Finite Group Databasebeta

← C29×#22888 #20317788

Subgroups — C29×#22888 #20317788

Order 7424.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3002C211yesmaximal, characteristic
2C2×C29×#443C211yesmaximal, characteristic, complemented
3C29×#2933C211yesmaximal, characteristic, complemented
4C22×C29×#104C211yesmaximal, characteristic, complemented
5C29×#2880C211yesmaximal, characteristic, complemented
6C29×#1974C211yesmaximal, characteristic, complemented
7C29×#1937C211yesmaximal, characteristic, complemented
8C29×#1929C211yesmaximal, characteristic, complemented
9C29×#1896C211yesmaximal, characteristic, complemented
10C29×#1876C211yesmaximal, characteristic, complemented
11C29×#1876C211yesmaximal, characteristic, complemented
12C29×#1866C211yesmaximal, characteristic, complemented
13C29×#1855C211yesmaximal, characteristic, complemented
14C29×#1764C211yesmaximal, characteristic, complemented
15C4×C29×C22⋊C8C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C2×C29×#135C2211yescharacteristic
18C2×C29×#135C2211yescharacteristic
19C2×C29×#131C2211yescharacteristic
20C2×C29×#131C2211yescharacteristic
21C2×C29×#131C2211yescharacteristic, complemented
22C22×M16×C29C2211yescharacteristic
23C29×#525C2211yescharacteristic
24C22×C42×C29C2211yescharacteristic
25C29×#452C411yescharacteristic, complemented
26C29×#452C411yescharacteristic, complemented
27C29×#451C411yescharacteristic, complemented
28C29×#450C411yescharacteristic, complemented
29C29×#449C411yescharacteristic, complemented
30C29×#449C411yescharacteristic, complemented
31C29×#448C411yescharacteristic, complemented
32C29×#447C411yescharacteristic, complemented
33C29×#443—24no—
34C29×#436—21no—
35C29×#435—21no—
36C29×#435—21no—
37C8×D4×C29—21no—
38C2×C29×#108C2211yescharacteristic, complemented
39C2×C29×#108C2211yescharacteristic, complemented
40C29×#424C2211yescharacteristic, complemented
41C2×C29×#104—24no—
42C2×C29×#104C2211yescharacteristic
43C2×C29×#104C2211yescharacteristic
44C2×C29×#104C2211yescharacteristic
45C2×C29×#104C2211yescharacteristic
46C2×C29×#104C2211yescharacteristic, complemented
47C2×C29×#104C2211yescharacteristic, complemented
48C29×#416C2211yescharacteristic
49C29×#416C2211yescharacteristic
50C29×#408—21no—
51C29×#408—21no—
52C29×#408C2211yescharacteristic
53C29×#408C2211yescharacteristic
54C29×#408C2211yescharacteristic, complemented
55C29×#407—21no—
56C29×#407C2211yescharacteristic
57C2×C29×C22⋊C8—21no—
58C2×C29×C22⋊C8C2211yescharacteristic
59C2×C29×C22⋊C8C2211yescharacteristic
60C29×#405C2211yescharacteristic, complemented
61C2×C4×C8×C29C2211yescharacteristic, complemented
62C2×C4×C8×C29C2211yescharacteristic, complemented
63C29×#341C2211yescharacteristic, complemented
64C29×#341C2211yescharacteristic, complemented
65C29×#339C2211yescharacteristic, complemented
66C29×#339C2211yescharacteristic, complemented
67C29×#336C2211yescharacteristic, complemented
