Finite Group Databasebeta

← C29×#21772 #20316672

Subgroups — C29×#21772 #20316672

Order 7424.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#537C211yesmaximal, characteristic
2C2×C29×#408C211yesmaximal, characteristic, complemented
3C29×#2311C211yesmaximal, characteristic, complemented
4C29×#1895C211yesmaximal, characteristic, complemented
5C29×#1894C211yesmaximal, characteristic, complemented
6C29×#1893C211yesmaximal, characteristic, complemented
7C29×#1892C211yesmaximal, characteristic, complemented
8C29×#1875C211yesmaximal, characteristic, complemented
9C29×#1874C211yesmaximal, characteristic, complemented
10C29×#1873C211yesmaximal, characteristic, complemented
11C29×#1872C211yesmaximal, characteristic, complemented
12C29×#1824C211yesmaximal, characteristic, complemented
13C29×#1823C211yesmaximal, characteristic, complemented
14C29×#1788C211yesmaximal, characteristic, complemented
15C29×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C22×#41×C29C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic
19C23×C8×C29C2211yescharacteristic
20C29×#537—24no—
21C29×#537C418yescomplemented
22C2×C29×C22⋊Q8—21no—
23C2×C29×C22⋊Q8C2211yescharacteristic
24C2×C29×C22⋊Q8C2211yescharacteristic
25C2×C29×#121—21no—
26C2×C29×#121—21no—
27C2×C29×#121—21no—
28C2×C29×#121C2211yescharacteristic
29C2×C29×#121C2211yescharacteristic
30C2×C29×#117C2211yescharacteristic
31C22×C4⋊C4×C29C2211yescharacteristic
32C22×C4⋊C4×C29C2211yescharacteristic
33C2×C29×#103C2211yescharacteristic
34C2×C29×#103C2211yescharacteristic
35C2×C29×#103C2211yescharacteristic
36C2×C29×#103C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×#102C2211yescharacteristic
39C2×C29×#102C2211yescharacteristic
40C2×C29×#102C2211yescharacteristic
41C29×#408—24no—
42C2×C29×C22⋊C8C2211yescharacteristic
43C2×C29×C22⋊C8C2211yescharacteristic
44C2×C29×C22⋊C8C2211yescharacteristic
45C2×C29×C22⋊C8C2211yescharacteristic
46C29×#391—21no—
47C29×#390—21no—
48C29×#386—21no—
49C29×#386—21no—
50C29×#380C2211yescharacteristic
51C29×#380C2211yescharacteristic
52C29×#380C2211yescharacteristic
53C29×#380C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C29×#340C2211yescharacteristic
62C2×#41×C29—22no—
63C2×#41×C29—41no—
64C2×#41×C29—41no—
65C2×#41×C29—41no—
66C2×#41×C29—41no—
67C2×#41×C29—41no—
68C2×#41×C29—41no—
69C2×#41×C29—41no—
70C2×#41×C29—41no—
71C2×#41×C29C2×C414yes—
72C2×#41×C29C2×C414yescomplemented
73C2×#41×C29D414yes—
74C22×Q8×C29D411yescharacteristic
75C22×Q8×C29C2311yescharacteristic
76C22×D4×C29—21no—
77C22×D4×C29—21no—
78C22×D4×C29—21no—
79C22×D4×C29D411yescharacteristic
80C22×D4×C29D411yescharacteristic
81C22×D4×C29D411yescharacteristic
82C22×D4×C29C2311yescharacteristic
83C23×C4×C29—21no—
84C23×C4×C29—21no—
85C23×C4×C29—21no—
86C23×C4×C29C2311yescharacteristic
87C23×C4×C29C2311yescharacteristic
88C23×C4×C29C2311yescharacteristic
89C2×M16×C29—22no—
