Finite Group Databasebeta

← C29×#25174 #20320074

Subgroups — C29×#25174 #20320074

Order 7424.

1234 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#459C211yesmaximal, characteristic, complemented
2C2×C29×#449C211yesmaximal, characteristic, complemented
3C2×C29×#449C211yesmaximal, characteristic, complemented
4C2×C29×#442C211yesmaximal, characteristic, complemented
5C29×#2428C211yesmaximal, characteristic, complemented
6C29×#2339C211yesmaximal, characteristic, complemented
7C29×#2066C211yesmaximal, characteristic, complemented
8C29×#2034C211yesmaximal, characteristic, complemented
9C29×#2033C211yesmaximal, characteristic, complemented
10C29×#2014C211yesmaximal, characteristic, complemented
11C29×#1973C211yesmaximal, characteristic, complemented
12C29×#1924C211yesmaximal, characteristic, complemented
13C29×#1879C211yesmaximal, characteristic, complemented
14C29×#1877C211yesmaximal, characteristic, complemented
15C29×#1862C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C22×SD16×C29C2211yescharacteristic
19C22×D8×C29C2211yescharacteristic
20C22×D8×C29C2211yescharacteristic
21C2×C29×#127C2211yescharacteristic
22C2×C29×#121—21no—
23C2×C29×#121C2211yescharacteristic
24C2×C29×#121C2211yescharacteristic
25C2×C4×D4×C29C2211yescharacteristic
26C2×C4×D4×C29C2211yescharacteristic
27C2×C4×D4×C29C2211yescharacteristic
28C29×#459—24no—
29C29×#449—24no—
30C29×#449—24no—
31C29×#442—24no—
32C2×C29×#107C2211yescharacteristic
33C2×C29×#106C2211yescharacteristic
34C2×C29×C4⋊C8C2211yescharacteristic
35C2×C29×#103C2211yescharacteristic
36C2×C29×#103C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×#102C2211yescharacteristic
39C2×C29×#102C2211yescharacteristic
40C2×C29×#102C2211yescharacteristic
41C2×C29×#102C2211yescharacteristic
42C2×C29×#102C2211yescharacteristic
43C2×C29×C22⋊C8C2211yescharacteristic
44C2×C29×C22⋊C8C2211yescharacteristic
45C2×C29×#97C2211yescharacteristic
46C29×#394—21no—
47C29×#392—21no—
48C29×#391C2211yescharacteristic
49C29×#391C2211yescharacteristic
50C29×#390C2211yescharacteristic
51C29×#389C2211yescharacteristic
52C29×#386—21no—
53C29×#386—21no—
54C29×#386—21no—
55C29×#381—21no—
56C29×#380C2211yescharacteristic
57C4×C22⋊C4×C29C2211yescharacteristic
58C2×C29×#95—21no—
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C29×#336C2211yescharacteristic
62C29×#336C2211yescharacteristic
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×C29—21no—
75C22×D4×C29C2311yescharacteristic
76C22×D4×C29C2311yescharacteristic
77C22×D4×C29C2311yescharacteristic
78C23×C4×C29—21no—
79C23×C4×C29—21no—
80C23×C4×C29—21no—
81C23×C4×C29—21no—
82C23×C4×C29C2311yescharacteristic
83C2×SD16×C29—22no—
84C2×SD16×C29—22no—
85C2×SD16×C29—22no—
86C2×SD16×C29—22no—
87C2×SD16×C29—41no—
88C2×SD16×C29—41no—
89C2×D8×C29—22no—
90C2×D8×C29—22no—
91C2×D8×C29—22no—
92C2×D8×C29—22no—
93C2×D8×C29—22no—
94C2×D8×C29D414yescomplemented
95C22×C8×C29C2311yescharacteristic
96C22×C8×C29C2311yescharacteristic
97C22×C8×C29C2311yescharacteristic
98C22×C8×C29C2311yescharacteristic
99C29×#127—22no—
100C29×#127—41no—
101C29×#121—22no—
102C29×#121—22no—