68C29×#336C2211yescharacteristic, complemented
69C2×#41×C29—21no—
70C2×#41×C29—21no—
71C2×#41×C29—22no—
72C2×#41×C29—22no—
73C2×#41×C29—41no—
74C2×#41×C29—41no—
75C2×#41×C29C2×C411yescharacteristic
76C2×#41×C29C2×C411yescharacteristic
77C2×#41×C29C2311yescharacteristic
78C2×#41×C29C2311yescharacteristic
79C2×#41×C29C2311yescharacteristic
80C22×Q8×C29C2×C411yescharacteristic
81C22×D4×C29—21no—
82C22×D4×C29C2×C411yescharacteristic
83C23×C4×C29—21no—
84C23×C4×C29—21no—
85C23×C4×C29C2311yescharacteristic
86C29×#135—22no—
87C29×#135—22no—
88C29×#135—41no—
89C29×#135—41no—
90C2×Q16×C29C2×C411yescharacteristic, complemented
91C2×Q16×C29C2×C411yescharacteristic, complemented
92C2×SD16×C29C2×C411yescharacteristic, complemented
93C2×SD16×C29C2×C411yescharacteristic, complemented
94C2×SD16×C29C2×C411yescharacteristic, complemented
95C2×SD16×C29C2×C411yescharacteristic, complemented
96C2×D8×C29C2×C411yescharacteristic, complemented
97C2×D8×C29C2×C411yescharacteristic, complemented
98C29×#131—22no—
99C29×#131—22no—
100C29×#131—22no—
101C29×#131—41no—
102C29×#131—41no—
103C29×#131—41no—
104C2×M16×C29—21no—
105C2×M16×C29—21no—
106C2×M16×C29—21no—
107C2×M16×C29—21no—
108C2×M16×C29—22no—
109C2×M16×C29—41no—
110C2×M16×C29C2311yescharacteristic
111C2×M16×C29C2311yescharacteristic
112C2×M16×C29C2311yescharacteristic
113C2×M16×C29C2311yescharacteristic
114C22×C8×C29—21no—
115C22×C8×C29—21no—
116C22×C8×C29—21no—
117C22×C8×C29—21no—
118C22×C8×C29C2311yescharacteristic
119C22×C8×C29C2311yescharacteristic
120C22×C8×C29C2311yescharacteristic
121C22×C8×C29C2311yescharacteristic
122C29×#123—21no—
123C29×C22⋊Q8C2×C411yescharacteristic
124C29×C22⋊Q8C2×C411yescharacteristic
125C29×#121C2×C411yescharacteristic
126C29×#121C2×C411yescharacteristic
127C29×#120—21no—
128C4×D4×C29—21no—
129C4×D4×C29—21no—
130C29×#117C2311yescharacteristic
131C2×C42×C29—22no—
132C2×C42×C29—21no—
133C2×C42×C29—41no—
134C2×C42×C29C2311yescharacteristic
135C2×C42×C29C2311yescharacteristic
136C29×#108—22no—
137C29×#108—41no—
138C29×C4⋊C8—21no—
139C29×C4⋊C8—21no—
140C29×#104—22no—
141C29×#104—22no—
142C29×#104—22no—
143C29×#104—22no—
144C29×#104—41no—
145C29×#104D414yescomplemented
146C29×#103C2×C411yescharacteristic, complemented
147C29×#103C2×C411yescharacteristic, complemented
148C29×#103C2×C411yescharacteristic, complemented
149C29×#103C2×C411yescharacteristic, complemented
150C29×#102C2×C411yescharacteristic, complemented
151C29×#102C2×C411yescharacteristic, complemented
152C29×#102C2×C411yescharacteristic, complemented
153C29×#102C2×C411yescharacteristic, complemented
154C29×C22⋊C8—21no—
155C29×C22⋊C8—21no—
156C29×C22⋊C8—21no—
157C29×C22⋊C8—21no—
158C29×C22⋊C8—21no—
159C29×C22⋊C8—21no—
160C29×C22⋊C8—21no—
161C29×C22⋊C8—21no—
162C29×C22⋊C8C2×C411yescharacteristic
163C29×C22⋊C8C2×C411yescharacteristic
164C29×C22⋊C8C2×C411yescharacteristic
165C29×C22⋊C8C2×C411yescharacteristic
