Finite Group Databasebeta

← C2×C29×#3346 #20356138

Subgroups — C2×C29×#3346 #20356138

Order 7424.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#554C211yesmaximal, characteristic, complemented
2C2×C29×#553C211yesmaximal, characteristic
3C29×#3346C2116yesmaximal, direct product factor
4C2×C29×#501C211yesmaximal, characteristic, complemented
5C2×C29×#484C211yesmaximal, characteristic, complemented
6C2×C29×#481C211yesmaximal, characteristic, complemented
7C2×C29×#485C211yesmaximal, characteristic, complemented
8C2×C29×#480C211yesmaximal, characteristic, complemented
9C2×C29×#479C211yesmaximal, characteristic, complemented
10C2×C29×#474C211yesmaximal, characteristic, complemented
11C2×C29×#468C211yesmaximal, characteristic, complemented
12C2×C29×#465C211yesmaximal, characteristic, complemented
13C2×C29×#440C211yesmaximal, characteristic, complemented
14C2×C29×#435C211yesmaximal, characteristic, complemented
15C2×C29×#428C211yesmaximal, characteristic, complemented
16C22×C29×#107C211yesmaximal, characteristic, complemented
17C22×SD16×C29C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic
19C23×C8×C29C2211yescharacteristic
20C29×#554—24no—
21C29×#554C2218yescomplemented
22C29×#553—24no—
23C29×#553C2218yes—
24C2×C29×C4⋊Q8C2211yescharacteristic
25C2×C29×#126—21no—
26C2×C29×#125—21no—
27C2×C29×#125C2211yescharacteristic
28C2×C29×#123—21no—
29C2×C29×C22⋊Q8—21no—
30C2×C29×C22⋊Q8—21no—
31C2×C29×C22⋊Q8C2211yescharacteristic
32C2×C29×C22⋊Q8C2211yescharacteristic
33C2×C29×#121—21no—
34C2×C29×#121C2211yescharacteristic
35C2×C29×#121C2211yescharacteristic
36C2×C4×Q8×C29C2211yescharacteristic
37C2×C4×D4×C29—21no—
38C2×C4×D4×C29—21no—
39C2×C4×D4×C29C2211yescharacteristic
40C2×C4×D4×C29C2211yescharacteristic
41C2×C29×#117C2211yescharacteristic
42C22×C4⋊C4×C29C2211yescharacteristic
43C22×C4⋊C4×C29C2211yescharacteristic
44C22×C4⋊C4×C29C2211yescharacteristic
45C29×#501C2218yescomplemented
46C29×#485C2218yescomplemented
47C29×#484C2218yescomplemented
48C29×#481C2218yescomplemented
49C29×#480C2218yescomplemented
50C29×#479C2218yescomplemented
51C29×#474C2218yescomplemented
52C29×#468C2218yescomplemented
53C29×#465C2218yescomplemented
54C29×#440C2218yescomplemented
55C29×#435C2218yescomplemented
56C29×#428C2218yescomplemented
57C2×C29×#107C2211yescharacteristic
58C2×C29×#107C2211yescharacteristic
59C2×C29×#107C2211yescharacteristic
60C2×C29×#107C2211yescharacteristic
61C2×C29×#107C2211yescharacteristic
62C2×C29×#107C2211yescharacteristic
63C2×C29×#107C2218yescomplemented
64C2×C29×#106C2211yescharacteristic
65C2×C29×#106C2211yescharacteristic
66C2×C29×#106C2211yescharacteristic
67C2×C29×C4⋊C8C2211yescharacteristic
68C2×C29×#103C2211yescharacteristic
69C2×C29×#103C2211yescharacteristic
70C2×C29×#103C2211yescharacteristic
71C2×C29×#102C2211yescharacteristic
72C2×C29×#102C2211yescharacteristic
73C2×C29×#102C2211yescharacteristic
74C2×C29×C22⋊C8C2211yescharacteristic
75C2×C29×C22⋊C8C2211yescharacteristic
76C2×C29×#97C2211yescharacteristic
77C22×Q8×C29—21no—
78C22×Q8×C29C2311yescharacteristic
