Finite Group Databasebeta

← C29×#24028 #20318928

Subgroups — C29×#24028 #20318928

Order 7424.

1250 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3489C211yesmaximal, characteristic
2C29×#3093C211yesmaximal, characteristic, complemented
3C29×#2896C211yesmaximal, characteristic, complemented
4C29×#2499C211yesmaximal, characteristic, complemented
5C29×#2040C211yesmaximal, characteristic, complemented
6C29×#2039C211yesmaximal, characteristic, complemented
7C29×#2038C211yesmaximal, characteristic, complemented
8C29×#2038C211yesmaximal, characteristic, complemented
9C29×#1901C211yesmaximal, characteristic, complemented
10C29×#1871C211yesmaximal, characteristic, complemented
11C29×#1860C211yesmaximal, characteristic, complemented
12C29×#1859C211yesmaximal, characteristic, complemented
13C29×#1793C211yesmaximal, characteristic, complemented
14C29×#1793C211yesmaximal, characteristic, complemented
15C29×#1789C211yesmaximal, characteristic, complemented
16C2×C29×2−1+4C2211yescharacteristic
17C22×#41×C29C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic
19D4×Q8×C29—21no—
20C29×#548—21no—
21C29×#547—21no—
22C29×#547—22no—
23C29×#546—21no—
24C29×#546—22no—
25C29×#537—21no—
26C29×#537C2211yescharacteristic
27C29×#536—21no—
28C29×#536C2211yescharacteristic
29C29×#525—21no—
30C29×#525C2211yescharacteristic
31C2×C29×C22⋊Q8—21no—
32C2×C29×C22⋊Q8C2211yescharacteristic
33C29×#520C2211yescharacteristic
34C2×C29×#117C2211yescharacteristic
35C29×#485—21no—
36C29×#485—21no—
37C29×#482—21no—
38C29×#482—21no—
39C29×#428C2211yescharacteristic, complemented
40C29×#428C2211yescharacteristic, complemented
41C2×C29×#104C2211yescharacteristic
42C2×C29×#104C2211yescharacteristic
43C2×C29×#104C2211yescharacteristic
44C2×C29×#104C2211yescharacteristic
45C2×C29×#104C2211yescharacteristic, complemented
46C2×C29×#104C2211yescharacteristic, complemented
47C29×#419—21no—
48C29×#418—21no—
49C29×#417C2211yescharacteristic
50C29×#417C2211yescharacteristic
51C29×#417C2211yescharacteristic
52C29×#417C2211yescharacteristic
53C29×#417C2211yescharacteristic, complemented
54C29×#417C2211yescharacteristic, complemented
55C29×#416—21no—
56C29×#416—21no—
57C2×C29×#101C2211yescharacteristic, complemented
58C2×C29×#101C2211yescharacteristic, complemented
59C29×#407C2211yescharacteristic
60C29×#397—22no—
61C29×#391C2211yescharacteristic, complemented
62C29×#391C2211yescharacteristic, complemented
63C29×#387—22no—
64C29×#384C2211yescharacteristic, complemented
65C29×#382C2211yescharacteristic, complemented
66C4×C22⋊C4×C29C2211yescharacteristic
67C29×#343C2211yescharacteristic, complemented
68C29×#343C2211yescharacteristic, complemented
69C29×#339C2211yescharacteristic, complemented
70C29×#339C2211yescharacteristic, complemented
71C29×2−1+4—22no—
72C29×2−1+4—22no—
73C29×2−1+4—41no—
74C29×2−1+4—41no—
75C2×#41×C29—21no—
76C2×#41×C29—21no—
77C2×#41×C29—21no—
78C2×#41×C29—22no—
79C2×#41×C29—21no—
80C2×#41×C29—22no—
81C2×#41×C29—22no—
82C2×#41×C29—41no—
83C2×#41×C29—41no—
84C2×#41×C29D411yescharacteristic
85C2×#41×C29D411yescharacteristic
86C2×#41×C29C2311yescharacteristic