166C29×C22⋊C8D411yescharacteristic
167C29×C22⋊C8D411yescharacteristic
168C29×C22⋊C8D411yescharacteristic
169C29×C22⋊C8D411yescharacteristic
170C29×#97—21no—
171C4×C8×C29—21no—
172C4×C8×C29—22no—
173C4×C8×C29—41no—
174C24×C29—21no—
175C24×C29#4111yescharacteristic
176#41×C29—21no—
177#41×C29—21no—
178#41×C29—22no—
179#41×C29—22no—
180#41×C29—21no—
181#41×C29—21no—
182#41×C29—21no—
183#41×C29—21no—
184#41×C29—21no—
185#41×C29—21no—
186#41×C29—21no—
187#41×C29—21no—
188#41×C29—42no—
189#41×C29—42no—
190#41×C29—41no—
191#41×C29—41no—
192#41×C29—42no—
193#41×C29—42no—
194#41×C29C2×D412yes—
195#41×C29#4112yes—
196C2×Q8×C29—21no—
197C2×Q8×C29—22no—
198C2×Q8×C29—41no—
199C2×Q8×C29C22×C411yescharacteristic
200C2×Q8×C29C22×C411yescharacteristic
201C2×Q8×C29C22×C411yescharacteristic
202C2×D4×C29—21no—
203C2×D4×C29—22no—
204C2×D4×C29—21no—
205C2×D4×C29—21no—
206C2×D4×C29—21no—
207C2×D4×C29—21no—
208C2×D4×C29—21no—
209C2×D4×C29—21no—
210C2×D4×C29—21no—
211C2×D4×C29—41no—
212C2×D4×C29—42no—
213C2×D4×C29—42no—
214C2×D4×C29C22×C411yescharacteristic
215C2×D4×C29C22×C411yescharacteristic
216C2×D4×C29C22×C411yescharacteristic
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—24no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—21no—
227C22×C4×C29—21no—
228C22×C4×C29—21no—
229C22×C4×C29—21no—
230C22×C4×C29—42no—
231C22×C4×C29—42no—
232C22×C4×C29—42no—
233C22×C4×C29—42no—
234C22×C4×C29C22×C411yescharacteristic
235C22×C4×C29C22×C411yescharacteristic
236C22×C4×C29C2×D411yescharacteristic
237C22×C4×C29C2×D411yescharacteristic
238C22×C4×C29#4111yescharacteristic
239C22×C4×C29C2411yescharacteristic
240Q16×C29—22no—
241Q16×C29—41no—
242SD16×C29—22no—
243SD16×C29—22no—
244SD16×C29—41no—
245SD16×C29—41no—
246D8×C29—22no—
247D8×C29—41no—
248M16×C29—21no—
249M16×C29—21no—
250M16×C29—21no—
251M16×C29—21no—
252M16×C29—21no—
253M16×C29—21no—
254M16×C29—21no—
255M16×C29—42no—
256M16×C29—42no—
257M16×C29—42no—
258M16×C29—42no—
259M16×C29C2×D412yes—
260C2×C8×C29—21no—
261C2×C8×C29—21no—
262C2×C8×C29—21no—
263C2×C8×C29—21no—
264C2×C8×C29—21no—
265C2×C8×C29—21no—
266C2×C8×C29—21no—
267C2×C8×C29—21no—
268C2×C8×C29—21no—
269C2×C8×C29—21no—
270C2×C8×C29—21no—
271C2×C8×C29—21no—
272C2×C8×C29—42no—
273C2×C8×C29—42no—
274C2×C8×C29—42no—
275C2×C8×C29—42no—
276C2×C8×C29C22×C411yescharacteristic
277C2×C8×C29C22×C411yescharacteristic
278C2×C8×C29C22×C411yescharacteristic
279C2×C8×C29C22×C411yescharacteristic
280C2×C8×C29C2×D411yescharacteristic
281C2×C8×C29C2×D411yescharacteristic
282C2×C8×C29C2×D411yescharacteristic
283C2×C8×C29C2×D411yescharacteristic
284C4⋊C4×C29—21no—
285C4⋊C4×C29—21no—
286C4⋊C4×C29C22×C411yescharacteristic
287C4⋊C4×C29C22×C411yescharacteristic
288C22⋊C4×C29—21no—
289C22⋊C4×C29—21no—
290C22⋊C4×C29—21no—
291C22⋊C4×C29—21no—
292C22⋊C4×C29—21no—
293C42×C29—21no—
294C42×C29—21no—
295C42×C29—21no—
296C42×C29—21no—
297C42×C29—42no—
298C42×C29C2×D412yes—