103C29×#121—44no—
104C29×#121—41no—
105C29×#121—41no—
106C4×D4×C29—22no—
107C4×D4×C29—22no—
108C4×D4×C29—22no—
109C4×D4×C29—41no—
110C4×D4×C29—41no—
111C4×D4×C29—41no—
112C2×C4⋊C4×C29—21no—
113C2×C4⋊C4×C29C2311yescharacteristic
114C2×C4⋊C4×C29C2311yescharacteristic
115C2×C4⋊C4×C29C2311yescharacteristic
116C2×C4⋊C4×C29C2311yescharacteristic
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×C29D411yescharacteristic
126C2×C22⋊C4×C29D411yescharacteristic
127C2×C42×C29C2311yescharacteristic
128C2×C42×C29C2311yescharacteristic
129C29×#107—41no—
130C29×#106—22no—
131C29×C4⋊C8—22no—
132C29×#103—22no—
133C29×#103—22no—
134C29×#102—22no—
135C29×#102—22no—
136C29×#102—22no—
137C29×#102—22no—
138C29×#102—41no—
139C29×#102D414yescomplemented
140C29×C22⋊C8—22no—
141C29×C22⋊C8—22no—
142C29×#97—22no—
143C29×#95—21no—
144C29×#95—21no—
145C29×#95—21no—
146C29×#95—21no—
147C29×#95—21no—
148C29×#95—21no—
149C29×#95D411yescharacteristic
150C29×#95D411yescharacteristic
151C24×C29—21no—
152C24×C29—21no—
153C24×C29—21no—
154C24×C29C2×D411yescharacteristic
155#41×C29—44no—
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×C29#4112yes—
165C2×D4×C29—24no—
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—21no—
177C2×D4×C29—21no—
178C2×D4×C29—21no—
179C2×D4×C29—21no—
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—42no—
190C2×D4×C29—81no—
191C2×D4×C29—81no—
192C2×D4×C29—81no—
193C2×D4×C29—81no—
194C2×D4×C29C2×D412yes—
195C2×D4×C29C2×D412yes—
196C2×D4×C29C2×D412yes—
197C2×D4×C29#4112yes—
198C22×C4×C29—24no—
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—42no—
211C22×C4×C29—42no—
212C22×C4×C29—42no—
213C22×C4×C29—42no—
214C22×C4×C29—42no—
215C22×C4×C29—42no—
216C22×C4×C29—42no—
217C22×C4×C29—42no—
218C22×C4×C29—81no—
219C22×C4×C29—81no—
220C22×C4×C29—81no—
221C22×C4×C29C2×D411yescharacteristic
222C22×C4×C29C2×D411yescharacteristic
223C22×C4×C29C2×D411yescharacteristic
224C22×C4×C29C2×D411yescharacteristic
225C22×C4×C29C2×D411yescharacteristic
226C22×C4×C29C2411yescharacteristic
227SD16×C29—44no—
228SD16×C29—44no—
229D8×C29—28no—
230D8×C29—44no—
231C2×C8×C29—21no—
232C2×C8×C29—21no—
233C2×C8×C29—21no—
234C2×C8×C29—21no—
235C2×C8×C29—21no—
236C2×C8×C29—21no—
237C2×C8×C29—21no—
238C2×C8×C29—21no—
239C2×C8×C29—21no—
240C2×C8×C29—21no—
241C2×C8×C29C2×D412yes—
242C2×C8×C29C2×D412yes—
243C4⋊C4×C29—21no—
244C4⋊C4×C29—21no—
245C4⋊C4×C29—21no—
246C4⋊C4×C29—21no—
247C4⋊C4×C29—21no—
248C4⋊C4×C29—21no—
249C4⋊C4×C29—21no—
250C4⋊C4×C29—42no—
251C4⋊C4×C29C2×D412yes—
252C22⋊C4×C29—22no—
253C22⋊C4×C29—41no—
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—
262C42×C29—21no—
263C42×C29—21no—
264C42×C29—21no—
265C42×C29—21no—
266#25174C2911yesmaximal, characteristic, direct product factor, Sylow
267C23×C29—22no—
268C23×C29—22no—
269C23×C29—22no—
270C23×C29—21no—
271C23×C29—22no—
272C23×C29—21no—
273C23×C29—21no—
274C23×C29—21no—
275C23×C29—21no—
276C23×C29—21no—
277C23×C29—21no—
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—41no—
291C23×C29—41no—
292C23×C29—41no—
293C23×C29—41no—
294C23×C29—41no—
295C23×C29C22×D411yescharacteristic
296Q8×C29—22no—
