Finite Group Databasebeta

← C29×#25131 #20320031

Subgroups — C29×#25131 #20320031

Order 7424.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#468C211yesmaximal, characteristic, complemented
2C2×C29×#449C211yesmaximal, characteristic, complemented
3C2×C29×#435C211yesmaximal, characteristic, complemented
4C2×C29×#416C211yesmaximal, characteristic, complemented
5C29×#2414C211yesmaximal, characteristic, complemented
6C29×#2407C211yesmaximal, characteristic, complemented
7C29×#2067C211yesmaximal, characteristic, complemented
8C29×#2055C211yesmaximal, characteristic, complemented
9C29×#2035C211yesmaximal, characteristic, complemented
10C29×#1999C211yesmaximal, characteristic, complemented
11C29×#1972C211yesmaximal, characteristic, complemented
12C29×#1935C211yesmaximal, characteristic, complemented
13C29×#1895C211yesmaximal, characteristic, complemented
14C29×#1893C211yesmaximal, characteristic, complemented
15C29×#1854C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C22×D8×C29C2211yescharacteristic
19C22×M16×C29C2211yescharacteristic
20C23×C8×C29C2211yescharacteristic
21C2×C29×C22⋊Q8C2211yescharacteristic
22C2×C29×#121C2211yescharacteristic
23C2×C29×#121C2211yescharacteristic
24C2×C29×#121C2211yescharacteristic
25C2×C4×D4×C29C2211yescharacteristic
26C2×C29×#117C2211yescharacteristic
27C29×#468—24no—
28C29×#449—24no—
29C29×#435—24no—
30C2×C29×#107C2211yescharacteristic
31C2×C29×#106C2211yescharacteristic
32C2×C29×C4⋊C8C2211yescharacteristic
33C29×#416—24no—
34C2×C29×#103C2211yescharacteristic
35C2×C29×#103C2211yescharacteristic
36C2×C29×#103C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×#102C2211yescharacteristic
39C2×C29×#102C2211yescharacteristic
40C2×C29×#102C2211yescharacteristic
41C2×C29×#102C2211yescharacteristic
42C2×C29×C22⋊C8C2211yescharacteristic
43C2×C29×C22⋊C8C2211yescharacteristic
44C2×C29×#97C2211yescharacteristic
45C29×#394—21no—
46C29×#394—21no—
47C29×#392—21no—
48C29×#392—21no—
49C29×#391C2211yescharacteristic
50C29×#390—21no—
51C29×#390C2211yescharacteristic
52C29×#390C2211yescharacteristic
53C29×#389C2211yescharacteristic
54C29×#388—21no—
55C29×#386—21no—
56C29×#385—21no—
57C29×#380C2211yescharacteristic
58C29×#380C2211yescharacteristic
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C29×#340C2211yescharacteristic
62C29×#340C2211yescharacteristic
63C2×#41×C29—22no—
64C2×#41×C29—22no—
65C2×#41×C29—22no—
66C2×#41×C29—22no—
67C2×#41×C29—41no—
68C2×#41×C29—41no—
69C22×Q8×C29C2311yescharacteristic
70C22×D4×C29—21no—
71C22×D4×C29—21no—
72C22×D4×C29—21no—
73C22×D4×C29—21no—
74C22×D4×C29D411yescharacteristic
75C22×D4×C29C2311yescharacteristic
76C22×D4×C29C2311yescharacteristic
77C23×C4×C29—21no—
78C23×C4×C29C2311yescharacteristic
79C23×C4×C29C2311yescharacteristic