79C22×D4×C29—21no—
80C22×D4×C29—21no—
81C22×D4×C29D411yescharacteristic
82C22×D4×C29C2311yescharacteristic
83C23×C4×C29—21no—
84C23×C4×C29—21no—
85C23×C4×C29—21no—
86C23×C4×C29—21no—
87C23×C4×C29C2311yescharacteristic
88C23×C4×C29C2311yescharacteristic
89C2×SD16×C29—24no—
90C2×SD16×C29C2314yes—
91C2×M16×C29—24no—
92C2×M16×C29C2314yes—
93C22×C8×C29—24no—
94C22×C8×C29C2311yescharacteristic
95C22×C8×C29C2311yescharacteristic
96C22×C8×C29C2311yescharacteristic
97C22×C8×C29C2314yes—
98C22×C8×C29C2311yescharacteristic
99C29×C4⋊Q8—22no—
100C29×C4⋊Q8C2314yes—
101C29×#126—28no—
102C29×#125—28no—
103C29×#125—22no—
104C29×#125C2314yes—
105C29×#123—28no—
106C29×C22⋊Q8—22no—
107C29×C22⋊Q8—22no—
108C29×C22⋊Q8—28no—
109C29×C22⋊Q8—28no—
110C29×C22⋊Q8C2314yes—
111C29×C22⋊Q8C2314yes—
112C29×#121—28no—
113C29×#121—22no—
114C29×#121—22no—
115C29×#121C2314yes—
116C29×#121C2314yes—
117C4×Q8×C29—22no—
118C4×Q8×C29C2314yes—
119C4×D4×C29—28no—
120C4×D4×C29—28no—
121C4×D4×C29—22no—
122C4×D4×C29D414yes—
123C4×D4×C29C2314yes—
124C4×D4×C29C2314yes—
125C29×#117—22no—
126C29×#117C2314yes—
127C2×C4⋊C4×C29—21no—
128C2×C4⋊C4×C29—21no—
129C2×C4⋊C4×C29—21no—
130C2×C4⋊C4×C29—22no—
131C2×C4⋊C4×C29—22no—
132C2×C4⋊C4×C29—22no—
133C2×C4⋊C4×C29—21no—
134C2×C4⋊C4×C29—21no—
135C2×C4⋊C4×C29—21no—
136C2×C4⋊C4×C29—21no—
137C2×C4⋊C4×C29—21no—
138C2×C4⋊C4×C29—21no—
139C2×C4⋊C4×C29D411yescharacteristic
140C2×C4⋊C4×C29C2311yescharacteristic
141C2×C4⋊C4×C29C2311yescharacteristic
142C2×C4⋊C4×C29C2311yescharacteristic
143C2×C4⋊C4×C29C2311yescharacteristic
144C2×C4⋊C4×C29C2311yescharacteristic
145C2×C4⋊C4×C29C2311yescharacteristic
146C2×C4⋊C4×C29C2314yes—
147C2×C4⋊C4×C29C2314yes—
148C2×C4⋊C4×C29C2314yes—
149C2×C22⋊C4×C29—21no—
150C2×C22⋊C4×C29—21no—
151C2×C22⋊C4×C29—21no—
152C2×C22⋊C4×C29—21no—
153C2×C22⋊C4×C29—21no—
154C2×C22⋊C4×C29—21no—
155C2×C22⋊C4×C29D411yescharacteristic
156C2×C22⋊C4×C29D411yescharacteristic
157C2×C42×C29—21no—
158C2×C42×C29—21no—
159C2×C42×C29C2311yescharacteristic
160C29×#107C2314yes—
161C29×#107C2314yes—
162C29×#107C2314yes—
163C29×#107C2314yes—
164C29×#107C2314yes—
165C29×#107C2314yes—
166C29×#106C2314yes—
167C29×#106C2314yes—
168C29×#106C2314yes—
169C29×C4⋊C8C2314yes—
170C29×#103C2314yes—
171C29×#103C2314yes—
172C29×#103C2314yes—
173C29×#102C2314yes—
174C29×#102C2314yes—
175C29×#102C2314yes—
176C29×C22⋊C8C2314yes—
177C29×C22⋊C8C2314yes—
178C29×#97C2314yes—
179C24×C29—21no—
180C24×C29C2×D411yescharacteristic
181C24×C29C2×D411yescharacteristic
182C2×Q8×C29—21no—
183C2×Q8×C29—24no—
184C2×Q8×C29—22no—
185C2×Q8×C29—22no—
186C2×Q8×C29—82no—
187C2×Q8×C29C2412yes—
188C2×D4×C29—24no—
189C2×D4×C29—24no—
190C2×D4×C29—24no—
191C2×D4×C29—21no—
192C2×D4×C29—22no—
193C2×D4×C29—22no—
194C2×D4×C29—44no—
195C2×D4×C29—82no—
196C2×D4×C29C2×D414yes—
197C2×D4×C29C2412yes—
198C22×C4×C29—22no—
199C22×C4×C29—22no—
200C22×C4×C29—22no—
201C22×C4×C29—22no—
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—24no—
210C22×C4×C29—24no—
211C22×C4×C29—24no—
212C22×C4×C29—24no—
213C22×C4×C29—82no—
214C22×C4×C29—82no—
215C22×C4×C29—82no—
