Finite Group Databasebeta

← C29×#18447 #20313347

Subgroups — C29×#18447 #20313347

Order 7424.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3534C211yesmaximal, characteristic
2C29×#3193C211yesmaximal, characteristic, complemented
3C29×#3190C211yesmaximal, characteristic, complemented
4C29×#2814C211yesmaximal, characteristic, complemented
5C29×#1612C211yesmaximal, characteristic, complemented
6C29×#1610C211yesmaximal, characteristic, complemented
7C29×#1609C211yesmaximal, characteristic, complemented
8C29×#1607C211yesmaximal, characteristic, complemented
9C29×#1606C211yesmaximal, characteristic, complemented
10C29×#1604C211yesmaximal, characteristic, complemented
11C29×#1603C211yesmaximal, characteristic, complemented
12C29×#1601C211yesmaximal, characteristic, complemented
13C29×#1519C211yesmaximal, characteristic, complemented
14C29×#1513C211yesmaximal, characteristic, complemented
15C29×#1468C211yesmaximal, characteristic, complemented
16C29×#562—21no—
17C29×#560—21no—
18C29×#553—21no—
19C29×#551—21no—
20C29×#546—21no—
21C29×#546—21no—
22C29×#546—21no—
23D42×C29—21no—
24C29×#540—21no—
25C29×#539—21no—
26C29×#539C2211yescharacteristic
27C29×#538—21no—
28C29×#538C2211yescharacteristic
29C29×#537C2211yescharacteristic
30C29×#534—21no—
31C29×#534C2211yescharacteristic
32C29×#525C2211yescharacteristic
33C2×C29×#123C2211yescharacteristic
34C2×C29×C22⋊Q8C2211yescharacteristic, complemented
35C2×C29×#121C2211yescharacteristic
36C29×#485—21no—
37C29×#484—21no—
38C29×#483C2211yescharacteristic, complemented
39C29×#480C2211yescharacteristic
40C29×#480C2211yescharacteristic, complemented
41C29×#480C2211yescharacteristic, complemented
42C29×#468—21no—
43C29×#468—21no—
44C29×#467—21no—
45C29×#465—21no—
46C29×#452—21no—
47C29×#451C2211yescharacteristic, complemented
48C29×#450—21no—
49C29×#448C2211yescharacteristic
50C29×#448C2211yescharacteristic, complemented
51C29×#448C2211yescharacteristic, complemented
52C29×#407C2211yescharacteristic, complemented
53C2×C29×C22⋊C8C2211yescharacteristic, complemented
54C29×#398—21no—
55C29×#398C2211yescharacteristic, complemented
56C29×#397—21no—
57C29×#397C2211yescharacteristic, complemented
58C29×#396—21no—
59C29×#395C2211yescharacteristic, complemented
60C29×#394—21no—
61C29×#393C2211yescharacteristic, complemented
62C29×#380C2211yescharacteristic, complemented
63C29×#328C2211yescharacteristic, complemented
64C29×#328C2211yescharacteristic, complemented
65C29×#327C2211yescharacteristic
66C29×#327C2211yescharacteristic
67C29×#327C2211yescharacteristic, complemented
68C29×#327C2211yescharacteristic, complemented
69C29×#327C2211yescharacteristic, complemented
70C29×#327C2211yescharacteristic, complemented
71C29×#324C2211yescharacteristic, complemented
72C29×#324C2211yescharacteristic, complemented
73C29×#323C2211yescharacteristic, complemented
74C29×#323C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C2×#41×C29D411yescharacteristic
77C22×Q8×C29C2311yescharacteristic
78C22×D4×C29—21no—
79C22×D4×C29—21no—
80C22×D4×C29—21no—
81C22×D4×C29D411yescharacteristic
82C22×D4×C29D411yescharacteristic
83C23×C4×C29C2311yescharacteristic
84C2×Q16×C29—21no—
85C2×SD16×C29—21no—
86C2×SD16×C29—21no—
87C2×SD16×C29—21no—
88C2×M16×C29—21no—