297Q8×C29—22no—
298Q8×C29—41no—
299Q8×C29—41no—
300D4×C29—22no—
301D4×C29—22no—
302D4×C29—22no—
303D4×C29—22no—
304D4×C29—22no—
305D4×C29—48no—
306D4×C29—41no—
307D4×C29—41no—
308D4×C29—41no—
309D4×C29—41no—
310D4×C29—41no—
311D4×C29—41no—
312D4×C29—84no—
313D4×C29—84no—
314D4×C29—84no—
315D4×C29—84no—
316D4×C29#12114yescomplemented
317C2×C4×C29—21no—
318C2×C4×C29—21no—
319C2×C4×C29—21no—
320C2×C4×C29—22no—
321C2×C4×C29—21no—
322C2×C4×C29—21no—
323C2×C4×C29—21no—
324C2×C4×C29—22no—
325C2×C4×C29—21no—
326C2×C4×C29—21no—
327C2×C4×C29—21no—
328C2×C4×C29—21no—
329C2×C4×C29—21no—
330C2×C4×C29—21no—
331C2×C4×C29—21no—
332C2×C4×C29—21no—
333C2×C4×C29—48no—
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—41no—
350C2×C4×C29—41no—
351C2×C4×C29—84no—
352C2×C4×C29—84no—
353C2×C4×C29—84no—
354C2×C4×C29AGL(1,ℤ/8)12yes—
355C2×C4×C29C22×D411yescharacteristic
356C2×C4×C29C22×D411yescharacteristic
357C2×C4×C29C2×#4111yescharacteristic
358C2×C4×C29C2×#4111yescharacteristic
359C2×C4×C29H(5,𝔽2)11yescharacteristic
360C2×C4×C29H(5,𝔽2)11yescharacteristic
361C8×C29—22no—
362C8×C29—22no—
363C8×C29—41no—
364C8×C29—41no—
365C2×#459C2×C2911yescharacteristic, complemented
366C2×#449C2×C2911yescharacteristic, complemented
367C2×#449C2×C2911yescharacteristic, complemented
368C2×#442C2×C2911yescharacteristic, complemented
369#2428C2×C2911yescharacteristic, complemented
370#2339C2×C2911yescharacteristic, complemented
371#2066C2×C2911yescharacteristic, complemented
372#2034C2×C2911yescharacteristic, complemented
373#2033C2×C2911yescharacteristic, complemented
374#2014C2×C2911yescharacteristic, complemented
375#1973C2×C2911yescharacteristic, complemented
376#1924C2×C2911yescharacteristic, complemented
377#1879C2×C2911yescharacteristic, complemented
378#1877C2×C2911yescharacteristic, complemented
379#1862C2×C2911yescharacteristic, complemented
380C22×C29—24no—
381C22×C29—42no—
382C22×C29—42no—
383C22×C29—42no—
384C22×C29—42no—
385C22×C29—42no—
386C22×C29—42no—
387C22×C29—41no—
388C22×C29—41no—
389C22×C29—41no—
390C22×C29—42no—
391C22×C29—41no—
392C22×C29—42no—
393C22×C29—42no—
394C22×C29—41no—
395C22×C29—41no—
396C22×C29—41no—
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×C29—81no—
406C22×C29—81no—
407C22×C29—81no—
408C22×C29#52511yescharacteristic
409C22×C29D4211yescharacteristic
410C22×C29D4211yescharacteristic
411C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
412C22×C29#57511yescharacteristic
413C22×C29#57611yescharacteristic
414C22×C29#57711yescharacteristic
415C4×C29—22no—
416C4×C29—41no—
417C4×C29—42no—
418C4×C29—41no—
419C4×C29—41no—
420C4×C29—41no—
421C4×C29—42no—
422C4×C29—81no—
423C4×C29—81no—
424C4×C29—81no—
425C4×C29C2×#12111yescharacteristic
426C4×C29#53811yescharacteristic
427C4×C29#54611yescharacteristic
428C4×C29#54611yescharacteristic
429C22×#41C22×C2911yescharacteristic
430C22×SD16C22×C2911yescharacteristic
431C22×SD16C22×C2911yescharacteristic
432C22×D8C22×C2911yescharacteristic
433C22×D8C22×C2911yescharacteristic
434C2×#127C22×C2911yescharacteristic
435C2×#121—21no—
436C2×#121C22×C2911yescharacteristic