216C22×C4×C29—82no—
217C22×C4×C29C2×D412yes—
218C22×C4×C29C2×D412yes—
219C22×C4×C29C2×D411yescharacteristic
220C22×C4×C29C2×D411yescharacteristic
221C22×C4×C29C2×D411yescharacteristic
222C22×C4×C29C2×D411yescharacteristic
223C22×C4×C29C2412yes—
224C22×C4×C29C2412yes—
225C22×C4×C29C2411yescharacteristic
226SD16×C29—28no—
227M16×C29—28no—
228C2×C8×C29—22no—
229C2×C8×C29—22no—
230C2×C8×C29—22no—
231C2×C8×C29—28no—
232C2×C8×C29#4114yes—
233C2×C8×C29C2412yes—
234C2×C8×C29C2412yes—
235C2×C8×C29C2412yes—
236C2×C8×C29C2412yes—
237C4⋊C4×C29—21no—
238C4⋊C4×C29—21no—
239C4⋊C4×C29—21no—
240C4⋊C4×C29—24no—
241C4⋊C4×C29—24no—
242C4⋊C4×C29—21no—
243C4⋊C4×C29—21no—
244C4⋊C4×C29—24no—
245C4⋊C4×C29—24no—
246C4⋊C4×C29—24no—
247C4⋊C4×C29—24no—
248C4⋊C4×C29—24no—
249C4⋊C4×C29—24no—
250C4⋊C4×C29—24no—
251C4⋊C4×C29—21no—
252C4⋊C4×C29C2×D414yes—
253C4⋊C4×C29C2412yes—
254C4⋊C4×C29C2412yes—
255C4⋊C4×C29C2412yes—
256C4⋊C4×C29C2412yes—
257C4⋊C4×C29C2412yes—
258C4⋊C4×C29C2412yes—
259C22⋊C4×C29—24no—
260C22⋊C4×C29—24no—
261C22⋊C4×C29—24no—
262C22⋊C4×C29—24no—
263C22⋊C4×C29—24no—
264C22⋊C4×C29—24no—
265C22⋊C4×C29C2×D414yes—
266C22⋊C4×C29C2×D414yes—
267C42×C29—24no—
268C42×C29—24no—
269C42×C29C2×D412yes—
270C42×C29C2412yes—
271C2×#3346C2911yesmaximal, characteristic, direct product factor, Sylow
272C23×C29—22no—
273C23×C29—22no—
274C23×C29—22no—
275C23×C29—22no—
276C23×C29—22no—
277C23×C29—22no—
278C23×C29—42no—
279C23×C29—42no—
280C23×C29—42no—
281C23×C29#13714yes—
282C23×C29C22×D412yes—
283C23×C29C22×D412yes—
284C23×C29C22×D411yescharacteristic
285Q8×C29—22no—
286Q8×C29—22no—
287Q8×C29—42no—
288Q8×C29—84no—
289D4×C29—28no—
290D4×C29—22no—
291D4×C29—22no—
292D4×C29—48no—
293D4×C29—42no—
294D4×C29—84no—
295C2×C4×C29—22no—
296C2×C4×C29—22no—
297C2×C4×C29—22no—
298C2×C4×C29—22no—
299C2×C4×C29—24no—
300C2×C4×C29—24no—
301C2×C4×C29—22no—
302C2×C4×C29—22no—
303C2×C4×C29—22no—
304C2×C4×C29—22no—
305C2×C4×C29—22no—
306C2×C4×C29—22no—
307C2×C4×C29—22no—
308C2×C4×C29—22no—
309C2×C4×C29—22no—
310C2×C4×C29—22no—
311C2×C4×C29—22no—
312C2×C4×C29—42no—
313C2×C4×C29—42no—
314C2×C4×C29—42no—
315C2×C4×C29—42no—
316C2×C4×C29—42no—
317C2×C4×C29—42no—
318C2×C4×C29—42no—
319C2×C4×C29—84no—
320C2×C4×C29—84no—
321C2×C4×C29—84no—
322C2×C4×C29—84no—
323C2×C4×C29C22×D412yes—
324C2×C4×C29C22×D412yes—
325C2×C4×C29C22×D412yes—
326C2×C4×C29C22×D412yes—
327C2×C4×C29C22×D411yescharacteristic
328C2×C4×C29C2×#4112yes—
329C2×C4×C292−1+412yes—
330C2×C4×C29C2511yescharacteristic
331C8×C29—22no—
332C8×C29—22no—
333C8×C29—22no—
334C8×C29C2×#4114yes—
335C2×#554C2×C2911yescharacteristic, complemented
336C2×#553C2×C2911yescharacteristic
337#3346C2×C29116yesdirect product factor
338C2×#501C2×C2911yescharacteristic, complemented
339C2×#484C2×C2911yescharacteristic, complemented
340C2×#481C2×C2911yescharacteristic, complemented
341C2×#485C2×C2911yescharacteristic, complemented
342C2×#480C2×C2911yescharacteristic, complemented
343C2×#479C2×C2911yescharacteristic, complemented
344C2×#474C2×C2911yescharacteristic, complemented
345C2×#468C2×C2911yescharacteristic, complemented