80C2×SD16×C29—22no—
81C2×SD16×C29—22no—
82C2×SD16×C29—41no—
83C2×D8×C29—22no—
84C2×D8×C29—22no—
85C2×D8×C29—41no—
86C2×M16×C29—22no—
87C2×M16×C29—22no—
88C2×M16×C29—41no—
89C22×C8×C29—22no—
90C22×C8×C29—22no—
91C22×C8×C29—41no—
92C22×C8×C29C2311yescharacteristic
93C22×C8×C29C2311yescharacteristic
94C22×C8×C29C2311yescharacteristic
95C22×C8×C29C2311yescharacteristic
96C29×C22⋊Q8—22no—
97C29×C22⋊Q8—41no—
98C29×#121—22no—
99C29×#121—22no—
100C29×#121—22no—
101C29×#121—22no—
102C29×#121—41no—
103C29×#121—41no—
104C4×D4×C29—22no—
105C4×D4×C29—22no—
106C29×#117—22no—
107C29×#117—41no—
108C2×C4⋊C4×C29—21no—
109C2×C4⋊C4×C29—21no—
110C2×C4⋊C4×C29D411yescharacteristic
111C2×C4⋊C4×C29C2311yescharacteristic
112C2×C4⋊C4×C29C2311yescharacteristic
113C2×C4⋊C4×C29C2311yescharacteristic
114C2×C4⋊C4×C29C2311yescharacteristic
115C2×C4⋊C4×C29C2311yescharacteristic
116C2×C22⋊C4×C29—21no—
117C2×C22⋊C4×C29—21no—
118C2×C22⋊C4×C29—21no—
119C2×C22⋊C4×C29—21no—
120C2×C22⋊C4×C29—21no—
121C2×C22⋊C4×C29—21no—
122C2×C22⋊C4×C29—21no—
123C2×C22⋊C4×C29—21no—
124C2×C22⋊C4×C29—21no—
125C2×C22⋊C4×C29—21no—
126C2×C22⋊C4×C29—21no—
127C2×C22⋊C4×C29D411yescharacteristic
128C2×C22⋊C4×C29D411yescharacteristic
129C2×C42×C29—21no—
130C2×C42×C29C2311yescharacteristic
131C29×#107—22no—
132C29×#106—41no—
133C29×C4⋊C8—22no—
134C29×#103—22no—
135C29×#103—22no—
136C29×#103D414yescomplemented
137C29×#102—22no—
138C29×#102—22no—
139C29×#102—22no—
140C29×#102—22no—
141C29×#102—41no—
142C29×C22⋊C8—22no—
143C29×C22⋊C8D414yescomplemented
144C29×#97—22no—
145C29×#95—21no—
146C29×#95—21no—
147C29×#95—21no—
148C29×#95—21no—
149C29×#95—21no—
150C24×C29—21no—
151C24×C29—21no—
152C24×C29C2×D411yescharacteristic
153C24×C29C2×D411yescharacteristic
154#41×C29—28no—
155#41×C29—44no—
156#41×C29—44no—
157#41×C29—44no—
158C2×Q8×C29—21no—
159C2×Q8×C29—21no—
160C2×Q8×C29—21no—
161C2×Q8×C29—21no—
162C2×Q8×C29—21no—
163C2×Q8×C29C2×D412yes—
164C2×D4×C29—22no—
165C2×D4×C29—21no—
166C2×D4×C29—21no—
167C2×D4×C29—21no—
168C2×D4×C29—21no—
169C2×D4×C29—21no—
170C2×D4×C29—21no—
171C2×D4×C29—21no—
172C2×D4×C29—21no—
173C2×D4×C29—21no—
174C2×D4×C29—21no—
175C2×D4×C29—21no—
176C2×D4×C29—41no—
177C2×D4×C29—41no—
178C2×D4×C29—42no—
179C2×D4×C29—42no—
180C2×D4×C29—42no—
181C2×D4×C29—42no—
182C2×D4×C29—42no—
183C2×D4×C29—42no—
184C2×D4×C29—42no—
185C2×D4×C29—42no—
186C2×D4×C29—81no—
187C2×D4×C29—81no—
188C2×D4×C29—81no—
189C2×D4×C29—81no—
190C2×D4×C29#4112yes—
191C22×C4×C29—21no—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—21no—
195C22×C4×C29—21no—
196C22×C4×C29—21no—
197C22×C4×C29—21no—
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—42no—
208C22×C4×C29—42no—
209C22×C4×C29—42no—
210C22×C4×C29C2×D411yescharacteristic
211C22×C4×C29C2×D411yescharacteristic
212C22×C4×C29C2×D411yescharacteristic
