Finite Group Databasebeta

← C29×#17604 #20312504

Subgroups — C29×#17604 #20312504

Order 7424.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3494C211yesmaximal, characteristic
2C29×#2924C211yesmaximal, characteristic, complemented
3C29×#2343C211yesmaximal, characteristic, complemented
4C29×#1521C211yesmaximal, characteristic, complemented
5C29×#1517C211yesmaximal, characteristic, complemented
6C29×#1516C211yesmaximal, characteristic, complemented
7C29×#1514C211yesmaximal, characteristic, complemented
8C29×#1512C211yesmaximal, characteristic, complemented
9C29×#1510C211yesmaximal, characteristic, complemented
10C29×#1509C211yesmaximal, characteristic, complemented
11C29×#1505C211yesmaximal, characteristic, complemented
12C29×#1504C211yesmaximal, characteristic, complemented
13C29×#1502C211yesmaximal, characteristic, complemented
14C29×#1500C211yesmaximal, characteristic, complemented
15C2×C29×#327C211yesmaximal, characteristic, complemented
16C29×#555—21no—
17C29×#553—21no—
18C29×#553—21no—
19C29×#551—21no—
20C29×#551—21no—
21C29×#547—21no—
22C29×#546—21no—
23C29×#546—21no—
24C29×#544C411yescharacteristic, complemented
25C29×#542C411yescharacteristic, complemented
26C29×#542C411yescharacteristic, complemented
27C29×#540C411yescharacteristic, complemented
28C29×#540C411yescharacteristic, complemented
29C29×#535C411yescharacteristic, complemented
30C29×#532C2211yescharacteristic
31C29×#532C2211yescharacteristic
32C29×#529C2211yescharacteristic
33C29×#529C2211yescharacteristic
34C29×#525C2211yescharacteristic
35C2×C29×#121C2211yescharacteristic
36C29×#520C411yescharacteristic, complemented
37C29×#518C411yescharacteristic, complemented
38C2×C29×#117C2211yescharacteristic
39C29×#433—21no—
40C29×#433—21no—
41C29×#432C2211yescharacteristic, complemented
42C29×#432C2211yescharacteristic, complemented
43C29×#431C2211yescharacteristic, complemented
44C29×#431C2211yescharacteristic, complemented
45C29×#424—21no—
46C29×#407C2211yescharacteristic
47C2×C29×C22⋊C8C2211yescharacteristic
48C29×#405—21no—
49C29×#387—21no—
50C29×#387—21no—
51C29×#385—21no—
52C29×#383C2211yescharacteristic, complemented
53C29×#382C2211yescharacteristic, complemented
54C29×#381C2211yescharacteristic
55C4×C4⋊C4×C29C2211yescharacteristic, complemented
56C4×C22⋊C4×C29—21no—
57C29×#376C2211yescharacteristic, complemented
58C2×C29×#95C2211yescharacteristic
59C29×#328C2211yescharacteristic, complemented
60C29×#328C2211yescharacteristic, complemented
61C29×#328C2211yescharacteristic, complemented
62C29×#328C2211yescharacteristic, complemented
63C29×#327C2211yescharacteristic
64C29×#327C2211yescharacteristic
65C29×#327C2211yescharacteristic
66C29×#327C2211yescharacteristic
67C29×#327C2211yescharacteristic
68C29×#327C2211yescharacteristic
69C29×#327C2211yescharacteristic
70C29×#327C2211yescharacteristic
71C29×#327C2211yescharacteristic, complemented
72C29×#327C2211yescharacteristic, complemented
73C29×#327C2211yescharacteristic, complemented
74C29×#327C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C2×#41×C29—21no—