87C2×#41×C29C2311yescharacteristic
88C2×#41×C29C2311yescharacteristic
89C22×Q8×C29—21no—
90C22×Q8×C29—21no—
91C22×Q8×C29D411yescharacteristic
92C22×Q8×C29C2311yescharacteristic
93C22×D4×C29—21no—
94C22×D4×C29D411yescharacteristic
95C23×C4×C29—21no—
96C23×C4×C29C2311yescharacteristic
97C2×M16×C29—21no—
98C2×M16×C29—41no—
99C2×M16×C29—41no—
100C2×M16×C29C2311yescharacteristic
101C2×M16×C29C2311yescharacteristic
102C2×M16×C29C2311yescharacteristic
103C2×M16×C29C2311yescharacteristic
104C22×C8×C29—21no—
105C29×C4⋊Q8—22no—
106C29×C4⋊Q8—21no—
107C29×#124—22no—
108C29×#124—21no—
109C29×#123—22no—
110C29×#123—22no—
111C29×#123—22no—
112C29×#123—21no—
113C29×#123—22no—
114C29×C22⋊Q8—22no—
115C29×C22⋊Q8—22no—
116C29×C22⋊Q8—22no—
117C29×C22⋊Q8—21no—
118C29×C22⋊Q8—21no—
119C29×C22⋊Q8—21no—
120C29×C22⋊Q8—21no—
121C29×C22⋊Q8—21no—
122C29×C22⋊Q8—21no—
123C29×C22⋊Q8—21no—
124C29×C22⋊Q8—21no—
125C29×C22⋊Q8D411yescharacteristic
126C29×C22⋊Q8D411yescharacteristic
127C29×#121—22no—
128C29×#121—22no—
129C29×#121—22no—
130C29×#121—21no—
131C29×#121—21no—
132C29×#121—22no—
133C29×#121D411yescharacteristic
134C29×#121D411yescharacteristic
135C29×#120—22no—
136C29×#120—21no—
137C4×Q8×C29—21no—
138C4×D4×C29—22no—
139C4×D4×C29—22no—
140C4×D4×C29—21no—
141C4×D4×C29—22no—
142C4×D4×C29—21no—
143C4×D4×C29—21no—
144C29×#117—21no—
145C29×#117—21no—
146C29×#117—21no—
147C29×#117—21no—
148C29×#117—21no—
149C29×#117C2311yescharacteristic
150C2×C4⋊C4×C29—22no—
151C2×C4⋊C4×C29—21no—
152C2×C4⋊C4×C29—22no—
153C2×C4⋊C4×C29D412yes—
154C2×C4⋊C4×C29C2311yescharacteristic
155C2×C4⋊C4×C29C2311yescharacteristic
156C2×C4⋊C4×C29C2311yescharacteristic
157C2×C22⋊C4×C29—22no—
158C2×C22⋊C4×C29—21no—
159C2×C22⋊C4×C29—21no—
160C2×C22⋊C4×C29D412yes—
161C2×C42×C29—21no—
162C2×C42×C29C2311yescharacteristic
163C2×C42×C29C2311yescharacteristic
164C29×#107—21no—
165C29×#107—21no—
166C29×#106—21no—
167C29×#106—21no—
168C29×#104—22no—
169C29×#104—22no—
170C29×#104—41no—
171C29×#104—41no—
172C29×#104—41no—
173C29×#104—41no—
174C29×#103—21no—
175C29×#103—21no—
176C29×#103—21no—
177C29×#103—21no—
178C29×#103—21no—
179C29×#103—21no—
180C29×#102—21no—
181C29×#102—21no—
182C29×#102—21no—
183C29×#102—21no—
184C29×#102—21no—
185C29×#102—21no—
186C29×#101—41no—
187C29×#101—41no—
188C29×C22⋊C8—21no—
189C29×C22⋊C8—21no—
190C29×#95—21no—
191C29×#95—22no—
192C29×#95—22no—
193C29×#95—22no—
194C24×C29—21no—
195C24×C29C2×D411yescharacteristic
196#41×C29—21no—
197#41×C29—21no—
198#41×C29—22no—
199#41×C29—22no—
200#41×C29—21no—
201#41×C29—21no—
202#41×C29—21no—
203#41×C29—21no—
204#41×C29—21no—
205#41×C29—21no—
206#41×C29—21no—
207#41×C29—21no—
208#41×C29—42no—
209#41×C29—42no—
210#41×C29—41no—
211#41×C29—41no—
212#41×C29—42no—
213#41×C29—42no—
214#41×C29—42no—
215#41×C29—42no—
216#41×C29—44no—
217#41×C29—44no—
218#41×C29—42no—
219#41×C29—42no—
220#41×C29#4112yes—
221#41×C29#4112yes—
222C2×Q8×C29—22no—
223C2×Q8×C29—21no—
224C2×Q8×C29—21no—
225C2×Q8×C29—21no—
226C2×Q8×C29—21no—
227C2×Q8×C29—21no—
228C2×Q8×C29—21no—
229C2×Q8×C29—21no—
230C2×Q8×C29—22no—
231C2×Q8×C29—41no—