89C22×C8×C29—21no—
90C29×#127—21no—
91C29×#126—21no—
92C29×#126—21no—
93C29×#126—21no—
94C29×#126—21no—
95C29×#125—21no—
96C29×#125—21no—
97C29×#124—21no—
98C29×#124—21no—
99C29×#124—21no—
100C29×#123—21no—
101C29×#123—21no—
102C29×#123—21no—
103C29×#123—21no—
104C29×#123—21no—
105C29×#123—21no—
106C29×#123—21no—
107C29×#123—21no—
108C29×#123—21no—
109C29×#123—21no—
110C29×#123—21no—
111C29×#123—21no—
112C29×#123—21no—
113C29×#123—21no—
114C29×C22⋊Q8—21no—
115C29×C22⋊Q8—21no—
116C29×C22⋊Q8—21no—
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⋊Q8D411yescharacteristic
124C29×C22⋊Q8C2311yescharacteristic
125C29×#121—21no—
126C29×#121—21no—
127C29×#121—21no—
128C29×#121—21no—
129C29×#121—21no—
130C29×#121—21no—
131C29×#121—21no—
132C29×#121—21no—
133C29×#121—21no—
134C29×#121—21no—
135C29×#121—21no—
136C29×#121—21no—
137C29×#121—21no—
138C29×#121—21no—
139C29×#121—21no—
140C29×#121D411yescharacteristic
141C29×#121D411yescharacteristic
142C29×#121D411yescharacteristic
143C29×#121C2311yescharacteristic
144C29×#121C2311yescharacteristic
145C29×#121C2311yescharacteristic
146C29×#120—21no—
147C29×#120—21no—
148C29×#120—21no—
149C29×#120—21no—
150C29×#120—21no—
151C29×#120—21no—
152C29×#120—21no—
153C29×#120—21no—
154C4×D4×C29—21no—
155C4×D4×C29—21no—
156C4×D4×C29—21no—
157C4×D4×C29—21no—
158C4×D4×C29—21no—
159C4×D4×C29—21no—
160C4×D4×C29—21no—
161C4×D4×C29—21no—
162C29×#117—21no—
163C29×#117D411yescharacteristic
164C2×C4⋊C4×C29—21no—
165C2×C4⋊C4×C29—21no—
166C2×C4⋊C4×C29—21no—
167C2×C4⋊C4×C29—21no—
168C2×C4⋊C4×C29D411yescharacteristic
169C2×C4⋊C4×C29D411yescharacteristic
170C2×C4⋊C4×C29C2311yescharacteristic
171C2×C4⋊C4×C29C2311yescharacteristic
172C2×C22⋊C4×C29—21no—
173C2×C22⋊C4×C29—21no—
174C2×C22⋊C4×C29—21no—
175C2×C22⋊C4×C29—21no—
176C2×C22⋊C4×C29—21no—
177C2×C22⋊C4×C29—21no—
178C2×C22⋊C4×C29—21no—
179C2×C22⋊C4×C29D411yescharacteristic
180C2×C22⋊C4×C29D411yescharacteristic
181C2×C22⋊C4×C29C2311yescharacteristic
182C29×#107—21no—
183C29×#107—21no—
184C29×#107—21no—
185C29×#106—21no—
186C29×#103—21no—
187C29×#103—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#103—21no—
191C29×#102—21no—
192C29×#102—21no—
193C29×#102—21no—
194C29×C22⋊C8—21no—
195C29×C22⋊C8—21no—
196C29×C22⋊C8C2311yescharacteristic
197C29×C22⋊C8C2311yescharacteristic
198C29×C22⋊C8C2311yescharacteristic
199C29×C22⋊C8C2311yescharacteristic
200C29×#95—21no—
201C29×#95—21no—
202C29×#95—21no—
203C29×#95—21no—
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29—21no—
207C24×C29—21no—
208C24×C29C2×D411yescharacteristic
209C24×C29C2×D411yescharacteristic
210#41×C29—81no—
211#41×C29—81no—
212#41×C29—81no—
213C2×Q8×C29—21no—
214C2×Q8×C29—21no—
215C2×Q8×C29—21no—
216C2×Q8×C29—81no—
217C2×Q8×C29C2×D411yescharacteristic
218C2×D4×C29—21no—
219C2×D4×C29—21no—
220C2×D4×C29—21no—
221C2×D4×C29—21no—
222C2×D4×C29—21no—
223C2×D4×C29—21no—
224C2×D4×C29—21no—
225C2×D4×C29—21no—
226C2×D4×C29—21no—
227C2×D4×C29—21no—
228C2×D4×C29—21no—
229C2×D4×C29—21no—
230C2×D4×C29—21no—
231C2×D4×C29—21no—
232C2×D4×C29—21no—
233C2×D4×C29—21no—
234C2×D4×C29—21no—
235C2×D4×C29—81no—
236C2×D4×C29—81no—
237C2×D4×C29—81no—
238C2×D4×C29—81no—
239C2×D4×C29—81no—
240C2×D4×C29—81no—
241C2×D4×C29—82no—
242C2×D4×C29C2×D411yescharacteristic