90C2×M16×C29—41no—
91C2×M16×C29—41no—
92C22×C8×C29—22no—
93C22×C8×C29—41no—
94C22×C8×C29—41no—
95C22×C8×C29C2311yescharacteristic
96C22×C8×C29C2311yescharacteristic
97C22×C8×C29C2311yescharacteristic
98C22×C8×C29C2311yescharacteristic
99C29×C22⋊Q8—28no—
100C29×C22⋊Q8—22no—
101C29×C22⋊Q8—22no—
102C29×C22⋊Q8C2×C414yes—
103C29×C22⋊Q8C2×C414yescomplemented
104C29×#121—28no—
105C29×#121—28no—
106C29×#121—28no—
107C29×#121—22no—
108C29×#121—22no—
109C29×#121C2×C414yes—
110C29×#121C2×C414yescomplemented
111C29×#117—41no—
112C29×#117—41no—
113C2×C4⋊C4×C29—21no—
114C2×C4⋊C4×C29—22no—
115C2×C4⋊C4×C29—21no—
116C2×C4⋊C4×C29—21no—
117C2×C4⋊C4×C29—21no—
118C2×C4⋊C4×C29—41no—
119C2×C4⋊C4×C29—41no—
120C2×C4⋊C4×C29C2×C414yescomplemented
121C2×C4⋊C4×C29C2311yescharacteristic
122C2×C4⋊C4×C29C2311yescharacteristic
123C2×C4⋊C4×C29C2311yescharacteristic
124C2×C4⋊C4×C29C2311yescharacteristic
125C2×C4⋊C4×C29C2311yescharacteristic
126C2×C4⋊C4×C29C2311yescharacteristic
127C2×C22⋊C4×C29—21no—
128C2×C22⋊C4×C29—21no—
129C2×C22⋊C4×C29—21no—
130C2×C22⋊C4×C29—21no—
131C2×C22⋊C4×C29—21no—
132C2×C22⋊C4×C29—21no—
133C2×C22⋊C4×C29—21no—
134C2×C22⋊C4×C29—21no—
135C2×C22⋊C4×C29—21no—
136C2×C42×C29—21no—
137C29×#103—41no—
138C29×#103—41no—
139C29×#103—41no—
140C29×#103—41no—
141C29×#102—41no—
142C29×#102—41no—
143C29×#102—41no—
144C29×#102—41no—
145C29×C22⋊C8—22no—
146C29×C22⋊C8—22no—
147C29×C22⋊C8—22no—
148C29×C22⋊C8—22no—
149C29×#95—21no—
150C29×#95—21no—
151C29×#95—21no—
152C29×#95—21no—
153C24×C29—21no—
154C24×C29C2×D411yescharacteristic
155C24×C29C2×D411yescharacteristic
156C24×C29C2×D411yescharacteristic
157#41×C29—44no—
158#41×C29—44no—
159#41×C29—44no—
160#41×C29—44no—
161#41×C29—44no—
162#41×C29—44no—
163#41×C29—44no—
164#41×C29—44no—
165C2×Q8×C29—21no—
166C2×Q8×C29—21no—
167C2×Q8×C29—21no—
168C2×Q8×C29—21no—
169C2×Q8×C29—21no—
170C2×Q8×C29—41no—
171C2×Q8×C29—41no—
172C2×Q8×C29C22⋊C414yes—
173C2×Q8×C29C22×C412yes—
174C2×D4×C29—24no—
175C2×D4×C29—24no—
176C2×D4×C29—24no—
177C2×D4×C29—21no—
178C2×D4×C29—21no—
179C2×D4×C29—21no—
180C2×D4×C29—21no—
181C2×D4×C29—21no—
182C2×D4×C29—41no—
183C2×D4×C29—41no—
184C2×D4×C29—41no—
185C2×D4×C29—41no—
186C2×D4×C29—41no—
187C2×D4×C29—41no—
188C2×D4×C29—42no—
189C2×D4×C29—42no—
190C2×D4×C29—81no—
191C2×D4×C29—81no—
192C2×D4×C29—81no—
193C2×D4×C29—81no—
194C2×D4×C29C22⋊C414yes—
195C2×D4×C29C22⋊C414yes—
196C2×D4×C29C22⋊C414yes—
197C2×D4×C29C22×C412yes—
198C22×C4×C29—21no—
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—21no—
206C22×C4×C29—21no—
207C22×C4×C29—21no—
208C22×C4×C29—21no—
209C22×C4×C29—21no—
210C22×C4×C29—21no—
211C22×C4×C29—21no—
212C22×C4×C29—21no—
213C22×C4×C29—24no—
214C22×C4×C29—24no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—42no—
220C22×C4×C29—42no—
221C22×C4×C29—42no—
222C22×C4×C29—81no—
223C22×C4×C29—81no—
224C22×C4×C29—81no—
225C22×C4×C29—81no—
226C22×C4×C29C22×C412yes—