77C2×#41×C29C2×C411yescharacteristic
78C22×D4×C29—21no—
79C22×D4×C29C2×C411yescharacteristic
80C23×C4×C29—21no—
81C23×C4×C29C2311yescharacteristic
82C2×M16×C29—21no—
83C22×C8×C29—21no—
84C29×C4⋊Q8—21no—
85C29×C4⋊Q8C2×C411yescharacteristic, complemented
86C29×C4⋊Q8C2×C411yescharacteristic, complemented
87C29×#127C2×C411yescharacteristic, complemented
88C29×#127C2×C411yescharacteristic, complemented
89C29×#126—21no—
90C29×#126—21no—
91C29×#126—21no—
92C29×#126—21no—
93C29×#125—21no—
94C29×#125C2×C411yescharacteristic, complemented
95C29×#125C2×C411yescharacteristic, complemented
96C29×#124—21no—
97C29×#124—21no—
98C29×#124—21no—
99C29×#124—21no—
100C29×#124C2×C411yescharacteristic, complemented
101C29×#124C2×C411yescharacteristic, complemented
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×C22⋊Q8—21no—
112C29×C22⋊Q8—21no—
113C29×C22⋊Q8—21no—
114C29×C22⋊Q8—21no—
115C29×C22⋊Q8C2×C411yescharacteristic
116C29×C22⋊Q8C2311yescharacteristic
117C29×#121—21no—
118C29×#121—21no—
119C29×#121—21no—
120C29×#121—21no—
121C29×#121—21no—
122C29×#121—21no—
123C29×#121—21no—
124C29×#121—21no—
125C29×#121—21no—
126C29×#121—21no—
127C29×#121C2×C411yescharacteristic
128C29×#121C2×C411yescharacteristic
129C29×#121C2×C411yescharacteristic
130C29×#121C2311yescharacteristic
131C29×#121C2311yescharacteristic
132C29×#121C2311yescharacteristic
133C29×#120—21no—
134C29×#120—21no—
135C29×#120—21no—
136C4×Q8×C29C2×C411yescharacteristic, complemented
137C4×Q8×C29C2×C411yescharacteristic, complemented
138C4×D4×C29—21no—
139C4×D4×C29—21no—
140C4×D4×C29—21no—
141C4×D4×C29—21no—
142C4×D4×C29—21no—
143C4×D4×C29—21no—
144C4×D4×C29—21no—
145C4×D4×C29—21no—
146C4×D4×C29—21no—
147C4×D4×C29—21no—
148C4×D4×C29C2×C411yescharacteristic, complemented
149C4×D4×C29C2×C411yescharacteristic, complemented
150C4×D4×C29C2×C411yescharacteristic, complemented
151C4×D4×C29C2×C411yescharacteristic, complemented
152C4×D4×C29C2×C411yescharacteristic, complemented
153C4×D4×C29C2×C411yescharacteristic, complemented
154C29×#117—21no—
155C29×#117—21no—
156C29×#117—21no—
157C29×#117C2×C411yescharacteristic
158C29×#117C2×C411yescharacteristic
159C29×#117C2×C411yescharacteristic
160C29×#117C2×C411yescharacteristic
161C29×#117C2×C411yescharacteristic
162C29×#117D411yescharacteristic
163C29×#117D411yescharacteristic
164C29×#117D411yescharacteristic
165C29×#117D411yescharacteristic
166C2×C4⋊C4×C29—21no—
167C2×C4⋊C4×C29—21no—
168C2×C4⋊C4×C29—21no—
169C2×C4⋊C4×C29C2×C411yescharacteristic
170C2×C4⋊C4×C29D411yescharacteristic
171C2×C4⋊C4×C29D411yescharacteristic
172C2×C22⋊C4×C29—21no—
173C2×C22⋊C4×C29—21no—
174C2×C22⋊C4×C29—21no—
175C2×C22⋊C4×C29—21no—
176C2×C22⋊C4×C29D411yescharacteristic
177C2×C22⋊C4×C29D411yescharacteristic
178C2×C42×C29—21no—
179C2×C42×C29—21no—
180C2×C42×C29C2311yescharacteristic
181C2×C42×C29C2311yescharacteristic
182C29×C4⋊C8—21no—
183C29×C4⋊C8—21no—
184C29×C4⋊C8—21no—
185C29×C4⋊C8—21no—
186C29×C22⋊C8—21no—
187C29×C22⋊C8—21no—
188C29×C22⋊C8C2311yescharacteristic
189C29×C22⋊C8C2311yescharacteristic