346C2×#465C2×C2911yescharacteristic, complemented
347C2×#440C2×C2911yescharacteristic, complemented
348C2×#435C2×C2911yescharacteristic, complemented
349C2×#428C2×C2911yescharacteristic, complemented
350C22×#107C2×C2911yescharacteristic, complemented
351C22×C29—28no—
352C22×C29—22no—
353C22×C29—22no—
354C22×C29—22no—
355C22×C29—22no—
356C22×C29—22no—
357C22×C29—44no—
358C22×C29—42no—
359C22×C29—42no—
360C22×C29—42no—
361C22×C29—84no—
362C22×C29#54712yes—
363C22×C29C2×#13714yes—
364C22×C29C2×#13712yes—
365C22×C29#57612yes—
366C22×C29C23×D411yescharacteristic
367C4×C29—22no—
368C4×C29—22no—
369C4×C29—22no—
370C4×C29—22no—
371C4×C29—42no—
372C4×C29—42no—
373C4×C29—42no—
374C4×C29—42no—
375C4×C29—42no—
376C4×C29—42no—
377C4×C29—42no—
378C4×C29#54712yes—
379C4×C29C22×#4111yescharacteristic
380C4×C29C2×2−1+411yescharacteristic
381C22×SD16C22×C2911yescharacteristic
382C22×M16C22×C2911yescharacteristic
383C23×C8C22×C2911yescharacteristic
384#554—24no—
385#554C22×C2918yescomplemented
386#553—24no—
387#553C22×C2918yes—
388C2×C4⋊Q8C22×C2911yescharacteristic
389C2×#126—21no—
390C2×#125—21no—
391C2×#125C22×C2911yescharacteristic
392C2×#123—21no—
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8C22×C2911yescharacteristic
396C2×C22⋊Q8C22×C2911yescharacteristic
397C2×#121—21no—
398C2×#121C22×C2911yescharacteristic
399C2×#121C22×C2911yescharacteristic
400C2×C4×Q8C22×C2911yescharacteristic
401C2×C4×D4—21no—
402C2×C4×D4—21no—
403C2×C4×D4C22×C2911yescharacteristic
404C2×C4×D4C22×C2911yescharacteristic
405C2×#117C22×C2911yescharacteristic
406C22×C4⋊C4C22×C2911yescharacteristic
407C22×C4⋊C4C22×C2911yescharacteristic
408C22×C4⋊C4C22×C2911yescharacteristic
409#501C22×C2918yescomplemented
410#485C22×C2918yescomplemented
411#484C22×C2918yescomplemented
412#481C22×C2918yescomplemented
413#480C22×C2918yescomplemented
414#479C22×C2918yescomplemented
415#474C22×C2918yescomplemented
416#468C22×C2918yescomplemented
417#465C22×C2918yescomplemented
418#440C22×C2918yescomplemented
419#435C22×C2918yescomplemented
420#428C22×C2918yescomplemented
421C2×#107C22×C2911yescharacteristic
422C2×#107C22×C2911yescharacteristic
423C2×#107C22×C2911yescharacteristic
424C2×#107C22×C2911yescharacteristic
425C2×#107C22×C2911yescharacteristic
426C2×#107C22×C2911yescharacteristic
427C2×#107C22×C2918yescomplemented
428C2×#106C22×C2911yescharacteristic
429C2×#106C22×C2911yescharacteristic
430C2×#106C22×C2911yescharacteristic
431C2×C4⋊C8C22×C2911yescharacteristic
432C2×#103C22×C2911yescharacteristic
433C2×#103C22×C2911yescharacteristic
434C2×#103C22×C2911yescharacteristic
435C2×#102C22×C2911yescharacteristic
436C2×#102C22×C2911yescharacteristic
437C2×#102C22×C2911yescharacteristic
438C2×C22⋊C8C22×C2911yescharacteristic
439C2×C22⋊C8C22×C2911yescharacteristic
440C2×#97C22×C2911yescharacteristic
441C2×C29—24no—
442C2×C29—42no—
443C2×C29—82no—
444C2×C29#334614yesdirect product factor
445C2×C29C2×#54711yescharacteristic
446C2×C29C22×#13711yescharacteristic
447C2×C29C2×#57611yescharacteristic
448C22×Q8—21no—
449C22×Q8C23×C2911yescharacteristic
