×C4×C29C22×C411yescharacteristic
170C22×C4×C29C22×C411yescharacteristic
171C22×C4×C29C22×C411yescharacteristic
172C22×C4×C29C22×C411yescharacteristic
173C22×C4×C29C2411yescharacteristic
174M16×C29—44no—
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—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29—21no—
193C2×C8×C29—21no—
194C2×C8×C29—21no—
195C2×C8×C29—21no—
196C2×C8×C29—21no—
197C2×C8×C29—44no—
198C2×C8×C29#4112yes—
199C2×C8×C29#4112yes—
200C4⋊C4×C29—22no—
201C4⋊C4×C29—41no—
202C4⋊C4×C29—41no—
203C4⋊C4×C29—41no—
204C4⋊C4×C29—41no—
205C4⋊C4×C29—41no—
206C4⋊C4×C29—41no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—22no—
209C22⋊C4×C29—41no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C22⋊C4×C29—41no—
214C22⋊C4×C29—41no—
215C22⋊C4×C29—41no—
216C22⋊C4×C29—41no—
217C22⋊C4×C29—41no—
218C22⋊C4×C29—41no—
219C42×C29—21no—
220C42×C29—21no—
221C42×C29—21no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—21no—
225C42×C29—21no—
226C42×C29—21no—
227#22334C2911yesmaximal, characteristic, direct product factor, Sylow
228C23×C29—21no—
229C23×C29—21no—
230C23×C29—21no—
231C23×C29—21no—
232C23×C29—21no—
233C23×C29—21no—
234C23×C29—21no—
235C23×C29—21no—
236C23×C29—21no—
237C23×C29—21no—
238C23×C29—21no—
239C23×C29—21no—
240C23×C29—21no—
241C23×C29—21no—
242C23×C29—21no—
243C23×C29—21no—
244C23×C29—21no—
245C23×C29—21no—
246C23×C29—21no—
247C23×C29—21no—
248C23×C29#13112yes—
249C23×C29C23×C411yescharacteristic
250D4×C29—44no—
251D4×C29—44no—
252D4×C29—44no—
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—21no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
269C2×C4×C29—21no—
270C2×C4×C29—21no—
271C2×C4×C29—21no—
272C2×C4×C29—21no—
273C2×C4×C29—21no—
274C2×C4×C29—21no—
275C2×C4×C29—21no—
276C2×C4×C29—21no—
277C2×C4×C29—21no—
278C2×C4×C29—21no—
279C2×C4×C29—21no—
280C2×C4×C29—21no—
281C2×C4×C29—21no—
282C2×C4×C29—21no—
283C2×C4×C29—21no—
284C2×C4×C29—21no—
285C2×C4×C29—41no—
286C2×C4×C29—41no—
287C2×C4×C29—41no—
288C2×C4×C29—41no—
289C2×C4×C29—41no—
290C2×C4×C29—41no—
291C2×C4×C29—41no—
292C2×C4×C29—41no—
293C2×C4×C29—41no—
294C2×C4×C29—41no—
295C2×C4×C29—41no—
296C2×C4×C29—41no—
297C2×C4×C29#13112yes—
298C2×C4×C29C2×#4111yescharacteristic
299C2×C4×C29C2×#4111yescharacteristic
300C2×C4×C29H(5,𝔽2)11yescharacteristic
301C2×C4×C29H(5,𝔽2)11yescharacteristic
302C2×C4×C29H(5,𝔽2)11yescharacteristic
303C2×C4×C29H(5,𝔽2)11yescharacteristic
304C8×C29—22no—
305C8×C29—22no—
306C8×C29—41no—
307C8×C29—41no—
308C8×C29—41no—
309C8×C29—41no—
310C8×C29—41no—
311C8×C29—41no—
312#2392C2×C2911yescharacteristic
313#1955C2×C2911yescharacteristic, complemented
314#1954C2×C2911yescharacteristic, complemented
315#1924C2×C2911yescharacteristic, complemented
316#1924C2×C2911yescharacteristic, complemented
317#1917C2×C2911yescharacteristic, complemented