190C29×C22⋊C8C2311yescharacteristic
191C29×C22⋊C8C2311yescharacteristic
192C29×#97—21no—
193C29×#97—21no—
194C4×C8×C29—21no—
195C4×C8×C29—21no—
196C29×#95—21no—
197C29×#95—21no—
198C29×#95—21no—
199C29×#95—21no—
200C29×#95—21no—
201C29×#95—21no—
202C29×#95C2311yescharacteristic
203C29×#95C2311yescharacteristic
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29—21no—
207C24×C29C2×D411yescharacteristic
208#41×C29—42no—
209#41×C29—81no—
210#41×C29—81no—
211#41×C29—81no—
212#41×C29—81no—
213C2×Q8×C29—21no—
214C2×Q8×C29—21no—
215C2×Q8×C29C22×C411yescharacteristic
216C2×D4×C29—21no—
217C2×D4×C29—21no—
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—42no—
229C2×D4×C29—81no—
230C2×D4×C29—81no—
231C2×D4×C29C22×C411yescharacteristic
232C2×D4×C29C22×C411yescharacteristic
233C2×D4×C29C22×C411yescharacteristic
234C22×C4×C29—21no—
235C22×C4×C29—21no—
236C22×C4×C29—21no—
237C22×C4×C29—21no—
238C22×C4×C29—21no—
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—42no—
247C22×C4×C29—42no—
248C22×C4×C29—42no—
249C22×C4×C29—81no—
250C22×C4×C29C22×C411yescharacteristic
251C22×C4×C29C22×C411yescharacteristic
252C22×C4×C29C2×D411yescharacteristic
253C22×C4×C29C2×D411yescharacteristic
254C22×C4×C29C2×D411yescharacteristic
255C22×C4×C29C2×D411yescharacteristic
256C22×C4×C29C2×D411yescharacteristic
257C22×C4×C29C2×D411yescharacteristic
258C22×C4×C29C2×D411yescharacteristic
259C22×C4×C29C2411yescharacteristic
260M16×C29—42no—
261C2×C8×C29—21no—
262C2×C8×C29—21no—
263C2×C8×C29—21no—
264C2×C8×C29—21no—
265C2×C8×C29—42no—
266C4⋊C4×C29—21no—
267C4⋊C4×C29—21no—
268C4⋊C4×C29—21no—
269C4⋊C4×C29—21no—
270C4⋊C4×C29—21no—
271C4⋊C4×C29—21no—
272C4⋊C4×C29—21no—
273C4⋊C4×C29—21no—
274C4⋊C4×C29—21no—
275C4⋊C4×C29—21no—
276C4⋊C4×C29—21no—
277C4⋊C4×C29—42no—
278C4⋊C4×C29—81no—
279C4⋊C4×C29C22⋊C411yescharacteristic
280C4⋊C4×C29C22⋊C411yescharacteristic
281C4⋊C4×C29C22⋊C411yescharacteristic
282C4⋊C4×C29C22⋊C411yescharacteristic
283C4⋊C4×C29C22⋊C411yescharacteristic
284C4⋊C4×C29C22⋊C411yescharacteristic
285C4⋊C4×C29C22⋊C411yescharacteristic
286C4⋊C4×C29C22⋊C411yescharacteristic
287C4⋊C4×C29C22×C411yescharacteristic
288C4⋊C4×C29C22×C411yescharacteristic
289C4⋊C4×C29C22×C411yescharacteristic
290C4⋊C4×C29C22×C411yescharacteristic
291C22⋊C4×C29—21no—
292C22⋊C4×C29—21no—
293C22⋊C4×C29—21no—
294C22⋊C4×C29—21no—
295C22⋊C4×C29—21no—
296C22⋊C4×C29—21no—
297C22⋊C4×C29—21no—
298C22⋊C4×C29—21no—
299C22⋊C4×C29—21no—
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—42no—
311C22⋊C4×C29C22⋊C411yescharacteristic
312C22⋊C4×C29C22⋊C411yescharacteristic
313C22⋊C4×C29C22⋊C411yescharacteristic
314C22⋊C4×C29C22⋊C411yescharacteristic
315C22⋊C4×C29C22⋊C411yescharacteristic
316C22⋊C4×C29C22⋊C411yescharacteristic
317C22⋊C4×C29C22⋊C411yescharacteristic
318C22⋊C4×C29C22⋊C411yescharacteristic
319C42×C29—21no—
320C42×C29—21no—
321C42×C29—21no—
322C42×C29—42no—
323C42×C29—81no—
324C42×C29C22×C411yescharacteristic
325C42×C29C22×C411yescharacteristic
326C42×C29C22×C411yescharacteristic
327C42×C29C22×C411yescharacteristic
328C42×C29C2×D411yescharacteristic