299#22888C2911yesmaximal, characteristic, direct product factor, Sylow
300C23×C29—21no—
301C23×C29—21no—
302C23×C29—21no—
303C23×C29—22no—
304C23×C29—21no—
305C23×C29—21no—
306C23×C29—41no—
307C23×C29—42no—
308C23×C29—42no—
309C23×C29—81no—
310C23×C29C4×D411yescharacteristic
311C23×C29C4×D411yescharacteristic
312C23×C29C2×#4111yescharacteristic
313Q8×C29—21no—
314Q8×C29—21no—
315Q8×C29—21no—
316Q8×C29—21no—
317Q8×C29—21no—
318Q8×C29—42no—
319Q8×C29C4×D412yes—
320D4×C29—22no—
321D4×C29—22no—
322D4×C29—21no—
323D4×C29—21no—
324D4×C29—21no—
325D4×C29—21no—
326D4×C29—21no—
327D4×C29—42no—
328D4×C29—42no—
329D4×C29—42no—
330D4×C29—41no—
331D4×C29—41no—
332D4×C29—41no—
333D4×C29—41no—
334D4×C29—42no—
335D4×C29—81no—
336D4×C29C4×D412yes—
337C2×C4×C29—22no—
338C2×C4×C29—22no—
339C2×C4×C29—21no—
340C2×C4×C29—22no—
341C2×C4×C29—21no—
342C2×C4×C29—21no—
343C2×C4×C29—21no—
344C2×C4×C29—21no—
345C2×C4×C29—21no—
346C2×C4×C29—21no—
347C2×C4×C29—21no—
348C2×C4×C29—22no—
349C2×C4×C29—21no—
350C2×C4×C29—22no—
351C2×C4×C29—21no—
352C2×C4×C29—21no—
353C2×C4×C29—22no—
354C2×C4×C29—21no—
355C2×C4×C29—21no—
356C2×C4×C29—21no—
357C2×C4×C29—21no—
358C2×C4×C29—42no—
359C2×C4×C29—42no—
360C2×C4×C29—42no—
361C2×C4×C29—48no—
362C2×C4×C29—41no—
363C2×C4×C29—41no—
364C2×C4×C29—41no—
365C2×C4×C29—41no—
366C2×C4×C29—41no—
367C2×C4×C29—41no—
368C2×C4×C29C4×D411yescharacteristic
369C2×C4×C29C4×D411yescharacteristic
370C2×C4×C29C23×C411yescharacteristic
371C2×C4×C29C22×D411yescharacteristic
372C2×C4×C29C22×D411yescharacteristic
373C2×C4×C29C2×#4111yescharacteristic
374C2×C4×C29H(5,𝔽2)11yescharacteristic
375C2×C4×C29H(5,𝔽2)11yescharacteristic
376C8×C29—21no—
377C8×C29—21no—
378C8×C29—21no—
379C8×C29—21no—
380C8×C29—21no—
381C8×C29—21no—
382C8×C29—22no—
383C8×C29—21no—
384C8×C29—21no—
385C8×C29—41no—
386C8×C29—41no—
387C8×C29—41no—
388#3002C2×C2911yescharacteristic
389C2×#443C2×C2911yescharacteristic, complemented
390#2933C2×C2911yescharacteristic, complemented
391C22×#104C2×C2911yescharacteristic, complemented
392#2880C2×C2911yescharacteristic, complemented
393#1974C2×C2911yescharacteristic, complemented
394#1937C2×C2911yescharacteristic, complemented
395#1929C2×C2911yescharacteristic, complemented
396#1896C2×C2911yescharacteristic, complemented
397#1876C2×C2911yescharacteristic, complemented
398#1876C2×C2911yescharacteristic, complemented
399#1866C2×C2911yescharacteristic, complemented
400#1855C2×C2911yescharacteristic, complemented
401#1764C2×C2911yescharacteristic, complemented
402C4×C22⋊C8C2×C2911yescharacteristic, complemented
403C22×C29—21no—
404C22×C29—21no—
405C22×C29—21no—
406C22×C29—21no—
407C22×C29—21no—
408C22×C29—22no—
409C22×C29—21no—
410C22×C29—21no—
411C22×C29—42no—
412C22×C29—42no—
413C22×C29—41no—
414C22×C29—41no—
415C22×C29—41no—
416C22×C29—41no—
417C22×C29—41no—
418C22×C29—41no—
419C22×C29—41no—
420C22×C29—41no—
421C22×C29—84no—
422C22×C29#44312yescomplemented