213C22×C4×C29C2×D411yescharacteristic
214C22×C4×C29C2×D412yes—
215C22×C4×C29#4112yes—
216C22×C4×C29C2411yescharacteristic
217SD16×C29—44no—
218D8×C29—44no—
219M16×C29—44no—
220C2×C8×C29—21no—
221C2×C8×C29—21no—
222C2×C8×C29—21no—
223C2×C8×C29—21no—
224C2×C8×C29—21no—
225C2×C8×C29—21no—
226C2×C8×C29—21no—
227C2×C8×C29—21no—
228C2×C8×C29—21no—
229C2×C8×C29—44no—
230C2×C8×C29C2×D412yes—
231C2×C8×C29C2×D412yes—
232C2×C8×C29C2×D412yes—
233C4⋊C4×C29—22no—
234C4⋊C4×C29—21no—
235C4⋊C4×C29—21no—
236C4⋊C4×C29—21no—
237C4⋊C4×C29—21no—
238C4⋊C4×C29—21no—
239C4⋊C4×C29—21no—
240C4⋊C4×C29—21no—
241C4⋊C4×C29—21no—
242C4⋊C4×C29—21no—
243C4⋊C4×C29—42no—
244C4⋊C4×C29—81no—
245C4⋊C4×C29C2×D412yes—
246C22⋊C4×C29—22no—
247C22⋊C4×C29—22no—
248C22⋊C4×C29—42no—
249C22⋊C4×C29—42no—
250C22⋊C4×C29—42no—
251C22⋊C4×C29—42no—
252C22⋊C4×C29—42no—
253C22⋊C4×C29—42no—
254C22⋊C4×C29—42no—
255C22⋊C4×C29—81no—
256C22⋊C4×C29—81no—
257C22⋊C4×C29—81no—
258C22⋊C4×C29—81no—
259C42×C29—21no—
260C42×C29—21no—
261C42×C29—42no—
262#25131C2911yesmaximal, characteristic, direct product factor, Sylow
263C23×C29—21no—
264C23×C29—21no—
265C23×C29—21no—
266C23×C29—21no—
267C23×C29—21no—
268C23×C29—21no—
269C23×C29—21no—
270C23×C29—21no—
271C23×C29—22no—
272C23×C29—21no—
273C23×C29—21no—
274C23×C29—21no—
275C23×C29—21no—
276C23×C29—21no—
277C23×C29—41no—
278C23×C29—41no—
279C23×C29—41no—
280C23×C29—41no—
281C23×C29—41no—
282C23×C29—41no—
283C23×C29—41no—
284C23×C29—41no—
285C23×C29—41no—
286C23×C29—41no—
287C23×C29—41no—
288C23×C29—41no—
289C23×C29—41no—
290C23×C29#12112yes—
291C23×C29C22×D411yescharacteristic
292Q8×C29—22no—
293Q8×C29—22no—
294Q8×C29—41no—
295Q8×C29—41no—
296D4×C29—22no—
297D4×C29—22no—
298D4×C29—44no—
299D4×C29—48no—
300D4×C29—41no—
301D4×C29—41no—
302D4×C29—41no—
303D4×C29—41no—
304D4×C29—41no—
305D4×C29—41no—
306D4×C29—84no—
307D4×C29—84no—
308D4×C29—84no—
309C2×C4×C29—21no—
310C2×C4×C29—21no—
311C2×C4×C29—22no—
312C2×C4×C29—22no—
313C2×C4×C29—22no—
314C2×C4×C29—22no—
315C2×C4×C29—21no—
316C2×C4×C29—21no—
317C2×C4×C29—21no—
318C2×C4×C29—22no—
319C2×C4×C29—21no—
320C2×C4×C29—22no—
321C2×C4×C29—21no—
322C2×C4×C29—21no—
323C2×C4×C29—21no—
324C2×C4×C29—21no—
325C2×C4×C29—21no—
326C2×C4×C29—48no—
327C2×C4×C29—41no—
328C2×C4×C29—41no—
329C2×C4×C29—41no—
330C2×C4×C29—41no—
331C2×C4×C29—41no—
332C2×C4×C29—41no—
333C2×C4×C29—41no—
334C2×C4×C29—41no—
335C2×C4×C29—41no—
336C2×C4×C29—41no—
337C2×C4×C29—41no—
338C2×C4×C29—41no—
339C2×C4×C29—41no—
340C2×C4×C29—41no—
341C2×C4×C29—41no—
342C2×C4×C29—41no—
343C2×C4×C29—41no—
344C2×C4×C29—41no—
345C2×C4×C29—41no—
346C2×C4×C29—41no—
347C2×C4×C29#12112yes—
348C2×C4×C29C22×D411yescharacteristic
349C2×C4×C29C22×D411yescharacteristic
350C2×C4×C29C2×#4111yescharacteristic
351C2×C4×C29C2×#4111yescharacteristic