329C42×C29C2×D411yescharacteristic
330C42×C29C2×D411yescharacteristic
331C42×C29C2×D411yescharacteristic
332#17604C2911yesmaximal, characteristic, direct product factor, Sylow
333C23×C29—21no—
334C23×C29—21no—
335C23×C29—22no—
336C23×C29—21no—
337C23×C29—21no—
338C23×C29—21no—
339C23×C29—41no—
340C23×C29—42no—
341C23×C29—81no—
342C23×C29—81no—
343C23×C29C2×C22⋊C411yescharacteristic
344C23×C29C2×C22⋊C411yescharacteristic
345C23×C29C22×D411yescharacteristic
346Q8×C29—41no—
347Q8×C29—81no—
348Q8×C29—81no—
349D4×C29—41no—
350D4×C29—41no—
351D4×C29—41no—
352D4×C29—42no—
353D4×C29—41no—
354D4×C29—41no—
355D4×C29—41no—
356D4×C29—41no—
357D4×C29—41no—
358D4×C29—41no—
359D4×C29—42no—
360D4×C29—81no—
361D4×C29—81no—
362D4×C29—81no—
363D4×C29—81no—
364D4×C29—81no—
365D4×C29—81no—
366D4×C29—81no—
367C2×C4×C29—21no—
368C2×C4×C29—21no—
369C2×C4×C29—21no—
370C2×C4×C29—21no—
371C2×C4×C29—22no—
372C2×C4×C29—22no—
373C2×C4×C29—22no—
374C2×C4×C29—21no—
375C2×C4×C29—21no—
376C2×C4×C29—21no—
377C2×C4×C29—21no—
378C2×C4×C29—21no—
379C2×C4×C29—41no—
380C2×C4×C29—41no—
381C2×C4×C29—41no—
382C2×C4×C29—41no—
383C2×C4×C29—41no—
384C2×C4×C29—41no—
385C2×C4×C29—42no—
386C2×C4×C29—41no—
387C2×C4×C29—41no—
388C2×C4×C29—41no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—41no—
393C2×C4×C29—41no—
394C2×C4×C29—41no—
395C2×C4×C29—41no—
396C2×C4×C29—41no—
397C2×C4×C29—81no—
398C2×C4×C29—81no—
399C2×C4×C29—81no—
400C2×C4×C29—81no—
401C2×C4×C29—81no—
402C2×C4×C29—81no—
403C2×C4×C29—81no—
404C2×C4×C29—84no—
405C2×C4×C29C2×C22⋊C411yescharacteristic
406C2×C4×C29C2×C22⋊C411yescharacteristic
407C2×C4×C29C2×C22⋊C411yescharacteristic
408C2×C4×C29C2×C22⋊C411yescharacteristic
409C2×C4×C29C2×C22⋊C411yescharacteristic
410C2×C4×C29C2×C22⋊C411yescharacteristic
411C2×C4×C29C2×C22⋊C411yescharacteristic
412C2×C4×C29C2×C22⋊C411yescharacteristic
413C2×C4×C29C2×C22⋊C411yescharacteristic
414C2×C4×C29C2×C22⋊C411yescharacteristic
415C2×C4×C29C23×C411yescharacteristic
416C2×C4×C29C22×D411yescharacteristic
417C8×C29—41no—
418C8×C29—41no—
419C8×C29—41no—
420C8×C29—41no—
421#3494C2×C2911yescharacteristic
422#2924C2×C2911yescharacteristic, complemented
423#2343C2×C2911yescharacteristic, complemented
424#1521C2×C2911yescharacteristic, complemented
425#1517C2×C2911yescharacteristic, complemented
426#1516C2×C2911yescharacteristic, complemented
427#1514C2×C2911yescharacteristic, complemented
428#1512C2×C2911yescharacteristic, complemented
429#1510C2×C2911yescharacteristic, complemented
430#1509C2×C2911yescharacteristic, complemented
431#1505C2×C2911yescharacteristic, complemented
432#1504C2×C2911yescharacteristic, complemented
433#1502C2×C2911yescharacteristic, complemented
434#1500C2×C2911yescharacteristic, complemented
435C2×#327C2×C2911yescharacteristic, complemented
436C22×C29—21no—
437C22×C29—21no—
438C22×C29—21no—
439C22×C29—21no—
440C22×C29—21no—
441C22×C29—21no—
442C22×C29—21no—
443C22×C29—42no—
444C22×C29—42no—
445C22×C29—41no—
446C22×C29—41no—
447C22×C29—41no—
448C22×C29—41no—
449C22×C29—41no—
450C22×C29—41no—
451C22×C29—41no—
