Finite Group Databasebeta

← C29×#25139 #20320039

Subgroups — C29×#25139 #20320039

Order 7424.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 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×#436C211yesmaximal, characteristic, complemented
4C2×C29×#417C211yesmaximal, characteristic, complemented
5C29×#2416C211yesmaximal, characteristic, complemented
6C29×#2407C211yesmaximal, characteristic, complemented
7C29×#2067C211yesmaximal, characteristic, complemented
8C29×#2055C211yesmaximal, characteristic, complemented
9C29×#2036C211yesmaximal, characteristic, complemented
10C29×#1999C211yesmaximal, characteristic, complemented
11C29×#1970C211yesmaximal, characteristic, complemented
12C29×#1933C211yesmaximal, characteristic, complemented
13C29×#1895C211yesmaximal, characteristic, complemented
14C29×#1895C211yesmaximal, characteristic, complemented
15C29×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C22×D8×C29C2211yescharacteristic
19C22×M16×C29C2211yescharacteristic
20C22×M16×C29C2211yescharacteristic
21C2×C29×C22⋊Q8C2211yescharacteristic
22C2×C29×#121—21no—
23C2×C29×#121C2211yescharacteristic
24C2×C29×#121C2211yescharacteristic
25C2×C29×#121C2211yescharacteristic
26C2×C4×D4×C29C2211yescharacteristic
27C22×C4⋊C4×C29C2211yescharacteristic
28C29×#468—24no—
29C29×#449—24no—
30C29×#436—24no—
31C2×C29×#107C2211yescharacteristic
32C2×C29×#107C2211yescharacteristic
33C2×C29×C4⋊C8C2211yescharacteristic
34C29×#417—24no—
35C2×C29×#103C2211yescharacteristic
36C2×C29×#103C2211yescharacteristic
37C2×C29×#103C2211yescharacteristic
38C2×C29×#102C2211yescharacteristic
39C2×C29×#102C2211yescharacteristic
40C2×C29×#102C2211yescharacteristic
41C2×C29×#102C2211yescharacteristic
42C2×C29×#102C2211yescharacteristic
43C2×C29×C22⋊C8C2211yescharacteristic
44C2×C29×C22⋊C8C2211yescharacteristic
45C2×C4×C8×C29C2211yescharacteristic
46C29×#396—21no—
47C29×#394—21no—
48C29×#394—21no—
49C29×#392—21no—
50C29×#391C2211yescharacteristic
51C29×#390C2211yescharacteristic
52C29×#390C2211yescharacteristic
53C29×#389C2211yescharacteristic
54C29×#386—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×C29—21no—
79C23×C4×C29C2311yescharacteristic
80C23×C4×C29C2311yescharacteristic
81C2×SD16×C29—22no—
82C2×SD16×C29—22no—
83C2×SD16×C29—41no—
84C2×D8×C29—22no—
85C2×D8×C29—22no—
86C2×D8×C29—41no—
87C2×M16×C29—22no—
88C2×M16×C29—22no—
89C2×M16×C29—22no—
90C2×M16×C29—22no—
91C2×M16×C29—41no—
92C2×M16×C29—41no—
93C22×C8×C29C2311yescharacteristic
94C22×C8×C29C2311yescharacteristic
95C22×C8×C29C2311yescharacteristic
96C22×C8×C29C2311yescharacteristic
97C29×C22⋊Q8—22no—
98C29×C22⋊Q8—41no—
99C29×#121—22no—
100C29×#121—22no—
101C29×#121—22no—
102C29×#121—22no—
103C29×#121—41no—
104C29×#121—41no—
105C29×#121—44no—
106C4×D4×C29—22no—
107C4×D4×C29—22no—
108C2×C4⋊C4×C29—22no—
109C2×C4⋊C4×C29—21no—
110C2×C4⋊C4×C29—21no—
111C2×C4⋊C4×C29—21no—
112C2×C4⋊C4×C29—41no—
113C2×C4⋊C4×C29D411yescharacteristic
114C2×C4⋊C4×C29C2311yescharacteristic
115C2×C4⋊C4×C29C2311yescharacteristic
116C2×C4⋊C4×C29C2311yescharacteristic