243C2×D4×C29C2×D411yescharacteristic
244C2×D4×C29C2×D411yescharacteristic
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—21no—
248C22×C4×C29—21no—
249C22×C4×C29—21no—
250C22×C4×C29—21no—
251C22×C4×C29—21no—
252C22×C4×C29—21no—
253C22×C4×C29—21no—
254C22×C4×C29—21no—
255C22×C4×C29—21no—
256C22×C4×C29—81no—
257C22×C4×C29C2×D411yescharacteristic
258C22×C4×C29C2×D411yescharacteristic
259C22×C4×C29C2×D411yescharacteristic
260C22×C4×C29C2×D411yescharacteristic
261C22×C4×C29C2×D411yescharacteristic
262C22×C4×C29C2×D411yescharacteristic
263C22×C4×C29C2×D411yescharacteristic
264C22×C4×C29C2×D411yescharacteristic
265C22×C4×C29C2411yescharacteristic
266Q16×C29—81no—
267SD16×C29—81no—
268SD16×C29—81no—
269SD16×C29—81no—
270M16×C29—81no—
271C2×C8×C29—21no—
272C2×C8×C29—21no—
273C2×C8×C29—21no—
274C2×C8×C29—21no—
275C2×C8×C29—81no—
276C4⋊C4×C29—21no—
277C4⋊C4×C29—21no—
278C4⋊C4×C29—21no—
279C4⋊C4×C29—21no—
280C4⋊C4×C29—21no—
281C4⋊C4×C29—21no—
282C4⋊C4×C29—21no—
283C4⋊C4×C29—21no—
284C4⋊C4×C29—21no—
285C4⋊C4×C29—21no—
286C4⋊C4×C29—21no—
287C4⋊C4×C29—21no—
288C4⋊C4×C29—21no—
289C4⋊C4×C29—21no—
290C4⋊C4×C29—21no—
291C4⋊C4×C29—41no—
292C4⋊C4×C29—41no—
293C4⋊C4×C29—81no—
294C4⋊C4×C29—81no—
295C4⋊C4×C29—81no—
296C4⋊C4×C29C2×D411yescharacteristic
297C4⋊C4×C29C2×D411yescharacteristic
298C4⋊C4×C29C2×D411yescharacteristic
299C4⋊C4×C29C2×D411yescharacteristic
300C22⋊C4×C29—21no—
301C22⋊C4×C29—21no—
302C22⋊C4×C29—21no—
303C22⋊C4×C29—21no—
304C22⋊C4×C29—21no—
305C22⋊C4×C29—21no—
306C22⋊C4×C29—21no—
307C22⋊C4×C29—21no—
308C22⋊C4×C29—21no—
309C22⋊C4×C29—21no—
310C22⋊C4×C29—21no—
311C22⋊C4×C29—21no—
312C22⋊C4×C29—21no—
313C22⋊C4×C29—21no—
314C22⋊C4×C29—21no—
315C22⋊C4×C29—21no—
316C22⋊C4×C29—21no—
317C22⋊C4×C29—21no—
318C22⋊C4×C29—21no—
319C22⋊C4×C29—21no—
320C22⋊C4×C29—21no—
321C22⋊C4×C29—21no—
322C22⋊C4×C29—21no—
323C22⋊C4×C29—21no—
324C22⋊C4×C29—21no—
325C22⋊C4×C29—41no—
326C22⋊C4×C29—41no—
327C22⋊C4×C29—81no—
328C22⋊C4×C29—81no—
329C22⋊C4×C29—81no—
330C42×C29—21no—
331C42×C29—21no—
332C42×C29—21no—
333#18447C2911yesmaximal, characteristic, direct product factor, Sylow
334C23×C29—21no—
335C23×C29—21no—
336C23×C29—21no—
337C23×C29—21no—
338C23×C29—21no—
339C23×C29—21no—
340C23×C29—21no—
341C23×C29—21no—
342C23×C29—41no—
343C23×C29—41no—
344C23×C29—42no—
345C23×C29—41no—
346C23×C29—41no—
347C23×C29—81no—
348C23×C29—81no—
349C23×C29—81no—
350C23×C29—81no—
351C23×C29—81no—
352C23×C29#12011yescharacteristic
353C23×C29#12011yescharacteristic
354C23×C29C22×D411yescharacteristic
355Q8×C29—41no—
356Q8×C29—41no—
357Q8×C29—41no—
358Q8×C29—41no—
359Q8×C29—41no—
360Q8×C29—81no—
361D4×C29—41no—
362D4×C29—41no—
363D4×C29—41no—
364D4×C29—42no—
365D4×C29—42no—
366D4×C29—41no—
367D4×C29—41no—
368D4×C29—41no—
369D4×C29—41no—
370D4×C29—41no—
371D4×C29—41no—
372D4×C29—81no—
373D4×C29—81no—
374D4×C29—81no—
375D4×C29—81no—
376D4×C29—81no—
377D4×C29—81no—
378D4×C29—81no—
379D4×C29—81no—
380D4×C29—81no—
381D4×C29—81no—
382D4×C29—81no—
383D4×C29—81no—
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—21no—
394C2×C4×C29—41no—
395C2×C4×C29—41no—
396C2×C4×C29—41no—
397C2×C4×C29—41no—
398C2×C4×C29—41no—
399C2×C4×C29—41no—
400C2×C4×C29—41no—
401C2×C4×C29—41no—
402C2×C4×C29—41no—
403C2×C4×C29—41no—