227C22×C4×C29C22×C412yes—
228C22×C4×C29C22×C412yes—
229C22×C4×C29C2×D411yescharacteristic
230C22×C4×C29C2×D411yescharacteristic
231C22×C4×C29C2×D411yescharacteristic
232C22×C4×C29C2×D412yes—
233C22×C4×C29C2×D412yes—
234C22×C4×C29C2×D412yes—
235C22×C4×C29C2411yescharacteristic
236M16×C29—44no—
237C2×C8×C29—21no—
238C2×C8×C29—21no—
239C2×C8×C29—21no—
240C2×C8×C29—21no—
241C2×C8×C29—21no—
242C2×C8×C29—21no—
243C2×C8×C29—21no—
244C2×C8×C29—21no—
245C2×C8×C29—21no—
246C2×C8×C29—21no—
247C2×C8×C29—21no—
248C2×C8×C29—21no—
249C2×C8×C29—44no—
250C4⋊C4×C29—24no—
251C4⋊C4×C29—24no—
252C4⋊C4×C29—24no—
253C4⋊C4×C29—21no—
254C4⋊C4×C29—21no—
255C4⋊C4×C29—21no—
256C4⋊C4×C29—21no—
257C4⋊C4×C29—21no—
258C4⋊C4×C29—21no—
259C4⋊C4×C29—21no—
260C4⋊C4×C29—21no—
261C4⋊C4×C29—21no—
262C4⋊C4×C29—21no—
263C4⋊C4×C29—42no—
264C4⋊C4×C29C22×C412yes—
265C4⋊C4×C29C22×C412yes—
266C22⋊C4×C29—24no—
267C22⋊C4×C29—24no—
268C22⋊C4×C29—24no—
269C22⋊C4×C29—24no—
270C22⋊C4×C29—42no—
271C22⋊C4×C29—81no—
272C22⋊C4×C29—81no—
273C22⋊C4×C29—81no—
274C22⋊C4×C29—81no—
275C42×C29—42no—
276#21772C2911yesmaximal, characteristic, direct product factor, Sylow
277C23×C29—21no—
278C23×C29—21no—
279C23×C29—21no—
280C23×C29—21no—
281C23×C29—21no—
282C23×C29—21no—
283C23×C29—21no—
284C23×C29—21no—
285C23×C29—21no—
286C23×C29—21no—
287C23×C29—21no—
288C23×C29—21no—
289C23×C29—21no—
290C23×C29—21no—
291C23×C29—21no—
292C23×C29—21no—
293C23×C29—21no—
294C23×C29—21no—
295C23×C29—22no—
296C23×C29—41no—
297C23×C29—41no—
298C23×C29—41no—
299C23×C29—41no—
300C23×C29—41no—
301C23×C29—41no—
302C23×C29C2×C22⋊C412yes—
303C23×C29C2×C22⋊C412yes—
304C23×C29C2×C22⋊C412yes—
305C23×C29C22×D411yescharacteristic
306Q8×C29—22no—
307Q8×C29—22no—
308Q8×C29—44no—
309Q8×C29—41no—
310Q8×C29—41no—
311D4×C29—22no—
312D4×C29—22no—
313D4×C29—44no—
314D4×C29—44no—
315D4×C29—44no—
316D4×C29—48no—
317D4×C29—41no—
318D4×C29—41no—
319D4×C29—84no—
320D4×C29—84no—
321C2×C4×C29—21no—
322C2×C4×C29—21no—
323C2×C4×C29—21no—
324C2×C4×C29—21no—
325C2×C4×C29—21no—
326C2×C4×C29—21no—
327C2×C4×C29—22no—
328C2×C4×C29—22no—
329C2×C4×C29—22no—
330C2×C4×C29—22no—
331C2×C4×C29—22no—
332C2×C4×C29—22no—
333C2×C4×C29—22no—
334C2×C4×C29—22no—
335C2×C4×C29—22no—
336C2×C4×C29—22no—
337C2×C4×C29—22no—
338C2×C4×C29—22no—
339C2×C4×C29—22no—
340C2×C4×C29—22no—
341C2×C4×C29—22no—
342C2×C4×C29—48no—
343C2×C4×C29—41no—
344C2×C4×C29—41no—
345C2×C4×C29—41no—
346C2×C4×C29—41no—
347C2×C4×C29—41no—
348C2×C4×C29—41no—
349C2×C4×C29—41no—
350C2×C4×C29—41no—
351C2×C4×C29—41no—
352C2×C4×C29—41no—
353C2×C4×C29—41no—
354C2×C4×C29—41no—
355C2×C4×C29—41no—
356C2×C4×C29—41no—
357C2×C4×C29—41no—
358C2×C4×C29—41no—
359C2×C4×C29—41no—
360C2×C4×C29—41no—
361C2×C4×C29—84no—
362C2×C4×C29—84no—
363C2×C4×C29C2×C22⋊C412yes—
364C2×C4×C29C2×C22⋊C412yes—
365C2×C4×C29C2×C22⋊C412yes—
366C2×C4×C29C23×C411yescharacteristic
367C2×C4×C29C22×D411yescharacteristic