437C2×#121C22×C2911yescharacteristic
438C2×C4×D4C22×C2911yescharacteristic
439C2×C4×D4C22×C2911yescharacteristic
440C2×C4×D4C22×C2911yescharacteristic
441#459—24no—
442#449—24no—
443#449—24no—
444#442—24no—
445C2×#107C22×C2911yescharacteristic
446C2×#106C22×C2911yescharacteristic
447C2×C4⋊C8C22×C2911yescharacteristic
448C2×#103C22×C2911yescharacteristic
449C2×#103C22×C2911yescharacteristic
450C2×#102C22×C2911yescharacteristic
451C2×#102C22×C2911yescharacteristic
452C2×#102C22×C2911yescharacteristic
453C2×#102C22×C2911yescharacteristic
454C2×#102C22×C2911yescharacteristic
455C2×#102C22×C2911yescharacteristic
456C2×C22⋊C8C22×C2911yescharacteristic
457C2×C22⋊C8C22×C2911yescharacteristic
458C2×#97C22×C2911yescharacteristic
459#394—21no—
460#392—21no—
461#391C22×C2911yescharacteristic
462#391C22×C2911yescharacteristic
463#390C22×C2911yescharacteristic
464#389C22×C2911yescharacteristic
465#386—21no—
466#386—21no—
467#386—21no—
468#381—21no—
469#380C22×C2911yescharacteristic
470C4×C22⋊C4C22×C2911yescharacteristic
471C2×#95—21no—
472#340C22×C2911yescharacteristic
473#340C22×C2911yescharacteristic
474#336C22×C2911yescharacteristic
475#336C22×C2911yescharacteristic
476C2×C29—44no—
477C2×C29—81no—
478C2×C29—82no—
479C2×C29—161no—
480C2×C29#242411yescharacteristic
481C2×C29#311511yescharacteristic
482C2×C29#311911yescharacteristic
483C2×C29#326411yescharacteristic
484C2×C29#326711yescharacteristic
485C2×C29#326811yescharacteristic
486C2×C29#327211yescharacteristic
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C23×C2911yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C23×C2911yescharacteristic
500C22×D4C23×C2911yescharacteristic
501C22×D4C23×C2911yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C2911yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8D4×C2914yescomplemented
519C22×C8C23×C2911yescharacteristic
520C22×C8C23×C2911yescharacteristic
521C22×C8C23×C2911yescharacteristic
522C22×C8C23×C2911yescharacteristic
523#127—22no—
524#127—41no—
525#121—22no—
526#121—22no—
527#121—44no—
528#121—41no—
529#121—41no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—41no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4C23×C2911yescharacteristic
538C2×C4⋊C4C23×C2911yescharacteristic
539C2×C4⋊C4C23×C2911yescharacteristic
540C2×C4⋊C4C23×C2911yescharacteristic
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⋊C4D4×C2911yescharacteristic
550C2×C22⋊C4D4×C2911yescharacteristic
551C2×C42C23×C2911yescharacteristic
552C2×C42C23×C2911yescharacteristic
553#107—41no—
554#106—22no—
555C4⋊C8—22no—
556#103—22no—
557#103—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—41no—
563#102D4×C2914yescomplemented
564C22⋊C8—22no—
565C22⋊C8—22no—
566#97—22no—
567#95—21no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95D4×C2911yescharacteristic
574#95D4×C2911yescharacteristic
575C29#2517411yescharacteristic, direct product factor, Sylow
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C2911yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C2912yes—
590C2×D4—24no—
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—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C2912yes—