117C2×C4⋊C4×C29C2311yescharacteristic
118C2×C4⋊C4×C29C2311yescharacteristic
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×C29—21no—
128C2×C22⋊C4×C29—21no—
129C2×C22⋊C4×C29D411yescharacteristic
130C2×C22⋊C4×C29D411yescharacteristic
131C2×C42×C29C2311yescharacteristic
132C29×#107—22no—
133C29×#107—41no—
134C29×C4⋊C8—22no—
135C29×#103—22no—
136C29×#103—22no—
137C29×#103D414yescomplemented
138C29×#102—22no—
139C29×#102—22no—
140C29×#102—22no—
141C29×#102—22no—
142C29×#102—41no—
143C29×C22⋊C8—22no—
144C29×C22⋊C8D414yescomplemented
145C4×C8×C29—22no—
146C29×#95—21no—
147C29×#95—21no—
148C29×#95—21no—
149C29×#95—21no—
150C29×#95—21no—
151C24×C29—21no—
152C24×C29—21no—
153C24×C29C2×D411yescharacteristic
154C24×C29C2×D411yescharacteristic
155#41×C29—28no—
156#41×C29—44no—
157#41×C29—44no—
158#41×C29—44no—
159C2×Q8×C29—21no—
160C2×Q8×C29—21no—
161C2×Q8×C29—21no—
162C2×Q8×C29—21no—
163C2×Q8×C29—21no—
164C2×Q8×C29C2×D412yes—
165C2×D4×C29—22no—
166C2×D4×C29—22no—
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—21no—
177C2×D4×C29—21no—
178C2×D4×C29—41no—
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—42no—
187C2×D4×C29—42no—
188C2×D4×C29—42no—
189C2×D4×C29—81no—
190C2×D4×C29—81no—
191C2×D4×C29#4112yes—
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—21no—
208C22×C4×C29—42no—
209C22×C4×C29—42no—
210C22×C4×C29—42no—
211C22×C4×C29—42no—
212C22×C4×C29—42no—
213C22×C4×C29—81no—
214C22×C4×C29C2×D411yescharacteristic
215C22×C4×C29C2×D411yescharacteristic
216C22×C4×C29C2×D411yescharacteristic
217C22×C4×C29C2×D412yes—
218C22×C4×C29C2×D411yescharacteristic
219C22×C4×C29#4112yes—
220C22×C4×C29C2411yescharacteristic
221SD16×C29—44no—
222D8×C29—44no—
223M16×C29—44no—
224M16×C29—44no—
225C2×C8×C29—21no—
226C2×C8×C29—21no—
227C2×C8×C29—21no—
228C2×C8×C29—21no—
229C2×C8×C29—21no—
230C2×C8×C29—21no—
231C2×C8×C29—21no—
232C2×C8×C29—21no—
233C2×C8×C29—21no—
234C2×C8×C29C2×D412yes—
235C2×C8×C29C2×D412yes—
236C2×C8×C29C2×D412yes—
237C4⋊C4×C29—22no—
238C4⋊C4×C29—21no—
239C4⋊C4×C29—21no—
240C4⋊C4×C29—21no—
241C4⋊C4×C29—21no—
242C4⋊C4×C29—21no—
243C4⋊C4×C29—21no—
244C4⋊C4×C29—21no—
245C4⋊C4×C29—21no—
246C4⋊C4×C29—21no—
247C4⋊C4×C29—42no—
248C4⋊C4×C29—42no—
249C4⋊C4×C29—42no—
250C4⋊C4×C29C2×D412yes—
251C22⋊C4×C29—22no—
252C22⋊C4×C29—22no—
253C22⋊C4×C29—42no—
254C22⋊C4×C29—42no—
255C22⋊C4×C29—42no—
256C22⋊C4×C29—42no—
257C22⋊C4×C29—42no—
258C22⋊C4×C29—42no—
259C22⋊C4×C29—42no—
260C22⋊C4×C29—81no—
261C22⋊C4×C29—81no—
262C22⋊C4×C29—81no—
263C42×C29—21no—
264C42×C29—21no—
265#25139C2911yesmaximal, characteristic, direct product factor, Sylow
266C23×C29—21no—
267C23×C29—21no—
268C23×C29—21no—
269C23×C29—21no—
270C23×C29—21no—
271C23×C29—21no—
272C23×C29—21no—
273C23×C29—21no—
274C23×C29—22no—
275C23×C29—21no—
276C23×C29—21no—
277C23×C29—21no—
278C23×C29—21no—
279C23×C29—21no—
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—41no—
291C23×C29—41no—
292C23×C29—41no—
293C23×C29#12112yes—
294C23×C29C22×D411yescharacteristic
295Q8×C29—22no—
296Q8×C29—22no—
297Q8×C29—41no—
298Q8×C29—41no—
299D4×C29—22no—