423C22×C29C2×C4×D411yescharacteristic
424C22×C29#54611yescharacteristic
425C22×C29#55111yescharacteristic
426C4×C29—24no—
427C4×C29—21no—
428C4×C29—21no—
429C4×C29—22no—
430C4×C29—42no—
431C4×C29—41no—
432C4×C29—41no—
433C4×C29—41no—
434C4×C29—41no—
435C4×C29C2×C4×D411yescharacteristic
436C4×C29#51811yescharacteristic
437C4×C29D4211yescharacteristic
438C4×C29#54611yescharacteristic
439C22×#41C22×C2911yescharacteristic
440C2×#135C22×C2911yescharacteristic
441C2×#135C22×C2911yescharacteristic
442C2×#131C22×C2911yescharacteristic
443C2×#131C22×C2911yescharacteristic
444C2×#131C22×C2911yescharacteristic, complemented
445C22×M16C22×C2911yescharacteristic
446#525C22×C2911yescharacteristic
447C22×C42C22×C2911yescharacteristic
448#452C4×C2911yescharacteristic, complemented
449#452C4×C2911yescharacteristic, complemented
450#451C4×C2911yescharacteristic, complemented
451#450C4×C2911yescharacteristic, complemented
452#449C4×C2911yescharacteristic, complemented
453#449C4×C2911yescharacteristic, complemented
454#448C4×C2911yescharacteristic, complemented
455#447C4×C2911yescharacteristic, complemented
456#443—24no—
457#436—21no—
458#435—21no—
459#435—21no—
460C8×D4—21no—
461C2×#108C22×C2911yescharacteristic, complemented
462C2×#108C22×C2911yescharacteristic, complemented
463#424C22×C2911yescharacteristic, complemented
464C2×#104—24no—
465C2×#104C22×C2911yescharacteristic
466C2×#104C22×C2911yescharacteristic
467C2×#104C22×C2911yescharacteristic
468C2×#104C22×C2911yescharacteristic
469C2×#104C22×C2911yescharacteristic, complemented
470C2×#104C22×C2911yescharacteristic, complemented
471#416C22×C2911yescharacteristic
472#416C22×C2911yescharacteristic
473#408—21no—
474#408—21no—
475#408C22×C2911yescharacteristic
476#408C22×C2911yescharacteristic
477#408C22×C2911yescharacteristic, complemented
478#407—21no—
479#407C22×C2911yescharacteristic
480C2×C22⋊C8—21no—
481C2×C22⋊C8C22×C2911yescharacteristic
482C2×C22⋊C8C22×C2911yescharacteristic
483#405C22×C2911yescharacteristic, complemented
484C2×C4×C8C22×C2911yescharacteristic, complemented
485C2×C4×C8C22×C2911yescharacteristic, complemented
486#341C22×C2911yescharacteristic, complemented
487#341C22×C2911yescharacteristic, complemented
488#339C22×C2911yescharacteristic, complemented
489#339C22×C2911yescharacteristic, complemented
490#336C22×C2911yescharacteristic, complemented
491#336C22×C2911yescharacteristic, complemented
492C2×C29—21no—
493C2×C29—22no—
494C2×C29—21no—
495C2×C29—41no—
496C2×C29—42no—
497C2×C29—81no—
498C2×C29—81no—
499C2×C29#235811yescharacteristic
500C2×C29C2×#44311yescharacteristic
501C2×C29#295611yescharacteristic
502C2×#41—21no—
503C2×#41—21no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41C2×C4×C2911yescharacteristic
509C2×#41C2×C4×C2911yescharacteristic
510C2×#41C23×C2911yescharacteristic
511C2×#41C23×C2911yescharacteristic
512C2×#41C23×C2911yescharacteristic