318#1916C2×C2911yescharacteristic, complemented
319#1870C2×C2911yescharacteristic, complemented
320#1870C2×C2911yescharacteristic, complemented
321#1869C2×C2911yescharacteristic, complemented
322#1869C2×C2911yescharacteristic, complemented
323#1818C2×C2911yescharacteristic, complemented
324#1753C2×C2911yescharacteristic, complemented
325C8×C22⋊C4C2×C2911yescharacteristic, complemented
326#1750C2×C2911yescharacteristic, complemented
327C22×C29—22no—
328C22×C29—22no—
329C22×C29—22no—
330C22×C29—41no—
331C22×C29—41no—
332C22×C29—41no—
333C22×C29—41no—
334C22×C29—41no—
335C22×C29—41no—
336C22×C29—41no—
337C22×C29—41no—
338C22×C29—41no—
339C22×C29—41no—
340C22×C29—41no—
341C22×C29—41no—
342C22×C29—41no—
343C22×C29—41no—
344C22×C29—41no—
345C22×C29—41no—
346C22×C29—41no—
347C22×C29—41no—
348C22×C29C4×#4111yescharacteristic
349C22×C29#51811yescharacteristic
350C22×C29#51811yescharacteristic
351C22×C29C2×#13111yescharacteristic
352C22×C29C2×#13111yescharacteristic
353C22×C29#56811yescharacteristic
354C22×C29#56811yescharacteristic
355C4×C29—22no—
356C4×C29—41no—
357C4×C29—41no—
358C4×C29—41no—
359C4×C29—41no—
360C4×C29—41no—
361C4×C29—41no—
362C4×C29—41no—
363C4×C29—41no—
364C4×C29—41no—
365C4×C29—41no—
366C4×C29#53811yescharacteristic
367C4×C29#53811yescharacteristic
368C4×C29#54011yescharacteristic
369C4×C29#54011yescharacteristic
370C22×M16C22×C2911yescharacteristic
371C23×C8C22×C2911yescharacteristic
372C2×C4×D4C22×C2911yescharacteristic
373C2×C4×D4C22×C2911yescharacteristic
374C2×C4×D4C22×C2911yescharacteristic
375C2×#117C22×C2911yescharacteristic
376C2×C4⋊C8C22×C2911yescharacteristic
377C2×C4⋊C8C22×C2911yescharacteristic
378C2×C22⋊C8C22×C2911yescharacteristic
379C2×C22⋊C8C22×C2911yescharacteristic
380C2×C22⋊C8C22×C2911yescharacteristic
381C2×C22⋊C8C22×C2911yescharacteristic
382C2×C22⋊C8C22×C2911yescharacteristic
383C2×C22⋊C8C22×C2911yescharacteristic
384C2×C22⋊C8C22×C2911yescharacteristic
385C2×C22⋊C8C22×C2911yescharacteristic
386C2×C22⋊C8C22×C2911yescharacteristic
387C2×C22⋊C8C22×C2911yescharacteristic
388C2×#97C22×C2911yescharacteristic
389C2×#97C22×C2911yescharacteristic
390C2×C4×C8C22×C2911yescharacteristic
391C2×C4×C8C22×C2911yescharacteristic
392#398C4×C2911yescharacteristic
393#397C4×C2911yescharacteristic
394#396C4×C2911yescharacteristic
395#396C4×C2911yescharacteristic
396#394C4×C2911yescharacteristic
397#394C4×C2911yescharacteristic
398#394C4×C2911yescharacteristic
399#392C4×C2911yescharacteristic
400C4×C4⋊C4C22×C2911yescharacteristic
401C4×C22⋊C4C22×C2911yescharacteristic
402C4×C22⋊C4C22×C2911yescharacteristic
403#336C22×C2911yescharacteristic
404#336C22×C2911yescharacteristic
405#336C22×C2911yescharacteristic
406#336C22×C2911yescharacteristic
407#336C22×C2911yescharacteristic
408#336C22×C2911yescharacteristic