232C2×Q8×C29—42no—
233C2×Q8×C29—42no—
234C2×Q8×C29—42no—
235C2×Q8×C29—42no—
236C2×Q8×C29C2×D411yescharacteristic
237C2×Q8×C29C2×D411yescharacteristic
238C2×Q8×C29C2×D411yescharacteristic
239C2×D4×C29—21no—
240C2×D4×C29—22no—
241C2×D4×C29—22no—
242C2×D4×C29—21no—
243C2×D4×C29—21no—
244C2×D4×C29—21no—
245C2×D4×C29—21no—
246C2×D4×C29—21no—
247C2×D4×C29—22no—
248C2×D4×C29—21no—
249C2×D4×C29—21no—
250C2×D4×C29—41no—
251C2×D4×C29—42no—
252C2×D4×C29—42no—
253C2×D4×C29C2×D411yescharacteristic
254C2×D4×C29C2×D411yescharacteristic
255C2×D4×C29C2×D411yescharacteristic
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—21no—
259C22×C4×C29—21no—
260C22×C4×C29—21no—
261C22×C4×C29—22no—
262C22×C4×C29—22no—
263C22×C4×C29—21no—
264C22×C4×C29—21no—
265C22×C4×C29—22no—
266C22×C4×C29—21no—
267C22×C4×C29—21no—
268C22×C4×C29—21no—
269C22×C4×C29—21no—
270C22×C4×C29—21no—
271C22×C4×C29—21no—
272C22×C4×C29—21no—
273C22×C4×C29—42no—
274C22×C4×C29—42no—
275C22×C4×C29C2×D412yes—
276C22×C4×C29C2×D411yescharacteristic
277C22×C4×C29C2×D411yescharacteristic
278C22×C4×C29C2×D411yescharacteristic
279C22×C4×C29C2×D411yescharacteristic
280C22×C4×C29C2×D411yescharacteristic
281C22×C4×C29C2×D412yes—
282C22×C4×C29C2411yescharacteristic
283M16×C29—21no—
284M16×C29—21no—
285M16×C29—21no—
286M16×C29—21no—
287M16×C29—21no—
288M16×C29—21no—
289M16×C29—21no—
290M16×C29—21no—
291M16×C29—42no—
292C2×C8×C29—21no—
293C2×C8×C29—21no—
294C2×C8×C29—21no—
295C2×C8×C29—21no—
296C2×C8×C29—42no—
297C4⋊C4×C29—22no—
298C4⋊C4×C29—22no—
299C4⋊C4×C29—22no—
300C4⋊C4×C29—22no—
301C4⋊C4×C29—21no—
302C4⋊C4×C29—22no—
303C4⋊C4×C29—22no—
304C4⋊C4×C29—21no—
305C4⋊C4×C29—21no—
306C4⋊C4×C29—21no—
307C4⋊C4×C29—21no—
308C4⋊C4×C29—21no—
309C4⋊C4×C29—21no—
310C4⋊C4×C29—21no—
311C4⋊C4×C29—44no—
312C4⋊C4×C29C2×D411yescharacteristic
313C4⋊C4×C29C2×D411yescharacteristic
314C22⋊C4×C29—22no—
315C22⋊C4×C29—22no—
316C22⋊C4×C29—22no—
317C22⋊C4×C29—22no—
318C22⋊C4×C29—22no—
319C22⋊C4×C29—21no—
320C22⋊C4×C29—22no—
321C22⋊C4×C29—22no—
322C22⋊C4×C29—21no—
323C22⋊C4×C29—21no—
324C22⋊C4×C29—21no—
325C22⋊C4×C29—21no—
326C22⋊C4×C29—42no—
327C22⋊C4×C29—41no—
328C22⋊C4×C29—41no—
329C42×C29—22no—
330C42×C29—21no—
331C42×C29—21no—
332C42×C29—21no—
333C42×C29—21no—
334C42×C29—21no—
335C42×C29—41no—
336C42×C29—41no—
337#24028C2911yesmaximal, characteristic, direct product factor, Sylow
338C23×C29—21no—
339C23×C29—21no—
340C23×C29—21no—
341C23×C29—21no—
342C23×C29—21no—
343C23×C29—41no—
344C23×C29—41no—
345C23×C29—42no—
346C23×C29—42no—
347C23×C29—81no—
348C23×C29#12011yescharacteristic
349C23×C29#12011yescharacteristic
350C23×C29C22×D411yescharacteristic
351Q8×C29—21no—
352Q8×C29—21no—
353Q8×C29—21no—
354Q8×C29—21no—
355Q8×C29—21no—
356Q8×C29—42no—
357Q8×C29—44no—
358Q8×C29—41no—
359Q8×C29—41no—
360Q8×C29—41no—
361Q8×C29—41no—
362Q8×C29#12312yes—
363D4×C29—22no—
364D4×C29—22no—
365D4×C29—21no—
366D4×C29—21no—
367D4×C29—21no—
368D4×C29—21no—
369D4×C29—21no—
370D4×C29—42no—
371D4×C29—42no—
372D4×C29—42no—
373D4×C29—42no—
374D4×C29—44no—
375D4×C29—41no—
376D4×C29—41no—
377D4×C29—41no—
378D4×C29—41no—
379D4×C29—81no—