513C22×Q8C2×C4×C2911yescharacteristic
514C22×D4—21no—
515C22×D4C2×C4×C2911yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C23×C2911yescharacteristic
519#135—22no—
520#135—22no—
521#135—41no—
522#135—41no—
523C2×Q16C2×C4×C2911yescharacteristic, complemented
524C2×Q16C2×C4×C2911yescharacteristic, complemented
525C2×SD16C2×C4×C2911yescharacteristic, complemented
526C2×SD16C2×C4×C2911yescharacteristic, complemented
527C2×SD16C2×C4×C2911yescharacteristic, complemented
528C2×SD16C2×C4×C2911yescharacteristic, complemented
529C2×D8C2×C4×C2911yescharacteristic, complemented
530C2×D8C2×C4×C2911yescharacteristic, complemented
531#131—22no—
532#131—22no—
533#131—22no—
534#131—41no—
535#131—41no—
536#131—41no—
537C2×M16—21no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—21no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16C23×C2911yescharacteristic
544C2×M16C23×C2911yescharacteristic
545C2×M16C23×C2911yescharacteristic
546C2×M16C23×C2911yescharacteristic
547C22×C8—21no—
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C2911yescharacteristic
552C22×C8C23×C2911yescharacteristic
553C22×C8C23×C2911yescharacteristic
554C22×C8C23×C2911yescharacteristic
555#123—21no—
556C22⋊Q8C2×C4×C2911yescharacteristic
557C22⋊Q8C2×C4×C2911yescharacteristic
558#121C2×C4×C2911yescharacteristic
559#121C2×C4×C2911yescharacteristic
560#120—21no—
561C4×D4—21no—
562C4×D4—21no—
563#117C23×C2911yescharacteristic
564C2×C42—22no—
565C2×C42—21no—
566C2×C42—41no—
567C2×C42C23×C2911yescharacteristic
568C2×C42C23×C2911yescharacteristic
569#108—22no—
570#108—41no—
571C4⋊C8—21no—
572C4⋊C8—21no—
573#104—22no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—41no—
578#104D4×C2914yescomplemented
579#103C2×C4×C2911yescharacteristic, complemented
580#103C2×C4×C2911yescharacteristic, complemented
581#103C2×C4×C2911yescharacteristic, complemented
582#103C2×C4×C2911yescharacteristic, complemented
583#102C2×C4×C2911yescharacteristic, complemented
584#102C2×C4×C2911yescharacteristic, complemented
585#102C2×C4×C2911yescharacteristic, complemented
586#102C2×C4×C2911yescharacteristic, complemented
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8C2×C4×C2911yescharacteristic
596C22⋊C8C2×C4×C2911yescharacteristic
597C22⋊C8C2×C4×C2911yescharacteristic
598C22⋊C8C2×C4×C2911yescharacteristic
599C22⋊C8D4×C2911yescharacteristic
600C22⋊C8D4×C2911yescharacteristic
601C22⋊C8D4×C2911yescharacteristic
602C22⋊C8D4×C2911yescharacteristic
603#97—21no—
604C4×C8—21no—
605C4×C8—22no—
606C4×C8—41no—
607C29#2288811yescharacteristic, direct product factor, Sylow
608C24—21no—
609C24#41×C2911yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41C2×D4×C2912yes—
629#41#41×C2912yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×C4×C2911yescharacteristic
634C2×Q8C22×C4×C2911yescharacteristic
635C2×Q8C22×C4×C2911yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×C4×C2911yescharacteristic