404C2×C4×C29—41no—
405C2×C4×C29—41no—
406C2×C4×C29—41no—
407C2×C4×C29—41no—
408C2×C4×C29—41no—
409C2×C4×C29—41no—
410C2×C4×C29—41no—
411C2×C4×C29—41no—
412C2×C4×C29—41no—
413C2×C4×C29—41no—
414C2×C4×C29—81no—
415C2×C4×C29—81no—
416C2×C4×C29—81no—
417C2×C4×C29—81no—
418C2×C4×C29—81no—
419C2×C4×C29—81no—
420C2×C4×C29—81no—
421C2×C4×C29#12011yescharacteristic
422C2×C4×C29#12011yescharacteristic
423C2×C4×C29C22×D411yescharacteristic
424C2×C4×C29C22×D411yescharacteristic
425C8×C29—41no—
426C8×C29—41no—
427C8×C29—41no—
428C8×C29—41no—
429#3534C2×C2911yescharacteristic
430#3193C2×C2911yescharacteristic, complemented
431#3190C2×C2911yescharacteristic, complemented
432#2814C2×C2911yescharacteristic, complemented
433#1612C2×C2911yescharacteristic, complemented
434#1610C2×C2911yescharacteristic, complemented
435#1609C2×C2911yescharacteristic, complemented
436#1607C2×C2911yescharacteristic, complemented
437#1606C2×C2911yescharacteristic, complemented
438#1604C2×C2911yescharacteristic, complemented
439#1603C2×C2911yescharacteristic, complemented
440#1601C2×C2911yescharacteristic, complemented
441#1519C2×C2911yescharacteristic, complemented
442#1513C2×C2911yescharacteristic, complemented
443#1468C2×C2911yescharacteristic, complemented
444C22×C29—21no—
445C22×C29—21no—
446C22×C29—21no—
447C22×C29—21no—
448C22×C29—21no—
449C22×C29—21no—
450C22×C29—21no—
451C22×C29—21no—
452C22×C29—41no—
453C22×C29—41no—
454C22×C29—41no—
455C22×C29—41no—
456C22×C29—41no—
457C22×C29—41no—
458C22×C29—41no—
459C22×C29—41no—
460C22×C29—41no—
461C22×C29—41no—
462C22×C29—41no—
463C22×C29—41no—
464C22×C29—81no—
465C22×C29—81no—
466C22×C29—81no—
467C22×C29—81no—
468C22×C29—162no—
469C22×C29—162no—
470C22×C29C2×#12011yescharacteristic
471C22×C29#57611yescharacteristic
472C22×C29#57711yescharacteristic
473C4×C29—21no—
474C4×C29—21no—
475C4×C29—21no—
476C4×C29—21no—
477C4×C29—41no—
478C4×C29—41no—
479C4×C29—41no—
480C4×C29—41no—
481C4×C29—41no—
482C4×C29—41no—
483C4×C29—41no—
484C4×C29—41no—
485C4×C29—81no—
486C4×C29—81no—
487C4×C29—81no—
488C4×C29—81no—
489#562—21no—
490#560—21no—
491#553—21no—
492#551—21no—
493#546—21no—
494#546—21no—
495#546—21no—
496D42—21no—
497#540—21no—
498#539—21no—
499#539C22×C2911yescharacteristic
500#538—21no—
501#538C22×C2911yescharacteristic
502#537C22×C2911yescharacteristic
503#534—21no—
504#534C22×C2911yescharacteristic
505#525C22×C2911yescharacteristic
506C2×#123C22×C2911yescharacteristic
507C2×C22⋊Q8C22×C2911yescharacteristic, complemented
508C2×#121C22×C2911yescharacteristic
509#485—21no—
510#484—21no—
511#483C22×C2911yescharacteristic, complemented
512#480C22×C2911yescharacteristic
513#480C22×C2911yescharacteristic, complemented
514#480C22×C2911yescharacteristic, complemented
515#468—21no—
516#468—21no—
517#467—21no—
518#465—21no—
519#452—21no—
520#451C22×C2911yescharacteristic, complemented
521#450—21no—
522#448C22×C2911yescharacteristic
523#448C22×C2911yescharacteristic, complemented
524#448C22×C2911yescharacteristic, complemented
525#407C22×C2911yescharacteristic, complemented
526C2×C22⋊C8C22×C2911yescharacteristic, complemented
527#398—21no—
528#398C22×C2911yescharacteristic, complemented
529#397—21no—
530#397C22×C2911yescharacteristic, complemented
531#396—21no—