452C22×C29—41no—
453C22×C29—41no—
454C22×C29—162no—
455C22×C29#41012yes—
456C22×C29C22×C22⋊C411yescharacteristic
457C22×C29#57611yescharacteristic
458C22×C29#57711yescharacteristic
459C4×C29—21no—
460C4×C29—21no—
461C4×C29—21no—
462C4×C29—21no—
463C4×C29—21no—
464C4×C29—21no—
465C4×C29—21no—
466C4×C29—21no—
467C4×C29—21no—
468C4×C29—21no—
469C4×C29—21no—
470C4×C29—21no—
471C4×C29—42no—
472C4×C29—41no—
473C4×C29—41no—
474C4×C29—41no—
475C4×C29—41no—
476C4×C29—41no—
477C4×C29—81no—
478C4×C29—81no—
479C4×C29—81no—
480#555—21no—
481#553—21no—
482#553—21no—
483#551—21no—
484#551—21no—
485#547—21no—
486#546—21no—
487#546—21no—
488#544C4×C2911yescharacteristic, complemented
489#542C4×C2911yescharacteristic, complemented
490#542C4×C2911yescharacteristic, complemented
491#540C4×C2911yescharacteristic, complemented
492#540C4×C2911yescharacteristic, complemented
493#535C4×C2911yescharacteristic, complemented
494#532C22×C2911yescharacteristic
495#532C22×C2911yescharacteristic
496#529C22×C2911yescharacteristic
497#529C22×C2911yescharacteristic
498#525C22×C2911yescharacteristic
499C2×#121C22×C2911yescharacteristic
500#520C4×C2911yescharacteristic, complemented
501#518C4×C2911yescharacteristic, complemented
502C2×#117C22×C2911yescharacteristic
503#433—21no—
504#433—21no—
505#432C22×C2911yescharacteristic, complemented
506#432C22×C2911yescharacteristic, complemented
507#431C22×C2911yescharacteristic, complemented
508#431C22×C2911yescharacteristic, complemented
509#424—21no—
510#407C22×C2911yescharacteristic
511C2×C22⋊C8C22×C2911yescharacteristic
512#405—21no—
513#387—21no—
514#387—21no—
515#385—21no—
516#383C22×C2911yescharacteristic, complemented
517#382C22×C2911yescharacteristic, complemented
518#381C22×C2911yescharacteristic
519C4×C4⋊C4C22×C2911yescharacteristic, complemented
520C4×C22⋊C4—21no—
521#376C22×C2911yescharacteristic, complemented
522C2×#95C22×C2911yescharacteristic
523#328C22×C2911yescharacteristic, complemented
524#328C22×C2911yescharacteristic, complemented
525#328C22×C2911yescharacteristic, complemented
526#328C22×C2911yescharacteristic, complemented
527#327C22×C2911yescharacteristic
528#327C22×C2911yescharacteristic
529#327C22×C2911yescharacteristic
530#327C22×C2911yescharacteristic
531#327C22×C2911yescharacteristic
532#327C22×C2911yescharacteristic
533#327C22×C2911yescharacteristic
534#327C22×C2911yescharacteristic
535#327C22×C2911yescharacteristic, complemented
536#327C22×C2911yescharacteristic, complemented
537#327C22×C2911yescharacteristic, complemented
538#327C22×C2911yescharacteristic, complemented
539C2×C29—21no—
540C2×C29—21no—
541C2×C29—22no—
542C2×C29—41no—
543C2×C29—81no—
544C2×C29—81no—
545C2×C29—81no—
546C2×C29C2×#41011yescharacteristic
547C2×C29#289711yescharacteristic
548C2×C29#290111yescharacteristic
549C2×#41—21no—
550C2×#41—21no—
551C2×#41C2×C4×C2911yescharacteristic
552C22×D4—21no—
553C22×D4C2×C4×C2911yescharacteristic
554C23×C4—21no—
555C23×C4C23×C2911yescharacteristic
556C2×M16—21no—
557C22×C8—21no—
558C4⋊Q8—21no—
559C4⋊Q8C2×C4×C2911yescharacteristic, complemented