300D4×C29—22no—
301D4×C29—44no—
302D4×C29—48no—
303D4×C29—41no—
304D4×C29—41no—
305D4×C29—41no—
306D4×C29—41no—
307D4×C29—41no—
308D4×C29—41no—
309D4×C29—84no—
310D4×C29—84no—
311D4×C29—84no—
312C2×C4×C29—21no—
313C2×C4×C29—21no—
314C2×C4×C29—21no—
315C2×C4×C29—21no—
316C2×C4×C29—22no—
317C2×C4×C29—22no—
318C2×C4×C29—22no—
319C2×C4×C29—22no—
320C2×C4×C29—21no—
321C2×C4×C29—21no—
322C2×C4×C29—21no—
323C2×C4×C29—22no—
324C2×C4×C29—22no—
325C2×C4×C29—21no—
326C2×C4×C29—21no—
327C2×C4×C29—21no—
328C2×C4×C29—48no—
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—41no—
348C2×C4×C29—41no—
349C2×C4×C29—84no—
350C2×C4×C29#12112yes—
351C2×C4×C29AGL(1,ℤ/8)12yes—
352C2×C4×C29C22×D411yescharacteristic
353C2×C4×C29C22×D411yescharacteristic
354C2×C4×C29C2×#4111yescharacteristic
355C2×C4×C29C2×#4111yescharacteristic
356C2×C4×C29H(5,𝔽2)11yescharacteristic
357C2×C4×C29H(5,𝔽2)11yescharacteristic
358C8×C29—22no—
359C8×C29—22no—
360C8×C29—22no—
361C8×C29—41no—
362C2×#468C2×C2911yescharacteristic, complemented
363C2×#449C2×C2911yescharacteristic, complemented
364C2×#436C2×C2911yescharacteristic, complemented
365C2×#417C2×C2911yescharacteristic, complemented
366#2416C2×C2911yescharacteristic, complemented
367#2407C2×C2911yescharacteristic, complemented
368#2067C2×C2911yescharacteristic, complemented
369#2055C2×C2911yescharacteristic, complemented
370#2036C2×C2911yescharacteristic, complemented
371#1999C2×C2911yescharacteristic, complemented
372#1970C2×C2911yescharacteristic, complemented
373#1933C2×C2911yescharacteristic, complemented
374#1895C2×C2911yescharacteristic, complemented
375#1895C2×C2911yescharacteristic, complemented
376#1852C2×C2911yescharacteristic, complemented
377C22×C29—22no—
378C22×C29—22no—
379C22×C29—22no—
380C22×C29—41no—
381C22×C29—41no—
382C22×C29—41no—
383C22×C29—41no—
384C22×C29—41no—
385C22×C29—42no—
386C22×C29—42no—
387C22×C29—41no—
388C22×C29—41no—
389C22×C29—41no—
390C22×C29—41no—
391C22×C29—41no—
392C22×C29—41no—
393C22×C29—42no—
394C22×C29—81no—
395C22×C29—81no—
396C22×C29—81no—
397C22×C29—81no—
398C22×C29—81no—
399C22×C29—81no—
400C22×C29—81no—
401C22×C29—81no—
402C22×C29—81no—
403C22×C29—81no—
404C22×C29—81no—
405C22×C29C2×#12111yescharacteristic
406C22×C29D4211yescharacteristic
407C22×C29#54611yescharacteristic
408C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C29#57511yescharacteristic
410C22×C29#57611yescharacteristic
411C22×C29#57811yescharacteristic
412C4×C29—22no—
413C4×C29—22no—
414C4×C29—41no—
415C4×C29—42no—
416C4×C29—42no—
417C4×C29—41no—
418C4×C29—81no—
419C4×C29—81no—
420C4×C29—81no—
421C4×C29—81no—
422C4×C29#52511yescharacteristic
423C4×C29#53811yescharacteristic
424C4×C29D4211yescharacteristic
425C4×C29#54611yescharacteristic
426C22×#41C22×C2911yescharacteristic
427C22×SD16C22×C2911yescharacteristic
428C22×D8C22×C2911yescharacteristic
429C22×M16C22×C2911yescharacteristic
430C22×M16C22×C2911yescharacteristic
431C2×C22⋊Q8C22×C2911yescharacteristic
432C2×#121—21no—
433C2×#121C22×C2911yescharacteristic
434C2×#121C22×C2911yescharacteristic