352C2×C4×C29H(5,𝔽2)11yescharacteristic
353C2×C4×C29H(5,𝔽2)11yescharacteristic
354C8×C29—22no—
355C8×C29—22no—
356C8×C29—22no—
357C8×C29—41no—
358C2×#468C2×C2911yescharacteristic, complemented
359C2×#449C2×C2911yescharacteristic, complemented
360C2×#435C2×C2911yescharacteristic, complemented
361C2×#416C2×C2911yescharacteristic, complemented
362#2414C2×C2911yescharacteristic, complemented
363#2407C2×C2911yescharacteristic, complemented
364#2067C2×C2911yescharacteristic, complemented
365#2055C2×C2911yescharacteristic, complemented
366#2035C2×C2911yescharacteristic, complemented
367#1999C2×C2911yescharacteristic, complemented
368#1972C2×C2911yescharacteristic, complemented
369#1935C2×C2911yescharacteristic, complemented
370#1895C2×C2911yescharacteristic, complemented
371#1893C2×C2911yescharacteristic, complemented
372#1854C2×C2911yescharacteristic, complemented
373C22×C29—22no—
374C22×C29—22no—
375C22×C29—22no—
376C22×C29—41no—
377C22×C29—41no—
378C22×C29—41no—
379C22×C29—41no—
380C22×C29—42no—
381C22×C29—41no—
382C22×C29—41no—
383C22×C29—41no—
384C22×C29—41no—
385C22×C29—42no—
386C22×C29—41no—
387C22×C29—41no—
388C22×C29—41no—
389C22×C29—42no—
390C22×C29—81no—
391C22×C29—81no—
392C22×C29—81no—
393C22×C29—81no—
394C22×C29—81no—
395C22×C29—81no—
396C22×C29—81no—
397C22×C29—81no—
398C22×C29—81no—
399C22×C29—81no—
400C22×C29—81no—
401C22×C29C2×#12111yescharacteristic
402C22×C29D4211yescharacteristic
403C22×C29#54611yescharacteristic
404C22×C29#57511yescharacteristic
405C22×C29#57511yescharacteristic
406C22×C29#57611yescharacteristic
407C22×C29#57711yescharacteristic
408C4×C29—22no—
409C4×C29—41no—
410C4×C29—42no—
411C4×C29—42no—
412C4×C29—41no—
413C4×C29—41no—
414C4×C29—81no—
415C4×C29—81no—
416C4×C29—81no—
417C4×C29—81no—
418C4×C29#52511yescharacteristic
419C4×C29#53811yescharacteristic
420C4×C29D4211yescharacteristic
421C4×C29#54611yescharacteristic
422C22×#41C22×C2911yescharacteristic
423C22×SD16C22×C2911yescharacteristic
424C22×D8C22×C2911yescharacteristic
425C22×M16C22×C2911yescharacteristic
426C23×C8C22×C2911yescharacteristic
427C2×C22⋊Q8C22×C2911yescharacteristic
428C2×#121C22×C2911yescharacteristic
429C2×#121C22×C2911yescharacteristic
430C2×#121C22×C2911yescharacteristic
431C2×C4×D4C22×C2911yescharacteristic
432C2×#117C22×C2911yescharacteristic
433#468—24no—
434#449—24no—
435#435—24no—
436C2×#107C22×C2911yescharacteristic
437C2×#106C22×C2911yescharacteristic
438C2×C4⋊C8C22×C2911yescharacteristic
439#416—24no—
440C2×#103C22×C2911yescharacteristic
441C2×#103C22×C2911yescharacteristic
442C2×#103C22×C2911yescharacteristic
443C2×#102C22×C2911yescharacteristic
444C2×#102C22×C2911yescharacteristic
445C2×#102C22×C2911yescharacteristic
446C2×#102C22×C2911yescharacteristic
447C2×#102C22×C2911yescharacteristic