450C22×D4—21no—
451C22×D4—21no—
452C22×D4D4×C2911yescharacteristic
453C22×D4C23×C2911yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4C23×C2911yescharacteristic
459C23×C4C23×C2911yescharacteristic
460C2×SD16—24no—
461C2×SD16C23×C2914yes—
462C2×M16—24no—
463C2×M16C23×C2914yes—
464C22×C8—24no—
465C22×C8C23×C2911yescharacteristic
466C22×C8C23×C2914yes—
467C22×C8C23×C2911yescharacteristic
468C22×C8C23×C2911yescharacteristic
469C22×C8C23×C2911yescharacteristic
470C4⋊Q8—22no—
471C4⋊Q8C23×C2914yes—
472#126—28no—
473#125—28no—
474#125—22no—
475#125C23×C2914yes—
476#123—28no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—28no—
480C22⋊Q8—28no—
481C22⋊Q8C23×C2914yes—
482C22⋊Q8C23×C2914yes—
483#121—28no—
484#121—22no—
485#121—22no—
486#121C23×C2914yes—
487#121C23×C2914yes—
488C4×Q8—22no—
489C4×Q8C23×C2914yes—
490C4×D4—28no—
491C4×D4—28no—
492C4×D4—22no—
493C4×D4D4×C2914yes—
494C4×D4C23×C2914yes—
495C4×D4C23×C2914yes—
496#117—22no—
497#117C23×C2914yes—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4D4×C2911yescharacteristic
511C2×C4⋊C4C23×C2911yescharacteristic
512C2×C4⋊C4C23×C2911yescharacteristic
513C2×C4⋊C4C23×C2911yescharacteristic
514C2×C4⋊C4C23×C2911yescharacteristic
515C2×C4⋊C4C23×C2911yescharacteristic
516C2×C4⋊C4C23×C2914yes—
517C2×C4⋊C4C23×C2914yes—
518C2×C4⋊C4C23×C2914yes—
519C2×C4⋊C4C23×C2911yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4D4×C2911yescharacteristic
527C2×C22⋊C4D4×C2911yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42C23×C2911yescharacteristic
531#107C23×C2914yes—
532#107C23×C2914yes—
533#107C23×C2914yes—
534#107C23×C2914yes—
535#107C23×C2914yes—
536#107C23×C2914yes—
537#106C23×C2914yes—
538#106C23×C2914yes—
539#106C23×C2914yes—
540C4⋊C8C23×C2914yes—
541#103C23×C2914yes—
542#103C23×C2914yes—
543#103C23×C2914yes—
544#102C23×C2914yes—
545#102C23×C2914yes—
546#102C23×C2914yes—
547C22⋊C8C23×C2914yes—
548C22⋊C8C23×C2914yes—
549#97C23×C2914yes—
550C29C2×#334611yescharacteristic, direct product factor, Sylow
551C24—21no—
552C24C2×D4×C2911yescharacteristic
553C24C2×D4×C2911yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C24×C2912yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—82no—
568C2×D4C2×D4×C2914yes—
569C2×D4C24×C2912yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4C2×D4×C2911yescharacteristic
590C22×C4C2×D4×C2911yescharacteristic
591C22×C4C2×D4×C2911yescharacteristic
592C22×C4C2×D4×C2911yescharacteristic
593C22×C4C2×D4×C2912yes—
594C22×C4C2×D4×C2912yes—
595C22×C4C24×C2912yes—
596C22×C4C24×C2912yes—
597C22×C4C24×C2911yescharacteristic
598SD16—28no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#41×C2914yes—
605C2×C8C24×C2912yes—
606C2×C8C24×C2912yes—
607C2×C8C24×C2912yes—
608C2×C8C24×C2912yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4C2×D4×C2914yes—
625C4⋊C4C24×C2912yes—
626C4⋊C4C24×C2912yes—
627C4⋊C4C24×C2912yes—
628C4⋊C4C24×C2912yes—
629C4⋊C4C24×C2912yes—
630C4⋊C4C24×C2912yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4C2×D4×C2914yes—
638C22⋊C4C2×D4×C2914yes—
639C42—24no—
640C42—24no—