649C2×D4C22×C4×C2911yescharacteristic
650C2×D4C22×C4×C2911yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22×C4×C2911yescharacteristic
669C22×C4C22×C4×C2911yescharacteristic
670C22×C4C2×D4×C2911yescharacteristic
671C22×C4C2×D4×C2911yescharacteristic
672C22×C4#41×C2911yescharacteristic
673C22×C4C24×C2911yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16C2×D4×C2912yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8C22×C4×C2911yescharacteristic
711C2×C8C22×C4×C2911yescharacteristic
712C2×C8C22×C4×C2911yescharacteristic
713C2×C8C22×C4×C2911yescharacteristic
714C2×C8C2×D4×C2911yescharacteristic
715C2×C8C2×D4×C2911yescharacteristic
716C2×C8C2×D4×C2911yescharacteristic
717C2×C8C2×D4×C2911yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×C4×C2911yescharacteristic
721C4⋊C4C22×C4×C2911yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42C2×D4×C2912yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23C4×D4×C2911yescharacteristic
744C23C4×D4×C2911yescharacteristic
745C23C2×#41×C2911yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8C4×D4×C2912yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4C4×D4×C2912yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—48no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4C4×D4×C2911yescharacteristic
802C2×C4C4×D4×C2911yescharacteristic
803C2×C4C23×C4×C2911yescharacteristic
804C2×C4C22×D4×C2911yescharacteristic
805C2×C4C22×D4×C2911yescharacteristic
806C2×C4C2×#41×C2911yescharacteristic
807C2×C4C29×H(5,𝔽2)11yescharacteristic
808C2×C4C29×H(5,𝔽2)11yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—22no—
816C8—21no—
817C8—21no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—22no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22C29×#44312yescomplemented
841C22C2×C4×D4×C2911yescharacteristic
842C22C29×#54611yescharacteristic
843C22C29×#55111yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4C2×C4×D4×C2911yescharacteristic
854C4C29×#51811yescharacteristic
855C4D42×C2911yescharacteristic
856C4C29×#54611yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2C29×#235811yescharacteristic
865C2C2×C29×#44311yescharacteristic
866C2C29×#295611yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
socleC22×C29C2×C4×D4
prime radicalC29×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C29×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#443C2semidirect
3. C29×#2933C2semidirect
4. C22×C29×#104C2semidirect
5. C29×#2880C2semidirect
6. C29×#1974C2semidirect
7. C29×#1937C2semidirect
8. C29×#1929C2semidirect
9. C29×#1896C2semidirect
10. C29×#1876C2semidirect
11. C29×#1876C2semidirect
12. C29×#1866C2semidirect
13. C29×#1855C2semidirect
14. C29×#1764C2semidirect
15. C4×C29×C22⋊C8C2semidirect
21. C2×C29×#131C22semidirect
25. C29×#452C4semidirect
26. C29×#452C4semidirect
27. C29×#451C4semidirect
28. C29×#450C4semidirect
29. C29×#449C4semidirect
30. C29×#449C4semidirect
