Finite Group Databasebeta

← C29×#25178 #20320078

Subgroups — C29×#25178 #20320078

Order 7424.

1134 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#463C211yesmaximal, characteristic, complemented
2C2×C29×#452C211yesmaximal, characteristic, complemented
3C2×C29×#449C211yesmaximal, characteristic
4C2×C29×#440C211yesmaximal, characteristic, complemented
5C29×#2426C211yesmaximal, characteristic, complemented
6C29×#2339C211yesmaximal, characteristic, complemented
7C29×#2068C211yesmaximal, characteristic, complemented
8C29×#2036C211yesmaximal, characteristic, complemented
9C29×#2033C211yesmaximal, characteristic, complemented
10C29×#2015C211yesmaximal, characteristic, complemented
11C29×#1973C211yesmaximal, characteristic, complemented
12C29×#1924C211yesmaximal, characteristic, complemented
13C29×#1879C211yesmaximal, characteristic, complemented
14C29×#1878C211yesmaximal, characteristic, complemented
15C29×#1862C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C22×Q16×C29C2211yescharacteristic
18C22×SD16×C29C2211yescharacteristic
19C22×SD16×C29C2211yescharacteristic
20C22×D8×C29C2211yescharacteristic
21C2×C29×#124C2211yescharacteristic
22C2×C29×C22⋊Q8C2211yescharacteristic
23C2×C29×#121C2211yescharacteristic
24C2×C4×Q8×C29C2211yescharacteristic
25C2×C4×D4×C29C2211yescharacteristic
26C2×C4×D4×C29C2211yescharacteristic
27C29×#463—24no—
28C29×#452—24no—
29C29×#449—24no—
30C29×#440—24no—
31C2×C29×#107C2211yescharacteristic
32C2×C29×#107C2211yescharacteristic
33C2×C29×C4⋊C8C2211yescharacteristic
34C2×C29×#103C2211yescharacteristic
35C2×C29×#103C2211yescharacteristic
36C2×C29×#103C2211yescharacteristic
37C2×C29×#103C2211yescharacteristic
38C2×C29×#102C2211yescharacteristic
39C2×C29×#102C2211yescharacteristic
40C2×C29×#102C2211yescharacteristic
41C2×C29×#102C2211yescharacteristic
42C2×C29×C22⋊C8C2211yescharacteristic
43C2×C29×C22⋊C8C2211yescharacteristic
44C2×C29×#97C2211yescharacteristic
45C29×#396—21no—
46C29×#394—21no—
47C29×#391C2211yescharacteristic
48C29×#391C2211yescharacteristic
49C29×#390—21no—
50C29×#390C2211yescharacteristic
51C29×#389C2211yescharacteristic
52C29×#388—21no—
53C29×#386—21no—
54C29×#386—21no—
55C29×#381—21no—
56C29×#380C2211yescharacteristic
57C4×C22⋊C4×C29C2211yescharacteristic
58C2×C29×#95—21no—
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C29×#336C2211yescharacteristic
62C29×#336C2211yescharacteristic
63C2×#41×C29—22no—
64C2×#41×C29—22no—
65C2×#41×C29—22no—
66C2×#41×C29—22no—
67C2×#41×C29—41no—
68C2×#41×C29—41no—
69C22×Q8×C29C2311yescharacteristic
70C22×Q8×C29C2311yescharacteristic
71C22×D4×C29—21no—
72C22×D4×C29—21no—
73C22×D4×C29C2311yescharacteristic
74C22×D4×C29C2311yescharacteristic
75C23×C4×C29—21no—
76C23×C4×C29—21no—
77C23×C4×C29—21no—