620C2×D4C2×D4×C2912yes—
621C2×D4C2×D4×C2912yes—
622C2×D4#41×C2912yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C2911yescharacteristic
647C22×C4C2×D4×C2911yescharacteristic
648C22×C4C2×D4×C2911yescharacteristic
649C22×C4C2×D4×C2911yescharacteristic
650C22×C4C2×D4×C2911yescharacteristic
651C22×C4C24×C2911yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C2912yes—
667C2×C8C2×D4×C2912yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C2912yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C2911yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4C29×#12114yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
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—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4C29×AGL(1,ℤ/8)12yes—
779C2×C4C22×D4×C2911yescharacteristic
780C2×C4C22×D4×C2911yescharacteristic
781C2×C4C2×#41×C2911yescharacteristic
782C2×C4C2×#41×C2911yescharacteristic
783C2×C4C29×H(5,𝔽2)11yescharacteristic
784C2×C4C29×H(5,𝔽2)11yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—42no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C29×#52511yescharacteristic
818C22D42×C2911yescharacteristic
819C22D42×C2911yescharacteristic
820C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
821C22C29×#57511yescharacteristic
822C22C29×#57611yescharacteristic
823C22C29×#57711yescharacteristic
824C4—22no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×C29×#12111yescharacteristic
835C4C29×#53811yescharacteristic
836C4C29×#54611yescharacteristic
837C4C29×#54611yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C29×#242411yescharacteristic
843C2C29×#311511yescharacteristic
844C2C29×#311911yescharacteristic
845C2C29×#326411yescharacteristic
846C2C29×#326711yescharacteristic
847C2C29×#326811yescharacteristic
848C2C29×#327211yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#459C2semidirect
2. C2×C29×#449C2semidirect
3. C2×C29×#449C2semidirect
4. C2×C29×#442C2semidirect
5. C29×#2428C2semidirect
6. C29×#2339C2semidirect
7. C29×#2066C2semidirect
8. C29×#2034C2semidirect
9. C29×#2033C2semidirect
10. C29×#2014C2semidirect
11. C29×#1973C2semidirect
12. C29×#1924C2semidirect
13. C29×#1879C2semidirect
14. C29×#1877C2semidirect
15. C29×#1862C2semidirect
94. C2×D8×C29D4semidirect
139. C29×#102D4semidirect
266. #25174C29direct (N × H)
316. D4×C29#121semidirect
365. C2×#459C2×C29semidirect
366. C2×#449C2×C29semidirect
367. C2×#449C2×C29semidirect
368. C2×#442C2×C29semidirect
369. #2428C2×C29semidirect
370. #2339C2×C29semidirect
371. #2066C2×C29semidirect
372. #2034C2×C29semidirect
373. #2033C2×C29semidirect
374. #2014C2×C29semidirect
375. #1973C2×C29semidirect
376. #1924C2×C29semidirect
377. #1879C2×C29semidirect
378. #1877C2×C29semidirect
379. #1862C2×C29semidirect
518. C2×D8D4×C29semidirect
563. #102D4×C29semidirect
575. C29#25174direct (N × H)
740. D4C29×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#4592
C2×C29×#4492
C2×C29×#4422
C29×#24282
C29×#23392
C29×#20662
C29×#20342
C29×#20332
C29×#20142
C29×#19732
C29×#19242
C29×#18792
C29×#18772
C29×#18622
#2517429