31. C29×#448C4semidirect
32. C29×#447C4semidirect
38. C2×C29×#108C22semidirect
39. C2×C29×#108C22semidirect
40. C29×#424C22semidirect
46. C2×C29×#104C22semidirect
47. C2×C29×#104C22semidirect
54. C29×#408C22semidirect
60. C29×#405C22semidirect
61. C2×C4×C8×C29C22semidirect
62. C2×C4×C8×C29C22semidirect
63. C29×#341C22semidirect
64. C29×#341C22semidirect
65. C29×#339C22semidirect
66. C29×#339C22semidirect
67. C29×#336C22semidirect
68. C29×#336C22semidirect
90. C2×Q16×C29C2×C4semidirect
91. C2×Q16×C29C2×C4semidirect
92. C2×SD16×C29C2×C4semidirect
93. C2×SD16×C29C2×C4semidirect
94. C2×SD16×C29C2×C4semidirect
95. C2×SD16×C29C2×C4semidirect
96. C2×D8×C29C2×C4semidirect
97. C2×D8×C29C2×C4semidirect
145. C29×#104D4semidirect
146. C29×#103C2×C4semidirect
147. C29×#103C2×C4semidirect
148. C29×#103C2×C4semidirect
149. C29×#103C2×C4semidirect
150. C29×#102C2×C4semidirect
151. C29×#102C2×C4semidirect
152. C29×#102C2×C4semidirect
153. C29×#102C2×C4semidirect
299. #22888C29direct (N × H)
389. C2×#443C2×C29semidirect
390. #2933C2×C29semidirect
391. C22×#104C2×C29semidirect
392. #2880C2×C29semidirect
393. #1974C2×C29semidirect
394. #1937C2×C29semidirect
395. #1929C2×C29semidirect
396. #1896C2×C29semidirect
397. #1876C2×C29semidirect
398. #1876C2×C29semidirect
399. #1866C2×C29semidirect
400. #1855C2×C29semidirect
401. #1764C2×C29semidirect
402. C4×C22⋊C8C2×C29semidirect
422. C22×C29#443semidirect
444. C2×#131C22×C29semidirect
448. #452C4×C29semidirect
449. #452C4×C29semidirect
450. #451C4×C29semidirect
451. #450C4×C29semidirect
452. #449C4×C29semidirect
453. #449C4×C29semidirect
454. #448C4×C29semidirect
455. #447C4×C29semidirect
461. C2×#108C22×C29semidirect
462. C2×#108C22×C29semidirect
463. #424C22×C29semidirect
469. C2×#104C22×C29semidirect
470. C2×#104C22×C29semidirect
477. #408C22×C29semidirect
483. #405C22×C29semidirect
484. C2×C4×C8C22×C29semidirect
485. C2×C4×C8C22×C29semidirect
486. #341C22×C29semidirect
487. #341C22×C29semidirect
488. #339C22×C29semidirect
489. #339C22×C29semidirect
490. #336C22×C29semidirect
491. #336C22×C29semidirect
523. C2×Q16C2×C4×C29semidirect
524. C2×Q16C2×C4×C29semidirect
525. C2×SD16C2×C4×C29semidirect
526. C2×SD16C2×C4×C29semidirect
527. C2×SD16C2×C4×C29semidirect
528. C2×SD16C2×C4×C29semidirect
529. C2×D8C2×C4×C29semidirect
530. C2×D8C2×C4×C29semidirect
578. #104D4×C29semidirect
579. #103C2×C4×C29semidirect
580. #103C2×C4×C29semidirect
581. #103C2×C4×C29semidirect
582. #103C2×C4×C29semidirect
583. #102C2×C4×C29semidirect
584. #102C2×C4×C29semidirect
585. #102C2×C4×C29semidirect
586. #102C2×C4×C29semidirect
607. C29#22888direct (N × H)
840. C22C29×#443semidirect

Maximal subgroups

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

subgroupindex
C29×#30022
C2×C29×#4432
C29×#29332
C22×C29×#1042
C29×#28802
C29×#19742
C29×#19372
C29×#19292
C29×#18962
C29×#18762
C29×#18662
C29×#18552
C29×#17642
C4×C29×C22⋊C82
#2288829