78C23×C4×C29C2311yescharacteristic
79C2×Q16×C29—22no—
80C2×Q16×C29—22no—
81C2×Q16×C29—41no—
82C2×SD16×C29—22no—
83C2×SD16×C29—22no—
84C2×SD16×C29—22no—
85C2×SD16×C29—22no—
86C2×SD16×C29—41no—
87C2×SD16×C29D414yescomplemented
88C2×D8×C29—22no—
89C2×D8×C29—22no—
90C2×D8×C29—22no—
91C22×C8×C29C2311yescharacteristic
92C22×C8×C29C2311yescharacteristic
93C22×C8×C29C2311yescharacteristic
94C22×C8×C29C2311yescharacteristic
95C29×#124—22no—
96C29×#124—41no—
97C29×C22⋊Q8—22no—
98C29×C22⋊Q8—41no—
99C29×#121—22no—
100C29×#121—41no—
101C4×Q8×C29—22no—
102C4×Q8×C29—41no—
103C4×D4×C29—22no—
104C4×D4×C29—22no—
105C4×D4×C29—41no—
106C4×D4×C29—41no—
107C2×C4⋊C4×C29—21no—
108C2×C4⋊C4×C29—21no—
109C2×C4⋊C4×C29—21no—
110C2×C4⋊C4×C29C2311yescharacteristic
111C2×C4⋊C4×C29C2311yescharacteristic
112C2×C4⋊C4×C29C2311yescharacteristic
113C2×C4⋊C4×C29C2311yescharacteristic
114C2×C22⋊C4×C29—21no—
115C2×C22⋊C4×C29—21no—
116C2×C22⋊C4×C29—21no—
117C2×C22⋊C4×C29—21no—
118C2×C22⋊C4×C29—21no—
119C2×C22⋊C4×C29—21no—
120C2×C22⋊C4×C29—21no—
121C2×C22⋊C4×C29—21no—
122C2×C22⋊C4×C29—21no—
123C2×C22⋊C4×C29D411yescharacteristic
124C2×C22⋊C4×C29D411yescharacteristic
125C2×C42×C29—21no—
126C2×C42×C29C2311yescharacteristic
127C2×C42×C29C2311yescharacteristic
128C29×#107—22no—
129C29×#107—41no—
130C29×C4⋊C8—22no—
131C29×#103—22no—
132C29×#103—22no—
133C29×#103—22no—
134C29×#103—22no—
135C29×#102—22no—
136C29×#102—22no—
137C29×#102—41no—
138C29×#102D414yes—
139C29×C22⋊C8—22no—
140C29×C22⋊C8—22no—
141C29×#97—22no—
142C29×#95—21no—
143C29×#95—21no—
144C29×#95—21no—
145C29×#95—21no—
146C29×#95—21no—
147C29×#95—21no—
148C29×#95D411yescharacteristic
149C29×#95D411yescharacteristic
150C24×C29—21no—
151C24×C29—21no—
152C24×C29C2×D411yescharacteristic
153#41×C29—44no—
154#41×C29—44no—
155#41×C29—44no—
156#41×C29—44no—
157C2×Q8×C29—21no—
158C2×Q8×C29—21no—
159C2×Q8×C29—21no—
160C2×Q8×C29—21no—
161C2×Q8×C29—21no—
162C2×Q8×C29—21no—
163C2×Q8×C29—21no—
164C2×Q8×C29—21no—
165C2×Q8×C29—21no—
166C2×Q8×C29—21no—
167C2×Q8×C29C2×D412yes—
168C2×Q8×C29#4112yes—
169C2×D4×C29—24no—
170C2×D4×C29—21no—
171C2×D4×C29—21no—
172C2×D4×C29—21no—
173C2×D4×C29—21no—
174C2×D4×C29—21no—
175C2×D4×C29—21no—
176C2×D4×C29—21no—
177C2×D4×C29—21no—
178C2×D4×C29—21no—
179C2×D4×C29—42no—
180C2×D4×C29—42no—
181C2×D4×C29—42no—
182C2×D4×C29—42no—
183C2×D4×C29—81no—
184C2×D4×C29C2×D412yes—
185C2×D4×C29C2×D412yes—
186C2×D4×C29#4112yes—
187C22×C4×C29—24no—
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—42no—
201C22×C4×C29—42no—
202C22×C4×C29—42no—
203C22×C4×C29—42no—
204C22×C4×C29—42no—
205C22×C4×C29—42no—
206C22×C4×C29—81no—
207C22×C4×C29—81no—
208C22×C4×C29C2×D411yescharacteristic
209C22×C4×C29C2×D411yescharacteristic
210C22×C4×C29C2×D411yescharacteristic
211C22×C4×C29C2×D411yescharacteristic