368C2×C4×C29H(5,𝔽2)11yescharacteristic
369C2×C4×C29H(5,𝔽2)11yescharacteristic
370C2×C4×C29H(5,𝔽2)11yescharacteristic
371C2×C4×C29H(5,𝔽2)11yescharacteristic
372C8×C29—41no—
373C8×C29—41no—
374C8×C29—41no—
375C8×C29—41no—
376C2×#537C2×C2911yescharacteristic
377C2×#408C2×C2911yescharacteristic, complemented
378#2311C2×C2911yescharacteristic, complemented
379#1895C2×C2911yescharacteristic, complemented
380#1894C2×C2911yescharacteristic, complemented
381#1893C2×C2911yescharacteristic, complemented
382#1892C2×C2911yescharacteristic, complemented
383#1875C2×C2911yescharacteristic, complemented
384#1874C2×C2911yescharacteristic, complemented
385#1873C2×C2911yescharacteristic, complemented
386#1872C2×C2911yescharacteristic, complemented
387#1824C2×C2911yescharacteristic, complemented
388#1823C2×C2911yescharacteristic, complemented
389#1788C2×C2911yescharacteristic, complemented
390#1788C2×C2911yescharacteristic, complemented
391C22×C29—22no—
392C22×C29—22no—
393C22×C29—22no—
394C22×C29—22no—
395C22×C29—22no—
396C22×C29—22no—
397C22×C29—22no—
398C22×C29—22no—
399C22×C29—22no—
400C22×C29—41no—
401C22×C29—41no—
402C22×C29—41no—
403C22×C29—41no—
404C22×C29—41no—
405C22×C29—41no—
406C22×C29—41no—
407C22×C29—41no—
408C22×C29—41no—
409C22×C29—41no—
410C22×C29—41no—
411C22×C29—41no—
412C22×C29—42no—
413C22×C29—42no—
414C22×C29—42no—
415C22×C29—81no—
416C22×C29—81no—
417C22×C29—81no—
418C22×C29—81no—
419C22×C29C22×C22⋊C411yescharacteristic
420C22×C29#53411yescharacteristic
421C22×C29#53411yescharacteristic
422C22×C29#57611yescharacteristic
423C22×C29#57711yescharacteristic
424C22×C29#57711yescharacteristic
425C22×C29#57811yescharacteristic
426C4×C29—22no—
427C4×C29—22no—
428C4×C29—22no—
429C4×C29—42no—
430C4×C29—42no—
431C4×C29—42no—
432C4×C29—81no—
433C4×C29—81no—
434C4×C29—81no—
435C4×C29—81no—
436C4×C29#51811yescharacteristic
437C4×C29#51811yescharacteristic
438C4×C29#53411yescharacteristic
439C4×C29#53411yescharacteristic
440C22×#41C22×C2911yescharacteristic
441C22×#41C22×C2911yescharacteristic
442C22×M16C22×C2911yescharacteristic
443C23×C8C22×C2911yescharacteristic
444#537—24no—
445#537C4×C2918yescomplemented
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8C22×C2911yescharacteristic
448C2×C22⋊Q8C22×C2911yescharacteristic
449C2×#121—21no—
450C2×#121—21no—
451C2×#121—21no—
452C2×#121C22×C2911yescharacteristic
453C2×#121C22×C2911yescharacteristic
454C2×#117C22×C2911yescharacteristic
455C22×C4⋊C4C22×C2911yescharacteristic
456C22×C4⋊C4C22×C2911yescharacteristic
457C2×#103C22×C2911yescharacteristic
458C2×#103C22×C2911yescharacteristic
459C2×#103C22×C2911yescharacteristic
460C2×#103C22×C2911yescharacteristic
461C2×#102C22×C2911yescharacteristic
462C2×#102C22×C2911yescharacteristic
463C2×#102C22×C2911yescharacteristic
464C2×#102C22×C2911yescharacteristic
465#408—24no—
466C2×C22⋊C8C22×C2911yescharacteristic