532#395C22×C2911yescharacteristic, complemented
533#394—21no—
534#393C22×C2911yescharacteristic, complemented
535#380C22×C2911yescharacteristic, complemented
536#328C22×C2911yescharacteristic, complemented
537#328C22×C2911yescharacteristic, complemented
538#327C22×C2911yescharacteristic
539#327C22×C2911yescharacteristic
540#327C22×C2911yescharacteristic, complemented
541#327C22×C2911yescharacteristic, complemented
542#327C22×C2911yescharacteristic, complemented
543#327C22×C2911yescharacteristic, complemented
544#324C22×C2911yescharacteristic, complemented
545#324C22×C2911yescharacteristic, complemented
546#323C22×C2911yescharacteristic, complemented
547#323C22×C2911yescharacteristic, complemented
548C2×C29—21no—
549C2×C29—21no—
550C2×C29—41no—
551C2×C29—41no—
552C2×C29—81no—
553C2×C29—81no—
554C2×C29—81no—
555C2×C29—81no—
556C2×C29#301211yescharacteristic
557C2×C29#302211yescharacteristic
558C2×C29#302611yescharacteristic
559C2×#41—21no—
560C2×#41D4×C2911yescharacteristic
561C22×Q8C23×C2911yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C2911yescharacteristic
566C22×D4D4×C2911yescharacteristic
567C23×C4C23×C2911yescharacteristic
568C2×Q16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×M16—21no—
573C22×C8—21no—
574#127—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#125—21no—
580#125—21no—
581#124—21no—
582#124—21no—
583#124—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8D4×C2911yescharacteristic
608C22⋊Q8C23×C2911yescharacteristic
609#121—21no—
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C2911yescharacteristic
625#121D4×C2911yescharacteristic
626#121D4×C2911yescharacteristic
627#121C23×C2911yescharacteristic
628#121C23×C2911yescharacteristic
629#121C23×C2911yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646#117—21no—
647#117D4×C2911yescharacteristic
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C2911yescharacteristic
653C2×C4⋊C4D4×C2911yescharacteristic
654C2×C4⋊C4C23×C2911yescharacteristic
655C2×C4⋊C4C23×C2911yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C2911yescharacteristic
664C2×C22⋊C4D4×C2911yescharacteristic
665C2×C22⋊C4C23×C2911yescharacteristic
666#107—21no—
667#107—21no—
668#107—21no—
669#106—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8—21no—
679C22⋊C8—21no—
680C22⋊C8C23×C2911yescharacteristic
681C22⋊C8C23×C2911yescharacteristic
682C22⋊C8C23×C2911yescharacteristic
683C22⋊C8C23×C2911yescharacteristic
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95C23×C2911yescharacteristic
689#95C23×C2911yescharacteristic
690C29#1844711yescharacteristic, direct product factor, Sylow
691C24—21no—
692C24—21no—
693C24C2×D4×C2911yescharacteristic
694C24C2×D4×C2911yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C2911yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C2911yescharacteristic
728C2×D4C2×D4×C2911yescharacteristic
729C2×D4C2×D4×C2911yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C2911yescharacteristic
743C22×C4C2×D4×C2911yescharacteristic
744C22×C4C2×D4×C2911yescharacteristic
745C22×C4C2×D4×C2911yescharacteristic
746C22×C4C2×D4×C2911yescharacteristic
747C22×C4C2×D4×C2911yescharacteristic
748C22×C4C2×D4×C2911yescharacteristic
749C22×C4C2×D4×C2911yescharacteristic