380D4×C29—82no—
381D4×C29#12312yes—
382C2×C4×C29—21no—
383C2×C4×C29—21no—
384C2×C4×C29—21no—
385C2×C4×C29—21no—
386C2×C4×C29—21no—
387C2×C4×C29—21no—
388C2×C4×C29—21no—
389C2×C4×C29—21no—
390C2×C4×C29—21no—
391C2×C4×C29—21no—
392C2×C4×C29—21no—
393C2×C4×C29—22no—
394C2×C4×C29—22no—
395C2×C4×C29—22no—
396C2×C4×C29—21no—
397C2×C4×C29—22no—
398C2×C4×C29—21no—
399C2×C4×C29—21no—
400C2×C4×C29—22no—
401C2×C4×C29—21no—
402C2×C4×C29—22no—
403C2×C4×C29—22no—
404C2×C4×C29—42no—
405C2×C4×C29—42no—
406C2×C4×C29—42no—
407C2×C4×C29—44no—
408C2×C4×C29—41no—
409C2×C4×C29—44no—
410C2×C4×C29—41no—
411C2×C4×C29—41no—
412C2×C4×C29—41no—
413C2×C4×C29—41no—
414C2×C4×C29—41no—
415C2×C4×C29—42no—
416C2×C4×C29—41no—
417C2×C4×C29—42no—
418C2×C4×C29—41no—
419C2×C4×C29—42no—
420C2×C4×C29—41no—
421C2×C4×C29—41no—
422C2×C4×C29—41no—
423C2×C4×C29—82no—
424C2×C4×C29#12011yescharacteristic
425C2×C4×C29#12011yescharacteristic
426C2×C4×C29C22×D411yescharacteristic
427C2×C4×C29C22×D411yescharacteristic
428C2×C4×C29C2×#4111yescharacteristic
429C2×C4×C29C2×#4111yescharacteristic
430C2×C4×C29H(5,𝔽2)11yescharacteristic
431C2×C4×C29H(5,𝔽2)11yescharacteristic
432C8×C29—41no—
433C8×C29—41no—
434C8×C29—41no—
435C8×C29—41no—
436#3489C2×C2911yescharacteristic
437#3093C2×C2911yescharacteristic, complemented
438#2896C2×C2911yescharacteristic, complemented
439#2499C2×C2911yescharacteristic, complemented
440#2040C2×C2911yescharacteristic, complemented
441#2039C2×C2911yescharacteristic, complemented
442#2038C2×C2911yescharacteristic, complemented
443#2038C2×C2911yescharacteristic, complemented
444#1901C2×C2911yescharacteristic, complemented
445#1871C2×C2911yescharacteristic, complemented
446#1860C2×C2911yescharacteristic, complemented
447#1859C2×C2911yescharacteristic, complemented
448#1793C2×C2911yescharacteristic, complemented
449#1793C2×C2911yescharacteristic, complemented
450#1789C2×C2911yescharacteristic, complemented
451C22×C29—21no—
452C22×C29—21no—
453C22×C29—21no—
454C22×C29—21no—
455C22×C29—22no—
456C22×C29—21no—
457C22×C29—21no—
458C22×C29—21no—
459C22×C29—21no—
460C22×C29—41no—
461C22×C29—41no—
462C22×C29—41no—
463C22×C29—41no—
464C22×C29—41no—
465C22×C29—41no—
466C22×C29—41no—
467C22×C29—41no—
468C22×C29—81no—
469C22×C29—81no—
470C22×C29—84no—
471C22×C29C2×#12011yescharacteristic
472C22×C29#54611yescharacteristic
473C22×C29#54611yescharacteristic
474C4×C29—21no—
475C4×C29—21no—
476C4×C29—22no—
477C4×C29—42no—
478C4×C29—42no—
479C4×C29—41no—
480C4×C29—41no—
481C4×C29—42no—
482C4×C29—41no—
483C4×C29—41no—
484C4×C29—81no—
485C4×C29—81no—
486C4×C29—81no—
487C4×C29C2×#12311yescharacteristic
488C4×C29#53411yescharacteristic
489C4×C29#54611yescharacteristic
490C4×C29#54611yescharacteristic
491C2×2−1+4C22×C2911yescharacteristic
492C22×#41C22×C2911yescharacteristic
493C22×M16C22×C2911yescharacteristic
494D4×Q8—21no—
495#548—21no—
496#547—21no—
497#547—22no—
498#546—21no—
499#546—22no—
500#537—21no—
501#537C22×C2911yescharacteristic
502#536—21no—
503#536C22×C2911yescharacteristic
504#525—21no—
505#525C22×C2911yescharacteristic
506C2×C22⋊Q8—21no—