467C2×C22⋊C8C22×C2911yescharacteristic
468C2×C22⋊C8C22×C2911yescharacteristic
469C2×C22⋊C8C22×C2911yescharacteristic
470#391—21no—
471#390—21no—
472#386—21no—
473#386—21no—
474#380C22×C2911yescharacteristic
475#380C22×C2911yescharacteristic
476#380C22×C2911yescharacteristic
477#380C22×C2911yescharacteristic
478#340C22×C2911yescharacteristic
479#340C22×C2911yescharacteristic
480#340C22×C2911yescharacteristic
481#340C22×C2911yescharacteristic
482#340C22×C2911yescharacteristic
483#340C22×C2911yescharacteristic
484#340C22×C2911yescharacteristic
485#340C22×C2911yescharacteristic
486C2×C29—42no—
487C2×C29—42no—
488C2×C29—42no—
489C2×C29—82no—
490C2×C29#230811yescharacteristic
491C2×C29#289711yescharacteristic
492C2×C29#289811yescharacteristic
493C2×C29#319811yescharacteristic
494C2×C29#320111yescharacteristic
495C2×C29#320311yescharacteristic
496C2×C29#320411yescharacteristic
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C2914yes—
507C2×#41C2×C4×C2914yescomplemented
508C2×#41D4×C2914yes—
509C22×Q8D4×C2911yescharacteristic
510C22×Q8C23×C2911yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C2911yescharacteristic
515C22×D4D4×C2911yescharacteristic
516C22×D4D4×C2911yescharacteristic
517C22×D4C23×C2911yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C2911yescharacteristic
522C23×C4C23×C2911yescharacteristic
523C23×C4C23×C2911yescharacteristic
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8C23×C2911yescharacteristic
531C22×C8C23×C2911yescharacteristic
532C22×C8C23×C2911yescharacteristic
533C22×C8C23×C2911yescharacteristic
534C22⋊Q8—28no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8C2×C4×C2914yes—
538C22⋊Q8C2×C4×C2914yescomplemented
539#121—28no—
540#121—28no—
541#121—28no—
542#121—22no—
543#121—22no—
544#121C2×C4×C2914yes—
545#121C2×C4×C2914yescomplemented
546#117—41no—
547#117—41no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4C2×C4×C2914yescomplemented
556C2×C4⋊C4C23×C2911yescharacteristic
557C2×C4⋊C4C23×C2911yescharacteristic
558C2×C4⋊C4C23×C2911yescharacteristic
559C2×C4⋊C4C23×C2911yescharacteristic
560C2×C4⋊C4C23×C2911yescharacteristic
561C2×C4⋊C4C23×C2911yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C42—21no—
572#103—41no—
573#103—41no—
574#103—41no—
575#103—41no—
576#102—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588C29#2177211yescharacteristic, direct product factor, Sylow
589C24—21no—
590C24C2×D4×C2911yescharacteristic
591C24C2×D4×C2911yescharacteristic
592C24C2×D4×C2911yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C2914yes—
609C2×Q8C22×C4×C2912yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C2914yes—
631C2×D4C22⋊C4×C2914yes—
632C2×D4C22⋊C4×C2914yes—
633C2×D4C22×C4×C2912yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C2912yes—
663C22×C4C22×C4×C2912yes—
664C22×C4C22×C4×C2912yes—
665C22×C4C2×D4×C2911yescharacteristic