448C2×C22⋊C8C22×C2911yescharacteristic
449C2×C22⋊C8C22×C2911yescharacteristic
450C2×#97C22×C2911yescharacteristic
451#394—21no—
452#394—21no—
453#392—21no—
454#392—21no—
455#391C22×C2911yescharacteristic
456#390—21no—
457#390C22×C2911yescharacteristic
458#390C22×C2911yescharacteristic
459#389C22×C2911yescharacteristic
460#388—21no—
461#386—21no—
462#385—21no—
463#380C22×C2911yescharacteristic
464#380C22×C2911yescharacteristic
465#340C22×C2911yescharacteristic
466#340C22×C2911yescharacteristic
467#340C22×C2911yescharacteristic
468#340C22×C2911yescharacteristic
469C2×C29—42no—
470C2×C29—81no—
471C2×C29—82no—
472C2×C29—161no—
473C2×C29#242411yescharacteristic
474C2×C29#305411yescharacteristic
475C2×C29#306211yescharacteristic
476C2×C29#326811yescharacteristic
477C2×C29#327111yescharacteristic
478C2×C29#330711yescharacteristic
479C2×C29#331911yescharacteristic
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—41no—
485C2×#41—41no—
486C22×Q8C23×C2911yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4D4×C2911yescharacteristic
492C22×D4C23×C2911yescharacteristic
493C22×D4C23×C2911yescharacteristic
494C23×C4—21no—
495C23×C4C23×C2911yescharacteristic
496C23×C4C23×C2911yescharacteristic
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×D8—22no—
501C2×D8—22no—
502C2×D8—41no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—41no—
506C22×C8—22no—
507C22×C8—22no—
508C22×C8—41no—
509C22×C8C23×C2911yescharacteristic
510C22×C8C23×C2911yescharacteristic
511C22×C8C23×C2911yescharacteristic
512C22×C8C23×C2911yescharacteristic
513C22⋊Q8—22no—
514C22⋊Q8—41no—
515#121—22no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—41no—
520#121—41no—
521C4×D4—22no—
522C4×D4—22no—
523#117—22no—
524#117—41no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4D4×C2911yescharacteristic
528C2×C4⋊C4C23×C2911yescharacteristic
529C2×C4⋊C4C23×C2911yescharacteristic
530C2×C4⋊C4C23×C2911yescharacteristic
531C2×C4⋊C4C23×C2911yescharacteristic
532C2×C4⋊C4C23×C2911yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4D4×C2911yescharacteristic
545C2×C22⋊C4D4×C2911yescharacteristic
546C2×C42—21no—
547C2×C42C23×C2911yescharacteristic
548#107—22no—
549#106—41no—
550C4⋊C8—22no—
551#103—22no—
552#103—22no—
553#103D4×C2914yescomplemented
554#102—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558#102—41no—
559C22⋊C8—22no—
560C22⋊C8D4×C2914yescomplemented
561#97—22no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567C29#2513111yescharacteristic, direct product factor, Sylow
568C24—21no—
569C24—21no—
570C24C2×D4×C2911yescharacteristic
571C24C2×D4×C2911yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C2912yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C2912yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C2911yescharacteristic