212C22×C4×C29C2×D411yescharacteristic
213C22×C4×C29C2411yescharacteristic
214Q16×C29—44no—
215SD16×C29—28no—
216SD16×C29—44no—
217D8×C29—44no—
218C2×C8×C29—21no—
219C2×C8×C29—21no—
220C2×C8×C29—21no—
221C2×C8×C29—21no—
222C2×C8×C29—21no—
223C2×C8×C29—21no—
224C2×C8×C29—21no—
225C2×C8×C29—21no—
226C2×C8×C29—21no—
227C2×C8×C29—21no—
228C2×C8×C29C2×D412yes—
229C2×C8×C29C2×D412yes—
230C4⋊C4×C29—21no—
231C4⋊C4×C29—21no—
232C4⋊C4×C29—21no—
233C4⋊C4×C29—21no—
234C4⋊C4×C29—21no—
235C4⋊C4×C29—21no—
236C4⋊C4×C29—21no—
237C4⋊C4×C29—42no—
238C4⋊C4×C29—42no—
239C4⋊C4×C29—81no—
240C4⋊C4×C29C2×D412yes—
241C22⋊C4×C29—41no—
242C22⋊C4×C29—41no—
243C22⋊C4×C29—42no—
244C22⋊C4×C29—42no—
245C22⋊C4×C29—42no—
246C22⋊C4×C29—42no—
247C22⋊C4×C29—42no—
248C22⋊C4×C29—42no—
249C22⋊C4×C29—42no—
250C22⋊C4×C29—81no—
251C22⋊C4×C29—81no—
252C42×C29—21no—
253C42×C29—21no—
254C42×C29—21no—
255C42×C29—21no—
256C42×C29—42no—
257#25178C2911yesmaximal, characteristic, direct product factor, Sylow
258C23×C29—22no—
259C23×C29—22no—
260C23×C29—22no—
261C23×C29—21no—
262C23×C29—21no—
263C23×C29—21no—
264C23×C29—21no—
265C23×C29—21no—
266C23×C29—21no—
267C23×C29—21no—
268C23×C29—41no—
269C23×C29—41no—
270C23×C29—41no—
271C23×C29—41no—
272C23×C29—41no—
273C23×C29—41no—
274C23×C29—41no—
275C23×C29—41no—
276C23×C29—41no—
277C23×C29—41no—
278C23×C29—41no—
279C23×C29C22×D411yescharacteristic
280Q8×C29—22no—
281Q8×C29—22no—
282Q8×C29—22no—
283Q8×C29—22no—
284Q8×C29—41no—
285Q8×C29—41no—
286Q8×C29—41no—
287Q8×C29—41no—
288D4×C29—22no—
289D4×C29—22no—
290D4×C29—22no—
291D4×C29—48no—
292D4×C29—41no—
293D4×C29—41no—
294D4×C29—41no—
295D4×C29—41no—
296D4×C29—84no—
297D4×C29#12114yes—
298C2×C4×C29—21no—
299C2×C4×C29—22no—
300C2×C4×C29—21no—
301C2×C4×C29—21no—
302C2×C4×C29—21no—
303C2×C4×C29—21no—
304C2×C4×C29—22no—
305C2×C4×C29—22no—
306C2×C4×C29—21no—
307C2×C4×C29—21no—
308C2×C4×C29—21no—
309C2×C4×C29—21no—
310C2×C4×C29—21no—
311C2×C4×C29—21no—
312C2×C4×C29—21no—
313C2×C4×C29—21no—
314C2×C4×C29—21no—
315C2×C4×C29—21no—
316C2×C4×C29—48no—
317C2×C4×C29—41no—
318C2×C4×C29—41no—
319C2×C4×C29—41no—
320C2×C4×C29—41no—
321C2×C4×C29—41no—
322C2×C4×C29—41no—
323C2×C4×C29—41no—
324C2×C4×C29—41no—
325C2×C4×C29—41no—
326C2×C4×C29—41no—
327C2×C4×C29—41no—
328C2×C4×C29—41no—
329C2×C4×C29—41no—
330C2×C4×C29—41no—
331C2×C4×C29—41no—
332C2×C4×C29—41no—
333C2×C4×C29—41no—
334C2×C4×C29—41no—
335C2×C4×C29—41no—
336C2×C4×C29—84no—
337C2×C4×C29—84no—
338C2×C4×C29C22×D411yescharacteristic
339C2×C4×C29C22×D411yescharacteristic
340C2×C4×C29C2×#4111yescharacteristic
341C2×C4×C29C2×#4111yescharacteristic
342C2×C4×C29H(5,𝔽2)11yescharacteristic
343C2×C4×C29H(5,𝔽2)11yescharacteristic
344C8×C29—22no—
345C8×C29—22no—
346C8×C29—41no—
347C8×C29—41no—
348C2×#463C2×C2911yescharacteristic, complemented