507C2×C22⋊Q8C22×C2911yescharacteristic
508#520C22×C2911yescharacteristic
509C2×#117C22×C2911yescharacteristic
510#485—21no—
511#485—21no—
512#482—21no—
513#482—21no—
514#428C22×C2911yescharacteristic, complemented
515#428C22×C2911yescharacteristic, complemented
516C2×#104C22×C2911yescharacteristic
517C2×#104C22×C2911yescharacteristic
518C2×#104C22×C2911yescharacteristic
519C2×#104C22×C2911yescharacteristic
520C2×#104C22×C2911yescharacteristic, complemented
521C2×#104C22×C2911yescharacteristic, complemented
522#419—21no—
523#418—21no—
524#417C22×C2911yescharacteristic
525#417C22×C2911yescharacteristic
526#417C22×C2911yescharacteristic
527#417C22×C2911yescharacteristic
528#417C22×C2911yescharacteristic, complemented
529#417C22×C2911yescharacteristic, complemented
530#416—21no—
531#416—21no—
532C2×#101C22×C2911yescharacteristic, complemented
533C2×#101C22×C2911yescharacteristic, complemented
534#407C22×C2911yescharacteristic
535#397—22no—
536#391C22×C2911yescharacteristic, complemented
537#391C22×C2911yescharacteristic, complemented
538#387—22no—
539#384C22×C2911yescharacteristic, complemented
540#382C22×C2911yescharacteristic, complemented
541C4×C22⋊C4C22×C2911yescharacteristic
542#343C22×C2911yescharacteristic, complemented
543#343C22×C2911yescharacteristic, complemented
544#339C22×C2911yescharacteristic, complemented
545#339C22×C2911yescharacteristic, complemented
546C2×C29—21no—
547C2×C29—21no—
548C2×C29—41no—
549C2×C29—41no—
550C2×C29—42no—
551C2×C29—81no—
552C2×C29—81no—
553C2×C29#240511yescharacteristic
554C2×C29#301811yescharacteristic
555C2×C29#302011yescharacteristic
5562−1+4—22no—
5572−1+4—22no—
5582−1+4—41no—
5592−1+4—41no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—22no—
564C2×#41—21no—
565C2×#41—22no—
566C2×#41—22no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C2911yescharacteristic
570C2×#41D4×C2911yescharacteristic
571C2×#41C23×C2911yescharacteristic
572C2×#41C23×C2911yescharacteristic
573C2×#41C23×C2911yescharacteristic
574C22×Q8—21no—
575C22×Q8—21no—
576C22×Q8D4×C2911yescharacteristic
577C22×Q8C23×C2911yescharacteristic
578C22×D4—21no—
579C22×D4D4×C2911yescharacteristic
580C23×C4—21no—
581C23×C4C23×C2911yescharacteristic
582C2×M16—21no—
583C2×M16—41no—
584C2×M16—41no—
585C2×M16C23×C2911yescharacteristic
586C2×M16C23×C2911yescharacteristic
587C2×M16C23×C2911yescharacteristic
588C2×M16C23×C2911yescharacteristic
589C22×C8—21no—
590C4⋊Q8—22no—
591C4⋊Q8—21no—
592#124—22no—
593#124—21no—
594#123—22no—
595#123—22no—
596#123—22no—
597#123—21no—
598#123—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C2911yescharacteristic
611C22⋊Q8D4×C2911yescharacteristic
612#121—22no—
613#121—22no—
614#121—22no—
615#121—21no—
616#121—21no—
617#121—22no—
618#121D4×C2911yescharacteristic
619#121D4×C2911yescharacteristic
620#120—22no—
621#120—21no—
622C4×Q8—21no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—21no—
626C4×D4—22no—
627C4×D4—21no—
628C4×D4—21no—
629#117—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117—21no—
634#117C23×C2911yescharacteristic
635C2×C4⋊C4—22no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4D4×C2912yes—