435C2×#121C22×C2911yescharacteristic
436C2×C4×D4C22×C2911yescharacteristic
437C22×C4⋊C4C22×C2911yescharacteristic
438#468—24no—
439#449—24no—
440#436—24no—
441C2×#107C22×C2911yescharacteristic
442C2×#107C22×C2911yescharacteristic
443C2×C4⋊C8C22×C2911yescharacteristic
444#417—24no—
445C2×#103C22×C2911yescharacteristic
446C2×#103C22×C2911yescharacteristic
447C2×#103C22×C2911yescharacteristic
448C2×#102C22×C2911yescharacteristic
449C2×#102C22×C2911yescharacteristic
450C2×#102C22×C2911yescharacteristic
451C2×#102C22×C2911yescharacteristic
452C2×#102C22×C2911yescharacteristic
453C2×C22⋊C8C22×C2911yescharacteristic
454C2×C22⋊C8C22×C2911yescharacteristic
455C2×C4×C8C22×C2911yescharacteristic
456#396—21no—
457#394—21no—
458#394—21no—
459#392—21no—
460#391C22×C2911yescharacteristic
461#390C22×C2911yescharacteristic
462#390C22×C2911yescharacteristic
463#389C22×C2911yescharacteristic
464#386—21no—
465#386—21no—
466#385—21no—
467#380C22×C2911yescharacteristic
468#380C22×C2911yescharacteristic
469#340C22×C2911yescharacteristic
470#340C22×C2911yescharacteristic
471#340C22×C2911yescharacteristic
472#340C22×C2911yescharacteristic
473C2×C29—42no—
474C2×C29—81no—
475C2×C29—82no—
476C2×C29—161no—
477C2×C29#242411yescharacteristic
478C2×C29#305511yescharacteristic
479C2×C29#306111yescharacteristic
480C2×C29#327411yescharacteristic
481C2×C29#327711yescharacteristic
482C2×C29#332211yescharacteristic
483C2×C29#333011yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8C23×C2911yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4D4×C2911yescharacteristic
496C22×D4C23×C2911yescharacteristic
497C22×D4C23×C2911yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C2911yescharacteristic
501C23×C4C23×C2911yescharacteristic
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—41no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—41no—
508C2×M16—22no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—41no—
513C2×M16—41no—
514C22×C8C23×C2911yescharacteristic
515C22×C8C23×C2911yescharacteristic
516C22×C8C23×C2911yescharacteristic
517C22×C8C23×C2911yescharacteristic
518C22⋊Q8—22no—
519C22⋊Q8—41no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—41no—
525#121—41no—
526#121—44no—
527C4×D4—22no—
528C4×D4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4D4×C2911yescharacteristic
535C2×C4⋊C4C23×C2911yescharacteristic
536C2×C4⋊C4C23×C2911yescharacteristic
537C2×C4⋊C4C23×C2911yescharacteristic
538C2×C4⋊C4C23×C2911yescharacteristic
539C2×C4⋊C4C23×C2911yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C2911yescharacteristic
551C2×C22⋊C4D4×C2911yescharacteristic
552C2×C42C23×C2911yescharacteristic
553#107—22no—
554#107—41no—
555C4⋊C8—22no—
556#103—22no—
557#103—22no—
558#103D4×C2914yescomplemented
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564C22⋊C8—22no—
565C22⋊C8D4×C2914yescomplemented
566C4×C8—22no—
567#95—21no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572C29#2513911yescharacteristic, direct product factor, Sylow
573C24—21no—
574C24—21no—
575C24C2×D4×C2911yescharacteristic