560C4⋊Q8C2×C4×C2911yescharacteristic, complemented
561#127C2×C4×C2911yescharacteristic, complemented
562#127C2×C4×C2911yescharacteristic, complemented
563#126—21no—
564#126—21no—
565#126—21no—
566#126—21no—
567#125—21no—
568#125C2×C4×C2911yescharacteristic, complemented
569#125C2×C4×C2911yescharacteristic, complemented
570#124—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#124C2×C4×C2911yescharacteristic, complemented
575#124C2×C4×C2911yescharacteristic, complemented
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8C2×C4×C2911yescharacteristic
590C22⋊Q8C23×C2911yescharacteristic
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121C2×C4×C2911yescharacteristic
602#121C2×C4×C2911yescharacteristic
603#121C2×C4×C2911yescharacteristic
604#121C23×C2911yescharacteristic
605#121C23×C2911yescharacteristic
606#121C23×C2911yescharacteristic
607#120—21no—
608#120—21no—
609#120—21no—
610C4×Q8C2×C4×C2911yescharacteristic, complemented
611C4×Q8C2×C4×C2911yescharacteristic, complemented
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4C2×C4×C2911yescharacteristic, complemented
623C4×D4C2×C4×C2911yescharacteristic, complemented
624C4×D4C2×C4×C2911yescharacteristic, complemented
625C4×D4C2×C4×C2911yescharacteristic, complemented
626C4×D4C2×C4×C2911yescharacteristic, complemented
627C4×D4C2×C4×C2911yescharacteristic, complemented
628#117—21no—
629#117—21no—
630#117—21no—
631#117C2×C4×C2911yescharacteristic
632#117C2×C4×C2911yescharacteristic
633#117C2×C4×C2911yescharacteristic
634#117C2×C4×C2911yescharacteristic
635#117C2×C4×C2911yescharacteristic
636#117D4×C2911yescharacteristic
637#117D4×C2911yescharacteristic
638#117D4×C2911yescharacteristic
639#117D4×C2911yescharacteristic
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4C2×C4×C2911yescharacteristic
644C2×C4⋊C4D4×C2911yescharacteristic
645C2×C4⋊C4D4×C2911yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4D4×C2911yescharacteristic
651C2×C22⋊C4D4×C2911yescharacteristic
652C2×C42—21no—
653C2×C42—21no—
654C2×C42C23×C2911yescharacteristic
655C2×C42C23×C2911yescharacteristic
656C4⋊C8—21no—
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8C23×C2911yescharacteristic
663C22⋊C8C23×C2911yescharacteristic
664C22⋊C8C23×C2911yescharacteristic
665C22⋊C8C23×C2911yescharacteristic
666#97—21no—
667#97—21no—
668C4×C8—21no—
669C4×C8—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95C23×C2911yescharacteristic
677#95C23×C2911yescharacteristic
678#95C23×C2911yescharacteristic
679#95C23×C2911yescharacteristic
680C29#1760411yescharacteristic, direct product factor, Sylow
681C24—21no—
682C24C2×D4×C2911yescharacteristic
683#41—42no—
684#41—81no—
685#41—81no—
686#41—81no—
687#41—81no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8C22×C4×C2911yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4C22×C4×C2911yescharacteristic
707C2×D4C22×C4×C2911yescharacteristic
708C2×D4C22×C4×C2911yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—81no—
725C22×C4C22×C4×C2911yescharacteristic
726C22×C4C22×C4×C2911yescharacteristic