750C22×C4C24×C2911yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C2911yescharacteristic
782C4⋊C4C2×D4×C2911yescharacteristic
783C4⋊C4C2×D4×C2911yescharacteristic
784C4⋊C4C2×D4×C2911yescharacteristic
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23C29×#12011yescharacteristic
837C23C29×#12011yescharacteristic
838C23C22×D4×C2911yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
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—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4C29×#12011yescharacteristic
906C2×C4C29×#12011yescharacteristic
907C2×C4C22×D4×C2911yescharacteristic
908C2×C4C22×D4×C2911yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×C29×#12011yescharacteristic
940C22C29×#57611yescharacteristic
941C22C29×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C29×#301211yescharacteristic
967C2C29×#302211yescharacteristic
968C2C29×#302611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3193C2semidirect
3. C29×#3190C2semidirect
4. C29×#2814C2semidirect
5. C29×#1612C2semidirect
6. C29×#1610C2semidirect
7. C29×#1609C2semidirect
8. C29×#1607C2semidirect
9. C29×#1606C2semidirect
10. C29×#1604C2semidirect
11. C29×#1603C2semidirect
12. C29×#1601C2semidirect
13. C29×#1519C2semidirect
14. C29×#1513C2semidirect
15. C29×#1468C2semidirect
34. C2×C29×C22⋊Q8C22semidirect
38. C29×#483C22semidirect
40. C29×#480C22semidirect
41. C29×#480C22semidirect
47. C29×#451C22semidirect
50. C29×#448C22semidirect
51. C29×#448C22semidirect
52. C29×#407C22semidirect
53. C2×C29×C22⋊C8C22semidirect
55. C29×#398C22semidirect
57. C29×#397C22semidirect
59. C29×#395C22semidirect
61. C29×#393C22semidirect
62. C29×#380C22semidirect
63. C29×#328C22semidirect
64. C29×#328C22semidirect
67. C29×#327C22semidirect
68. C29×#327C22semidirect
69. C29×#327C22semidirect
70. C29×#327C22semidirect
71. C29×#324C22semidirect
72. C29×#324C22semidirect
73. C29×#323C22semidirect
74. C29×#323C22semidirect
333. #18447C29direct (N × H)
430. #3193C2×C29semidirect
431. #3190C2×C29semidirect
432. #2814C2×C29semidirect
433. #1612C2×C29semidirect
434. #1610C2×C29semidirect
435. #1609C2×C29semidirect
436. #1607C2×C29semidirect
437. #1606C2×C29semidirect
438. #1604C2×C29semidirect
439. #1603C2×C29semidirect
440. #1601C2×C29semidirect
441. #1519C2×C29semidirect
442. #1513C2×C29semidirect
443. #1468C2×C29semidirect
507. C2×C22⋊Q8C22×C29semidirect
511. #483C22×C29semidirect
513. #480C22×C29semidirect
514. #480C22×C29semidirect
520. #451C22×C29semidirect
523. #448C22×C29semidirect
524. #448C22×C29semidirect
525. #407C22×C29semidirect
526. C2×C22⋊C8C22×C29semidirect
528. #398C22×C29semidirect
530. #397C22×C29semidirect
532. #395C22×C29semidirect
534. #393C22×C29semidirect
535. #380C22×C29semidirect
536. #328C22×C29semidirect
537. #328C22×C29semidirect
540. #327C22×C29semidirect
541. #327C22×C29semidirect
542. #327C22×C29semidirect
543. #327C22×C29semidirect
544. #324C22×C29semidirect
545. #324C22×C29semidirect
546. #323C22×C29semidirect
547. #323C22×C29semidirect
690. C29#18447direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35342
C29×#31932
C29×#31902
C29×#28142
C29×#16122
C29×#16102
C29×#16092
C29×#16072
C29×#16062
C29×#16042
C29×#16032
C29×#16012
C29×#15192
C29×#15132
C29×#14682
#1844729