349C2×#452C2×C2911yescharacteristic, complemented
350C2×#449C2×C2911yescharacteristic
351C2×#440C2×C2911yescharacteristic, complemented
352#2426C2×C2911yescharacteristic, complemented
353#2339C2×C2911yescharacteristic, complemented
354#2068C2×C2911yescharacteristic, complemented
355#2036C2×C2911yescharacteristic, complemented
356#2033C2×C2911yescharacteristic, complemented
357#2015C2×C2911yescharacteristic, complemented
358#1973C2×C2911yescharacteristic, complemented
359#1924C2×C2911yescharacteristic, complemented
360#1879C2×C2911yescharacteristic, complemented
361#1878C2×C2911yescharacteristic, complemented
362#1862C2×C2911yescharacteristic, complemented
363C22×C29—24no—
364C22×C29—42no—
365C22×C29—42no—
366C22×C29—42no—
367C22×C29—42no—
368C22×C29—42no—
369C22×C29—42no—
370C22×C29—41no—
371C22×C29—41no—
372C22×C29—41no—
373C22×C29—41no—
374C22×C29—41no—
375C22×C29—41no—
376C22×C29—41no—
377C22×C29—81no—
378C22×C29—81no—
379C22×C29—81no—
380C22×C29—81no—
381C22×C29—81no—
382C22×C29—81no—
383C22×C29—81no—
384C22×C29#52511yescharacteristic
385C22×C29D4211yescharacteristic
386C22×C29D4211yescharacteristic
387C22×C29#57511yescharacteristic
388C22×C29#57511yescharacteristic
389C22×C29#57611yescharacteristic
390C22×C29#57811yescharacteristic
391C4×C29—41no—
392C4×C29—42no—
393C4×C29—42no—
394C4×C29—41no—
395C4×C29—41no—
396C4×C29—41no—
397C4×C29—41no—
398C4×C29—42no—
399C4×C29—81no—
400C4×C29—81no—
401C4×C29—81no—
402C4×C29C2×#12111yescharacteristic
403C4×C29#53811yescharacteristic
404C4×C29#54611yescharacteristic
405C4×C29#54611yescharacteristic
406C22×#41C22×C2911yescharacteristic
407C22×Q16C22×C2911yescharacteristic
408C22×SD16C22×C2911yescharacteristic
409C22×SD16C22×C2911yescharacteristic
410C22×D8C22×C2911yescharacteristic
411C2×#124C22×C2911yescharacteristic
412C2×C22⋊Q8C22×C2911yescharacteristic
413C2×#121C22×C2911yescharacteristic
414C2×C4×Q8C22×C2911yescharacteristic
415C2×C4×D4C22×C2911yescharacteristic
416C2×C4×D4C22×C2911yescharacteristic
417#463—24no—
418#452—24no—
419#449—24no—
420#440—24no—
421C2×#107C22×C2911yescharacteristic
422C2×#107C22×C2911yescharacteristic
423C2×C4⋊C8C22×C2911yescharacteristic
424C2×#103C22×C2911yescharacteristic
425C2×#103C22×C2911yescharacteristic
426C2×#103C22×C2911yescharacteristic
427C2×#103C22×C2911yescharacteristic
428C2×#102C22×C2911yescharacteristic
429C2×#102C22×C2911yescharacteristic
430C2×#102C22×C2911yescharacteristic
431C2×#102C22×C2911yescharacteristic
432C2×C22⋊C8C22×C2911yescharacteristic
433C2×C22⋊C8C22×C2911yescharacteristic
434C2×#97C22×C2911yescharacteristic
435#396—21no—
436#394—21no—
437#391C22×C2911yescharacteristic
438#391C22×C2911yescharacteristic
439#390—21no—
440#390C22×C2911yescharacteristic
441#389C22×C2911yescharacteristic