727C22×C4C2×D4×C2911yescharacteristic
728C22×C4C2×D4×C2911yescharacteristic
729C22×C4C2×D4×C2911yescharacteristic
730C22×C4C2×D4×C2911yescharacteristic
731C22×C4C2×D4×C2911yescharacteristic
732C22×C4C2×D4×C2911yescharacteristic
733C22×C4C2×D4×C2911yescharacteristic
734C22×C4C24×C2911yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—42no—
753C4⋊C4—81no—
754C4⋊C4C22⋊C4×C2911yescharacteristic
755C4⋊C4C22⋊C4×C2911yescharacteristic
756C4⋊C4C22⋊C4×C2911yescharacteristic
757C4⋊C4C22⋊C4×C2911yescharacteristic
758C4⋊C4C22⋊C4×C2911yescharacteristic
759C4⋊C4C22⋊C4×C2911yescharacteristic
760C4⋊C4C22⋊C4×C2911yescharacteristic
761C4⋊C4C22⋊C4×C2911yescharacteristic
762C4⋊C4C22×C4×C2911yescharacteristic
763C4⋊C4C22×C4×C2911yescharacteristic
764C4⋊C4C22×C4×C2911yescharacteristic
765C4⋊C4C22×C4×C2911yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—42no—
786C22⋊C4C22⋊C4×C2911yescharacteristic
787C22⋊C4C22⋊C4×C2911yescharacteristic
788C22⋊C4C22⋊C4×C2911yescharacteristic
789C22⋊C4C22⋊C4×C2911yescharacteristic
790C22⋊C4C22⋊C4×C2911yescharacteristic
791C22⋊C4C22⋊C4×C2911yescharacteristic
792C22⋊C4C22⋊C4×C2911yescharacteristic
793C22⋊C4C22⋊C4×C2911yescharacteristic
794C42—21no—
795C42—21no—
796C42—21no—
797C42—42no—
798C42—81no—
799C42C22×C4×C2911yescharacteristic
800C42C22×C4×C2911yescharacteristic
801C42C22×C4×C2911yescharacteristic
802C42C22×C4×C2911yescharacteristic
803C42C2×D4×C2911yescharacteristic
804C42C2×D4×C2911yescharacteristic
805C42C2×D4×C2911yescharacteristic
806C42C2×D4×C2911yescharacteristic
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23C2×C22⋊C4×C2911yescharacteristic
818C23C2×C22⋊C4×C2911yescharacteristic
819C23C22×D4×C2911yescharacteristic
820Q8—41no—
821Q8—81no—
822Q8—81no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—42no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—81no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—84no—
879C2×C4C2×C22⋊C4×C2911yescharacteristic
880C2×C4C2×C22⋊C4×C2911yescharacteristic
881C2×C4C2×C22⋊C4×C2911yescharacteristic
882C2×C4C2×C22⋊C4×C2911yescharacteristic
883C2×C4C2×C22⋊C4×C2911yescharacteristic
884C2×C4C2×C22⋊C4×C2911yescharacteristic
885C2×C4C2×C22⋊C4×C2911yescharacteristic
886C2×C4C2×C22⋊C4×C2911yescharacteristic
887C2×C4C2×C22⋊C4×C2911yescharacteristic
888C2×C4C2×C22⋊C4×C2911yescharacteristic
889C2×C4C23×C4×C2911yescharacteristic
890C2×C4C22×D4×C2911yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—162no—
914C22C29×#41012yes—
915C22C22×C22⋊C4×C2911yescharacteristic
916C22C29×#57611yescharacteristic
917C22C29×#57711yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2C2×C29×#41011yescharacteristic
947C2C29×#289711yescharacteristic
948C2C29×#290111yescharacteristic
subgroupG/H
center, socleC22×C29C22×C22⋊C4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3494C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2924C2semidirect
3. C29×#2343C2semidirect
4. C29×#1521C2semidirect
5. C29×#1517C2semidirect
6. C29×#1516C2semidirect
7. C29×#1514C2semidirect
8. C29×#1512C2semidirect