576C24C2×D4×C2911yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C2912yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C2912yes—
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—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C2911yescharacteristic
637C22×C4C2×D4×C2911yescharacteristic
638C22×C4C2×D4×C2911yescharacteristic
639C22×C4C2×D4×C2912yes—
640C22×C4C2×D4×C2911yescharacteristic
641C22×C4#41×C2912yes—
642C22×C4C24×C2911yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8C2×D4×C2912yes—
657C2×C8C2×D4×C2912yes—
658C2×C8C2×D4×C2912yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C2912yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23C29×#12112yes—
715C23C22×D4×C2911yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
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×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—84no—
771C2×C4C29×#12112yes—
772C2×C4C29×AGL(1,ℤ/8)12yes—
773C2×C4C22×D4×C2911yescharacteristic
774C2×C4C22×D4×C2911yescharacteristic
775C2×C4C2×#41×C2911yescharacteristic
776C2×C4C2×#41×C2911yescharacteristic
777C2×C4C29×H(5,𝔽2)11yescharacteristic
778C2×C4C29×H(5,𝔽2)11yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×C29×#12111yescharacteristic
812C22D42×C2911yescharacteristic
813C22C29×#54611yescharacteristic
814C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
815C22C29×#57511yescharacteristic
816C22C29×#57611yescharacteristic
817C22C29×#57811yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4C29×#52511yescharacteristic
829C4C29×#53811yescharacteristic
830C4D42×C2911yescharacteristic
831C4C29×#54611yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2C29×#242411yescharacteristic
837C2C29×#305511yescharacteristic
838C2C29×#306111yescharacteristic
839C2C29×#327411yescharacteristic
840C2C29×#327711yescharacteristic
841C2C29×#332211yescharacteristic
842C2C29×#333011yescharacteristic
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×#436C2semidirect
4. C2×C29×#417C2semidirect
5. C29×#2416C2semidirect
6. C29×#2407C2semidirect
7. C29×#2067C2semidirect
8. C29×#2055C2semidirect
9. C29×#2036C2semidirect
10. C29×#1999C2semidirect
11. C29×#1970C2semidirect
12. C29×#1933C2semidirect
13. C29×#1895C2semidirect
14. C29×#1895C2semidirect
15. C29×#1852C2semidirect
137. C29×#103D4semidirect
144. C29×C22⋊C8D4semidirect
265. #25139C29direct (N × H)
362. C2×#468C2×C29semidirect
363. C2×#449C2×C29semidirect
364. C2×#436C2×C29semidirect
365. C2×#417C2×C29semidirect
366. #2416C2×C29semidirect
367. #2407C2×C29semidirect
368. #2067C2×C29semidirect
369. #2055C2×C29semidirect
370. #2036C2×C29semidirect
371. #1999C2×C29semidirect
372. #1970C2×C29semidirect
373. #1933C2×C29semidirect
374. #1895C2×C29semidirect
375. #1895C2×C29semidirect
376. #1852C2×C29semidirect
558. #103D4×C29semidirect
565. C22⋊C8D4×C29semidirect
572. C29#25139direct (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×#4362
C2×C29×#4172
C29×#24162
C29×#24072
C29×#20672
C29×#20552
C29×#20362
C29×#19992
C29×#19702
C29×#19332
C29×#18952
C29×#18522
#2513929