442#388—21no—
443#386—21no—
444#386—21no—
445#381—21no—
446#380C22×C2911yescharacteristic
447C4×C22⋊C4C22×C2911yescharacteristic
448C2×#95—21no—
449#340C22×C2911yescharacteristic
450#340C22×C2911yescharacteristic
451#336C22×C2911yescharacteristic
452#336C22×C2911yescharacteristic
453C2×C29—44no—
454C2×C29—81no—
455C2×C29—161no—
456C2×C29#242411yescharacteristic
457C2×C29#311111yescharacteristic
458C2×C29#312411yescharacteristic
459C2×C29#326811yescharacteristic
460C2×C29#326911yescharacteristic
461C2×C29#326911yescharacteristic
462C2×C29#327311yescharacteristic
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—41no—
468C2×#41—41no—
469C22×Q8C23×C2911yescharacteristic
470C22×Q8C23×C2911yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4C23×C2911yescharacteristic
474C22×D4C23×C2911yescharacteristic
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—21no—
478C23×C4C23×C2911yescharacteristic
479C2×Q16—22no—
480C2×Q16—22no—
481C2×Q16—41no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—41no—
487C2×SD16D4×C2914yescomplemented
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C2911yescharacteristic
492C22×C8C23×C2911yescharacteristic
493C22×C8C23×C2911yescharacteristic
494C22×C8C23×C2911yescharacteristic
495#124—22no—
496#124—41no—
497C22⋊Q8—22no—
498C22⋊Q8—41no—
499#121—22no—
500#121—41no—
501C4×Q8—22no—
502C4×Q8—41no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—41no—
506C4×D4—41no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4C23×C2911yescharacteristic
511C2×C4⋊C4C23×C2911yescharacteristic
512C2×C4⋊C4C23×C2911yescharacteristic
513C2×C4⋊C4C23×C2911yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4D4×C2911yescharacteristic
524C2×C22⋊C4D4×C2911yescharacteristic
525C2×C42—21no—
526C2×C42C23×C2911yescharacteristic
527C2×C42C23×C2911yescharacteristic
528#107—22no—
529#107—41no—
530C4⋊C8—22no—
531#103—22no—
532#103—22no—
533#103—22no—
534#103—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102D4×C2914yes—
539C22⋊C8—22no—
540C22⋊C8—22no—
541#97—22no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95D4×C2911yescharacteristic
549#95D4×C2911yescharacteristic
550C29#2517811yescharacteristic, direct product factor, Sylow
551C24—21no—
552C24—21no—
553C24C2×D4×C2911yescharacteristic
554#41—44no—
555#41—44no—
556#41—44no—
557#41—44no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8C2×D4×C2912yes—
569C2×Q8#41×C2912yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—81no—
585C2×D4C2×D4×C2912yes—
586C2×D4C2×D4×C2912yes—
587C2×D4#41×C2912yes—
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C2911yescharacteristic
610C22×C4C2×D4×C2911yescharacteristic
611C22×C4C2×D4×C2911yescharacteristic
612C22×C4C2×D4×C2911yescharacteristic
613C22×C4C2×D4×C2911yescharacteristic