9. C29×#1510C2semidirect
10. C29×#1509C2semidirect
11. C29×#1505C2semidirect
12. C29×#1504C2semidirect
13. C29×#1502C2semidirect
14. C29×#1500C2semidirect
15. C2×C29×#327C2semidirect
24. C29×#544C4semidirect
25. C29×#542C4semidirect
26. C29×#542C4semidirect
27. C29×#540C4semidirect
28. C29×#540C4semidirect
29. C29×#535C4semidirect
36. C29×#520C4semidirect
37. C29×#518C4semidirect
41. C29×#432C22semidirect
42. C29×#432C22semidirect
43. C29×#431C22semidirect
44. C29×#431C22semidirect
52. C29×#383C22semidirect
53. C29×#382C22semidirect
55. C4×C4⋊C4×C29C22semidirect
57. C29×#376C22semidirect
59. C29×#328C22semidirect
60. C29×#328C22semidirect
61. C29×#328C22semidirect
62. C29×#328C22semidirect
71. C29×#327C22semidirect
72. C29×#327C22semidirect
73. C29×#327C22semidirect
74. C29×#327C22semidirect
85. C29×C4⋊Q8C2×C4semidirect
86. C29×C4⋊Q8C2×C4semidirect
87. C29×#127C2×C4semidirect
88. C29×#127C2×C4semidirect
94. C29×#125C2×C4semidirect
95. C29×#125C2×C4semidirect
100. C29×#124C2×C4semidirect
101. C29×#124C2×C4semidirect
136. C4×Q8×C29C2×C4semidirect
137. C4×Q8×C29C2×C4semidirect
148. C4×D4×C29C2×C4semidirect
149. C4×D4×C29C2×C4semidirect
150. C4×D4×C29C2×C4semidirect
151. C4×D4×C29C2×C4semidirect
152. C4×D4×C29C2×C4semidirect
153. C4×D4×C29C2×C4semidirect
332. #17604C29direct (N × H)
422. #2924C2×C29semidirect
423. #2343C2×C29semidirect
424. #1521C2×C29semidirect
425. #1517C2×C29semidirect
426. #1516C2×C29semidirect
427. #1514C2×C29semidirect
428. #1512C2×C29semidirect
429. #1510C2×C29semidirect
430. #1509C2×C29semidirect
431. #1505C2×C29semidirect
432. #1504C2×C29semidirect
433. #1502C2×C29semidirect
434. #1500C2×C29semidirect
435. C2×#327C2×C29semidirect
488. #544C4×C29semidirect
489. #542C4×C29semidirect
490. #542C4×C29semidirect
491. #540C4×C29semidirect
492. #540C4×C29semidirect
493. #535C4×C29semidirect
500. #520C4×C29semidirect
501. #518C4×C29semidirect
505. #432C22×C29semidirect
506. #432C22×C29semidirect
507. #431C22×C29semidirect
508. #431C22×C29semidirect
516. #383C22×C29semidirect
517. #382C22×C29semidirect
519. C4×C4⋊C4C22×C29semidirect
521. #376C22×C29semidirect
523. #328C22×C29semidirect
524. #328C22×C29semidirect
525. #328C22×C29semidirect
526. #328C22×C29semidirect
535. #327C22×C29semidirect
536. #327C22×C29semidirect
537. #327C22×C29semidirect
538. #327C22×C29semidirect
559. C4⋊Q8C2×C4×C29semidirect
560. C4⋊Q8C2×C4×C29semidirect
561. #127C2×C4×C29semidirect
562. #127C2×C4×C29semidirect
568. #125C2×C4×C29semidirect
569. #125C2×C4×C29semidirect
574. #124C2×C4×C29semidirect
575. #124C2×C4×C29semidirect
610. C4×Q8C2×C4×C29semidirect
611. C4×Q8C2×C4×C29semidirect
622. C4×D4C2×C4×C29semidirect
623. C4×D4C2×C4×C29semidirect
624. C4×D4C2×C4×C29semidirect
625. C4×D4C2×C4×C29semidirect
626. C4×D4C2×C4×C29semidirect
627. C4×D4C2×C4×C29semidirect
680. C29#17604direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34942
C29×#29242
C29×#23432
C29×#15212
C29×#15172
C29×#15162
C29×#15142
C29×#15122
C29×#15102
C29×#15092
C29×#15052
C29×#15042
C29×#15022
C29×#15002
C2×C29×#3272
#1760429