639C2×C4⋊C4C23×C2911yescharacteristic
640C2×C4⋊C4C23×C2911yescharacteristic
641C2×C4⋊C4C23×C2911yescharacteristic
642C2×C22⋊C4—22no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C2912yes—
646C2×C42—21no—
647C2×C42C23×C2911yescharacteristic
648C2×C42C23×C2911yescharacteristic
649#107—21no—
650#107—21no—
651#106—21no—
652#106—21no—
653#104—22no—
654#104—22no—
655#104—41no—
656#104—41no—
657#104—41no—
658#104—41no—
659#103—21no—
660#103—21no—
661#103—21no—
662#103—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671#101—41no—
672#101—41no—
673C22⋊C8—21no—
674C22⋊C8—21no—
675#95—21no—
676#95—22no—
677#95—22no—
678#95—22no—
679C29#2402811yescharacteristic, direct product factor, Sylow
680C24—21no—
681C24C2×D4×C2911yescharacteristic
682#41—21no—
683#41—21no—
684#41—22no—
685#41—22no—
686#41—21no—
687#41—21no—
688#41—21no—
689#41—21no—
690#41—21no—
691#41—21no—
692#41—21no—
693#41—21no—
694#41—42no—
695#41—42no—
696#41—41no—
697#41—41no—
698#41—42no—
699#41—42no—
700#41—42no—
701#41—42no—
702#41—44no—
703#41—44no—
704#41—42no—
705#41—42no—
706#41#41×C2912yes—
707#41#41×C2912yes—
708C2×Q8—22no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—22no—
717C2×Q8—41no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8C2×D4×C2911yescharacteristic
723C2×Q8C2×D4×C2911yescharacteristic
724C2×Q8C2×D4×C2911yescharacteristic
725C2×D4—21no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4C2×D4×C2911yescharacteristic
740C2×D4C2×D4×C2911yescharacteristic
741C2×D4C2×D4×C2911yescharacteristic
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4C2×D4×C2912yes—
762C22×C4C2×D4×C2911yescharacteristic
763C22×C4C2×D4×C2911yescharacteristic
764C22×C4C2×D4×C2911yescharacteristic
765C22×C4C2×D4×C2911yescharacteristic
766C22×C4C2×D4×C2911yescharacteristic
767C22×C4C2×D4×C2912yes—
768C22×C4C24×C2911yescharacteristic
769M16—21no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—42no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—42no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—21no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—44no—
798C4⋊C4C2×D4×C2911yescharacteristic
799C4⋊C4C2×D4×C2911yescharacteristic
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—21no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—42no—
813C22⋊C4—41no—
814C22⋊C4—41no—
815C42—22no—
816C42—21no—
817C42—21no—
818C42—21no—
819C42—21no—
820C42—21no—
821C42—41no—
822C42—41no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—41no—
829C23—41no—
830C23—42no—
831C23—42no—
832C23—81no—
833C23C29×#12011yescharacteristic
834C23C29×#12011yescharacteristic
835C23C22×D4×C2911yescharacteristic
836Q8—21no—
837Q8—21no—
838Q8—21no—
839Q8—21no—
840Q8—21no—
841Q8—42no—
842Q8—44no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8C29×#12312yes—
848D4—22no—
849D4—22no—
850D4—21no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—21no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—44no—
859D4—42no—
860D4—41no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—81no—
865D4—82no—