666C22×C4C2×D4×C2911yescharacteristic
667C22×C4C2×D4×C2911yescharacteristic
668C22×C4C2×D4×C2912yes—
669C22×C4C2×D4×C2912yes—
670C22×C4C2×D4×C2912yes—
671C22×C4C24×C2911yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C2912yes—
701C4⋊C4C22×C4×C2912yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C2912yes—
738C23C2×C22⋊C4×C2912yes—
739C23C2×C22⋊C4×C2912yes—
740C23C22×D4×C2911yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C2912yes—
799C2×C4C2×C22⋊C4×C2912yes—
800C2×C4C2×C22⋊C4×C2912yes—
801C2×C4C23×C4×C2911yescharacteristic
802C2×C4C22×D4×C2911yescharacteristic
803C2×C4C29×H(5,𝔽2)11yescharacteristic
804C2×C4C29×H(5,𝔽2)11yescharacteristic
805C2×C4C29×H(5,𝔽2)11yescharacteristic
806C2×C4C29×H(5,𝔽2)11yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C2911yescharacteristic
840C22C29×#53411yescharacteristic
841C22C29×#53411yescharacteristic
842C22C29×#57611yescharacteristic
843C22C29×#57711yescharacteristic
844C22C29×#57711yescharacteristic
845C22C29×#57811yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C29×#51811yescharacteristic
857C4C29×#51811yescharacteristic
858C4C29×#53411yescharacteristic
859C4C29×#53411yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2C29×#230811yescharacteristic
865C2C29×#289711yescharacteristic
866C2C29×#289811yescharacteristic
867C2C29×#319811yescharacteristic
868C2C29×#320111yescharacteristic
869C2C29×#320311yescharacteristic
870C2C29×#320411yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#537C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C22×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#408C2semidirect
3. C29×#2311C2semidirect
4. C29×#1895C2semidirect
5. C29×#1894C2semidirect
6. C29×#1893C2semidirect
7. C29×#1892C2semidirect
8. C29×#1875C2semidirect
9. C29×#1874C2semidirect
10. C29×#1873C2semidirect
11. C29×#1872C2semidirect
12. C29×#1824C2semidirect
13. C29×#1823C2semidirect
14. C29×#1788C2semidirect
15. C29×#1788C2semidirect
21. C29×#537C4semidirect
72. C2×#41×C29C2×C4semidirect
103. C29×C22⋊Q8C2×C4semidirect
110. C29×#121C2×C4semidirect
120. C2×C4⋊C4×C29C2×C4semidirect
276. #21772C29direct (N × H)
377. C2×#408C2×C29semidirect
378. #2311C2×C29semidirect
379. #1895C2×C29semidirect
380. #1894C2×C29semidirect
381. #1893C2×C29semidirect
382. #1892C2×C29semidirect
383. #1875C2×C29semidirect
384. #1874C2×C29semidirect
385. #1873C2×C29semidirect
386. #1872C2×C29semidirect
387. #1824C2×C29semidirect
388. #1823C2×C29semidirect
389. #1788C2×C29semidirect
390. #1788C2×C29semidirect
445. #537C4×C29semidirect
507. C2×#41C2×C4×C29semidirect
538. C22⋊Q8C2×C4×C29semidirect
545. #121C2×C4×C29semidirect
555. C2×C4⋊C4C2×C4×C29semidirect
588. C29#21772direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5372
C2×C29×#4082
C29×#23112
C29×#18952
C29×#18942
C29×#18932
C29×#18922
C29×#18752
C29×#18742
C29×#18732
C29×#18722
C29×#18242
C29×#18232
C29×#17882
#2177229