629C22×C4C2×D4×C2911yescharacteristic
630C22×C4C2×D4×C2911yescharacteristic
631C22×C4C2×D4×C2911yescharacteristic
632C22×C4C2×D4×C2912yes—
633C22×C4#41×C2912yes—
634C22×C4C24×C2911yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C2912yes—
649C2×C8C2×D4×C2912yes—
650C2×C8C2×D4×C2912yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C2912yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23C29×#12112yes—
708C23C22×D4×C2911yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4C29×#12112yes—
765C2×C4C22×D4×C2911yescharacteristic
766C2×C4C22×D4×C2911yescharacteristic
767C2×C4C2×#41×C2911yescharacteristic
768C2×C4C2×#41×C2911yescharacteristic
769C2×C4C29×H(5,𝔽2)11yescharacteristic
770C2×C4C29×H(5,𝔽2)11yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×C29×#12111yescharacteristic
804C22D42×C2911yescharacteristic
805C22C29×#54611yescharacteristic
806C22C29×#57511yescharacteristic
807C22C29×#57511yescharacteristic
808C22C29×#57611yescharacteristic
809C22C29×#57711yescharacteristic
810C4—22no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—41no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C29×#52511yescharacteristic
821C4C29×#53811yescharacteristic
822C4D42×C2911yescharacteristic
823C4C29×#54611yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2C29×#242411yescharacteristic
829C2C29×#305411yescharacteristic
830C2C29×#306211yescharacteristic
831C2C29×#326811yescharacteristic
832C2C29×#327111yescharacteristic
833C2C29×#330711yescharacteristic
834C2C29×#331911yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#468C2semidirect
2. C2×C29×#449C2semidirect
3. C2×C29×#435C2semidirect
4. C2×C29×#416C2semidirect
5. C29×#2414C2semidirect
6. C29×#2407C2semidirect
7. C29×#2067C2semidirect
8. C29×#2055C2semidirect
9. C29×#2035C2semidirect
10. C29×#1999C2semidirect
11. C29×#1972C2semidirect
12. C29×#1935C2semidirect
13. C29×#1895C2semidirect
14. C29×#1893C2semidirect
15. C29×#1854C2semidirect
136. C29×#103D4semidirect
143. C29×C22⋊C8D4semidirect
262. #25131C29direct (N × H)
358. C2×#468C2×C29semidirect
359. C2×#449C2×C29semidirect
360. C2×#435C2×C29semidirect
361. C2×#416C2×C29semidirect
362. #2414C2×C29semidirect
363. #2407C2×C29semidirect
364. #2067C2×C29semidirect
365. #2055C2×C29semidirect
366. #2035C2×C29semidirect
367. #1999C2×C29semidirect
368. #1972C2×C29semidirect
369. #1935C2×C29semidirect
370. #1895C2×C29semidirect
371. #1893C2×C29semidirect
372. #1854C2×C29semidirect
553. #103D4×C29semidirect
560. C22⋊C8D4×C29semidirect
567. C29#25131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4682
C2×C29×#4492
C2×C29×#4352
C2×C29×#4162
C29×#24142
C29×#24072
C29×#20672
C29×#20552
C29×#20352
C29×#19992
C29×#19722
C29×#19352
C29×#18952
C29×#18932
C29×#18542
#2513129