409#336C22×C2911yescharacteristic
410#336C22×C2911yescharacteristic
411#336C22×C2911yescharacteristic
412#336C22×C2911yescharacteristic
413C2×C29—42no—
414C2×C29—81no—
415C2×C29—81no—
416C2×C29#233311yescharacteristic
417C2×C29#296611yescharacteristic
418C2×C29#296711yescharacteristic
419C2×C29#297611yescharacteristic
420C2×C29#297611yescharacteristic
421C2×C29#297611yescharacteristic
422C2×C29#298111yescharacteristic
423C22×D4C2×C4×C2911yescharacteristic
424C22×D4C2×C4×C2911yescharacteristic
425C22×D4C2×C4×C2911yescharacteristic
426C23×C4C23×C2911yescharacteristic
427C23×C4C23×C2911yescharacteristic
428C23×C4C23×C2911yescharacteristic
429C2×M16—22no—
430C2×M16—41no—
431C2×M16—41no—
432C22×C8—22no—
433C22×C8—41no—
434C22×C8—41no—
435C22×C8C23×C2911yescharacteristic
436C22×C8C23×C2911yescharacteristic
437C22×C8C23×C2911yescharacteristic
438C22×C8C23×C2911yescharacteristic
439C22×C8C23×C2911yescharacteristic
440C22×C8C23×C2911yescharacteristic
441C22×C8C23×C2911yescharacteristic
442C22×C8C23×C2911yescharacteristic
443C4×D4—41no—
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449#117—41no—
450#117—41no—
451C2×C4⋊C4C2×C4×C2911yescharacteristic
452C2×C4⋊C4C2×C4×C2911yescharacteristic
453C2×C4⋊C4C2×C4×C2911yescharacteristic
454C2×C4⋊C4C2×C4×C2911yescharacteristic
455C2×C4⋊C4C2×C4×C2911yescharacteristic
456C2×C4⋊C4C2×C4×C2911yescharacteristic
457C2×C4⋊C4C2×C4×C2911yescharacteristic
458C2×C22⋊C4C2×C4×C2911yescharacteristic
459C2×C22⋊C4C2×C4×C2911yescharacteristic
460C2×C22⋊C4C2×C4×C2911yescharacteristic
461C2×C22⋊C4C2×C4×C2911yescharacteristic
462C2×C22⋊C4C2×C4×C2911yescharacteristic
463C2×C22⋊C4C2×C4×C2911yescharacteristic
464C2×C22⋊C4C2×C4×C2911yescharacteristic
465C2×C22⋊C4C2×C4×C2911yescharacteristic
466C2×C22⋊C4C2×C4×C2911yescharacteristic
467C2×C22⋊C4C2×C4×C2911yescharacteristic
468C2×C22⋊C4C2×C4×C2911yescharacteristic
469C2×C22⋊C4C2×C4×C2911yescharacteristic
470C2×C42C23×C2911yescharacteristic
471C2×C42C23×C2911yescharacteristic
472C2×C42C23×C2911yescharacteristic
473C2×C42C23×C2911yescharacteristic
474C4⋊C8—41no—
475C4⋊C8—41no—
476C22⋊C8—22no—
477C22⋊C8—22no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480C22⋊C8—41no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486#97—41no—
487#97—41no—
488C4×C8—41no—
489C4×C8—41no—
490#95C2×C4×C2911yescharacteristic
491#95C2×C4×C2911yescharacteristic
492#95C2×C4×C2911yescharacteristic
493#95C2×C4×C2911yescharacteristic
494#95C2×C4×C2911yescharacteristic
495#95C2×C4×C2911yescharacteristic
496C29#2233411yescharacteristic, direct product factor, Sylow
497C24C22×C4×C2911yescharacteristic
498C24C22×C4×C2911yescharacteristic
499C24C22×C4×C2911yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C22×C4×C2911yescharacteristic
528C22×C4C22×C4×C2911yescharacteristic