866D4C29×#12312yes—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—41no—
904C2×C4—42no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—82no—
909C2×C4C29×#12011yescharacteristic
910C2×C4C29×#12011yescharacteristic
911C2×C4C22×D4×C2911yescharacteristic
912C2×C4C22×D4×C2911yescharacteristic
913C2×C4C2×#41×C2911yescharacteristic
914C2×C4C2×#41×C2911yescharacteristic
915C2×C4C29×H(5,𝔽2)11yescharacteristic
916C2×C4C29×H(5,𝔽2)11yescharacteristic
917C8—41no—
918C8—41no—
919C8—41no—
920C8—41no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—22no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22C2×C29×#12011yescharacteristic
942C22C29×#54611yescharacteristic
943C22C29×#54611yescharacteristic
944C4—21no—
945C4—21no—
946C4—22no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—41no—
951C4—42no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4C2×C29×#12311yescharacteristic
958C4C29×#53411yescharacteristic
959C4C29×#54611yescharacteristic
960C4C29×#54611yescharacteristic
961C2—21no—
962C2—21no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—81no—
967C2—81no—
968C2C29×#240511yescharacteristic
969C2C29×#301811yescharacteristic
970C2C29×#302011yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3093C2semidirect
3. C29×#2896C2semidirect
4. C29×#2499C2semidirect
5. C29×#2040C2semidirect
6. C29×#2039C2semidirect
7. C29×#2038C2semidirect
8. C29×#2038C2semidirect
9. C29×#1901C2semidirect
10. C29×#1871C2semidirect
11. C29×#1860C2semidirect
12. C29×#1859C2semidirect
13. C29×#1793C2semidirect
14. C29×#1793C2semidirect
15. C29×#1789C2semidirect
39. C29×#428C22semidirect
40. C29×#428C22semidirect
45. C2×C29×#104C22semidirect
46. C2×C29×#104C22semidirect
53. C29×#417C22semidirect
54. C29×#417C22semidirect
57. C2×C29×#101C22semidirect
58. C2×C29×#101C22semidirect
61. C29×#391C22semidirect
62. C29×#391C22semidirect
64. C29×#384C22semidirect
65. C29×#382C22semidirect
67. C29×#343C22semidirect
68. C29×#343C22semidirect
69. C29×#339C22semidirect
70. C29×#339C22semidirect
337. #24028C29direct (N × H)
437. #3093C2×C29semidirect
438. #2896C2×C29semidirect
439. #2499C2×C29semidirect
440. #2040C2×C29semidirect
441. #2039C2×C29semidirect
442. #2038C2×C29semidirect
443. #2038C2×C29semidirect
444. #1901C2×C29semidirect
445. #1871C2×C29semidirect
446. #1860C2×C29semidirect
447. #1859C2×C29semidirect
448. #1793C2×C29semidirect
449. #1793C2×C29semidirect
450. #1789C2×C29semidirect
514. #428C22×C29semidirect
515. #428C22×C29semidirect
520. C2×#104C22×C29semidirect
521. C2×#104C22×C29semidirect
528. #417C22×C29semidirect
529. #417C22×C29semidirect
532. C2×#101C22×C29semidirect
533. C2×#101C22×C29semidirect
536. #391C22×C29semidirect
537. #391C22×C29semidirect
539. #384C22×C29semidirect
540. #382C22×C29semidirect
542. #343C22×C29semidirect
543. #343C22×C29semidirect
544. #339C22×C29semidirect
545. #339C22×C29semidirect
679. C29#24028direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34892
C29×#30932
C29×#28962
C29×#24992
C29×#20402
C29×#20392
C29×#20382
C29×#19012
C29×#18712
C29×#18602
C29×#18592
C29×#17932
C29×#17892
#2402829