641C42C2×D4×C2912yes—
642C42C24×C2912yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23C29×#13714yes—
653C23C22×D4×C2912yes—
654C23C22×D4×C2912yes—
655C23C22×D4×C2911yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4C22×D4×C2912yes—
695C2×C4C22×D4×C2912yes—
696C2×C4C22×D4×C2912yes—
697C2×C4C22×D4×C2912yes—
698C2×C4C22×D4×C2911yescharacteristic
699C2×C4C2×#41×C2912yes—
700C2×C4C29×2−1+412yes—
701C2×C4C25×C2911yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#41×C2914yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22C29×#54712yes—
718C22C2×C29×#13714yes—
719C22C2×C29×#13712yes—
720C22C29×#57612yes—
721C22C23×D4×C2911yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4C29×#54712yes—
734C4C22×#41×C2911yescharacteristic
735C4C2×C29×2−1+411yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2C29×#334614yesdirect product factor
740C2C2×C29×#54711yescharacteristic
741C2C22×C29×#13711yescharacteristic
742C2C2×C29×#57611yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC2×C29×#553C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#554C2semidirect
3. C29×#3346C2direct (N × H)
4. C2×C29×#501C2semidirect
5. C2×C29×#484C2semidirect
6. C2×C29×#481C2semidirect
7. C2×C29×#485C2semidirect
8. C2×C29×#480C2semidirect
9. C2×C29×#479C2semidirect
10. C2×C29×#474C2semidirect
11. C2×C29×#468C2semidirect
12. C2×C29×#465C2semidirect
13. C2×C29×#440C2semidirect
14. C2×C29×#435C2semidirect
15. C2×C29×#428C2semidirect
16. C22×C29×#107C2semidirect
21. C29×#554C22semidirect
45. C29×#501C22semidirect
46. C29×#485C22semidirect
47. C29×#484C22semidirect
48. C29×#481C22semidirect
49. C29×#480C22semidirect
50. C29×#479C22semidirect
51. C29×#474C22semidirect
52. C29×#468C22semidirect
53. C29×#465C22semidirect
54. C29×#440C22semidirect
55. C29×#435C22semidirect
56. C29×#428C22semidirect
63. C2×C29×#107C22semidirect
271. C2×#3346C29direct (N × H)
335. C2×#554C2×C29semidirect
337. #3346C2×C29direct (N × H)
338. C2×#501C2×C29semidirect
339. C2×#484C2×C29semidirect
340. C2×#481C2×C29semidirect
341. C2×#485C2×C29semidirect
342. C2×#480C2×C29semidirect
343. C2×#479C2×C29semidirect
344. C2×#474C2×C29semidirect
345. C2×#468C2×C29semidirect
346. C2×#465C2×C29semidirect
347. C2×#440C2×C29semidirect
348. C2×#435C2×C29semidirect
349. C2×#428C2×C29semidirect
350. C22×#107C2×C29semidirect
385. #554C22×C29semidirect
409. #501C22×C29semidirect
410. #485C22×C29semidirect
411. #484C22×C29semidirect
412. #481C22×C29semidirect
413. #480C22×C29semidirect
414. #479C22×C29semidirect
415. #474C22×C29semidirect
416. #468C22×C29semidirect
417. #465C22×C29semidirect
418. #440C22×C29semidirect
419. #435C22×C29semidirect
420. #428C22×C29semidirect
427. C2×#107C22×C29semidirect
444. C2×C29#3346direct (N × H)
550. C29C2×#3346direct (N × H)
739. C2C29×#3346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5542
C2×C29×#5532
C29×#33462
C2×C29×#5012
C2×C29×#4842
C2×C29×#4812
C2×C29×#4852
C2×C29×#4802
C2×C29×#4792
C2×C29×#4742
C2×C29×#4682
C2×C29×#4652
C2×C29×#4402
C2×C29×#4352
C2×C29×#4282
C22×C29×#1072
C2×#334629