614C22×C4C24×C2911yescharacteristic
615Q16—44no—
616SD16—28no—
617SD16—44no—
618D8—44no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8C2×D4×C2912yes—
630C2×C8C2×D4×C2912yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C4⋊C4C2×D4×C2912yes—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—42no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23C22×D4×C2911yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—48no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697D4C29×#12114yes—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—48no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4C22×D4×C2911yescharacteristic
739C2×C4C22×D4×C2911yescharacteristic
740C2×C4C2×#41×C2911yescharacteristic
741C2×C4C2×#41×C2911yescharacteristic
742C2×C4C29×H(5,𝔽2)11yescharacteristic
743C2×C4C29×H(5,𝔽2)11yescharacteristic
744C8—22no—
745C8—22no—
746C8—41no—
747C8—41no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C29×#52511yescharacteristic
770C22D42×C2911yescharacteristic
771C22D42×C2911yescharacteristic
772C22C29×#57511yescharacteristic
773C22C29×#57511yescharacteristic
774C22C29×#57611yescharacteristic
775C22C29×#57811yescharacteristic
776C4—41no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4C2×C29×#12111yescharacteristic
788C4C29×#53811yescharacteristic
789C4C29×#54611yescharacteristic
790C4C29×#54611yescharacteristic
791C2—44no—
792C2—81no—
793C2—161no—
794C2C29×#242411yescharacteristic
795C2C29×#311111yescharacteristic
796C2C29×#312411yescharacteristic
797C2C29×#326811yescharacteristic
798C2C29×#326911yescharacteristic
799C2C29×#326911yescharacteristic
800C2C29×#327311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#463C2semidirect
2. C2×C29×#452C2semidirect
4. C2×C29×#440C2semidirect
5. C29×#2426C2semidirect
6. C29×#2339C2semidirect
7. C29×#2068C2semidirect
8. C29×#2036C2semidirect
9. C29×#2033C2semidirect
10. C29×#2015C2semidirect
11. C29×#1973C2semidirect
12. C29×#1924C2semidirect
13. C29×#1879C2semidirect
14. C29×#1878C2semidirect
15. C29×#1862C2semidirect
87. C2×SD16×C29D4semidirect
257. #25178C29direct (N × H)
348. C2×#463C2×C29semidirect
349. C2×#452C2×C29semidirect
351. C2×#440C2×C29semidirect
352. #2426C2×C29semidirect
353. #2339C2×C29semidirect
354. #2068C2×C29semidirect
355. #2036C2×C29semidirect
356. #2033C2×C29semidirect
357. #2015C2×C29semidirect
358. #1973C2×C29semidirect
359. #1924C2×C29semidirect
360. #1879C2×C29semidirect
361. #1878C2×C29semidirect
362. #1862C2×C29semidirect
487. C2×SD16D4×C29semidirect
550. C29#25178direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4632
C2×C29×#4522
C2×C29×#4492
C2×C29×#4402
C29×#24262
C29×#23392
C29×#20682
C29×#20362
C29×#20332
C29×#20152
C29×#19732
C29×#19242
C29×#18792
C29×#18782
C29×#18622
#2517829