529C22×C4C22×C4×C2911yescharacteristic
530C22×C4C22×C4×C2911yescharacteristic
531C22×C4C22×C4×C2911yescharacteristic
532C22×C4C22×C4×C2911yescharacteristic
533C22×C4C22×C4×C2911yescharacteristic
534C22×C4C22×C4×C2911yescharacteristic
535C22×C4C22×C4×C2911yescharacteristic
536C22×C4C22×C4×C2911yescharacteristic
537C22×C4C22×C4×C2911yescharacteristic
538C22×C4C24×C2911yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—44no—
563C2×C8#41×C2912yes—
564C2×C8#41×C2912yes—
565C4⋊C4—22no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23C29×#13112yes—
613C23C23×C4×C2911yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4C29×#13112yes—
662C2×C4C2×#41×C2911yescharacteristic
663C2×C4C2×#41×C2911yescharacteristic
664C2×C4C29×H(5,𝔽2)11yescharacteristic
665C2×C4C29×H(5,𝔽2)11yescharacteristic
666C2×C4C29×H(5,𝔽2)11yescharacteristic
667C2×C4C29×H(5,𝔽2)11yescharacteristic
668C8—22no—
669C8—22no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22C4×#41×C2911yescharacteristic
698C22C29×#51811yescharacteristic
699C22C29×#51811yescharacteristic
700C22C2×C29×#13111yescharacteristic
701C22C2×C29×#13111yescharacteristic
702C22C29×#56811yescharacteristic
703C22C29×#56811yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4C29×#53811yescharacteristic
716C4C29×#53811yescharacteristic
717C4C29×#54011yescharacteristic
718C4C29×#54011yescharacteristic
719C2—42no—
720C2—81no—
721C2—81no—
722C2C29×#233311yescharacteristic
723C2C29×#296611yescharacteristic
724C2C29×#296711yescharacteristic
725C2C29×#297611yescharacteristic
726C2C29×#297611yescharacteristic
727C2C29×#297611yescharacteristic
728C2C29×#298111yescharacteristic
subgroupG/H
centerC22×C4×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC22×C4C24×C29
socleC23×C29C23×C4
prime radicalC29×#392C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1955C2semidirect
3. C29×#1954C2semidirect
4. C29×#1924C2semidirect
5. C29×#1924C2semidirect
6. C29×#1917C2semidirect
7. C29×#1916C2semidirect
8. C29×#1870C2semidirect
9. C29×#1870C2semidirect
10. C29×#1869C2semidirect
11. C29×#1869C2semidirect
12. C29×#1818C2semidirect
13. C29×#1753C2semidirect
14. C8×C22⋊C4×C29C2semidirect
15. C29×#1750C2semidirect
227. #22334C29direct (N × H)
313. #1955C2×C29semidirect
314. #1954C2×C29semidirect
315. #1924C2×C29semidirect
316. #1924C2×C29semidirect
317. #1917C2×C29semidirect
318. #1916C2×C29semidirect
319. #1870C2×C29semidirect
320. #1870C2×C29semidirect
321. #1869C2×C29semidirect
322. #1869C2×C29semidirect
323. #1818C2×C29semidirect
324. #1753C2×C29semidirect
325. C8×C22⋊C4C2×C29semidirect
326. #1750C2×C29semidirect
496. C29#22334direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23922
C29×#19552
C29×#19542
C29×#19242
C29×#19172
C29×#19162
C29×#18702
C29×#18692
C29×#18182
C29×#17532
C8×C22⋊C4×C292
C29×#17502
#2233429