Finite Group Databasebeta

← C29×#24235 #20319135

Subgroups — C29×#24235 #20319135

Order 7424.

1376 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3500C211yesmaximal, characteristic
2C29×#3037C211yesmaximal, characteristic, complemented
3C2×C29×#456C211yesmaximal, characteristic, complemented
4C2×C29×#455C211yesmaximal, characteristic, complemented
5C4×C29×#137C211yesmaximal, characteristic, complemented
6C29×#2545C211yesmaximal, characteristic, complemented
7C29×#2038C211yesmaximal, characteristic, complemented
8C29×#2037C211yesmaximal, characteristic, complemented
9C29×#2005C211yesmaximal, characteristic, complemented
10C29×#2004C211yesmaximal, characteristic, complemented
11C29×#1980C211yesmaximal, characteristic, complemented
12C29×#1967C211yesmaximal, characteristic, complemented
13C29×#1806C211yesmaximal, characteristic, complemented
14C29×#1793C211yesmaximal, characteristic, complemented
15C29×#1792C211yesmaximal, characteristic, complemented
16C2×C29×2−1+4C2211yescharacteristic
17C2×C29×H(5,𝔽2)C2211yescharacteristic
18C2×C29×#137C2211yescharacteristic
19C2×C29×#137C2211yescharacteristic
20C2×C29×#137C2211yescharacteristic, complemented
21C29×#548—21no—
22C29×#548—21no—
23C29×#546—21no—
24C29×#546—21no—
25C29×#546—22no—
26C29×#546—22no—
27C29×#536—21no—
28C29×#536C2211yescharacteristic
29C29×#535—21no—
30C29×#535C2211yescharacteristic
31C29×#532—21no—
32C29×#532C2211yescharacteristic
33C2×C29×C4⋊Q8C2211yescharacteristic, complemented
34C2×C29×#124—21no—
35C2×C29×#124C2211yescharacteristic
36C2×C29×#124C2211yescharacteristic
37C4×#41×C29C2211yescharacteristic
38C2×C4×Q8×C29C2211yescharacteristic, complemented
39C29×#464—21no—
40C29×#464—21no—
41C29×#462—21no—
42C29×#460—21no—
43C29×#456—24no—
44C29×#455—24no—
45C29×#441—21no—
46C29×#440—21no—
47C4×Q16×C29—21no—
48C4×SD16×C29—21no—
49C29×#428C2211yescharacteristic, complemented
50C29×#423C2211yescharacteristic, complemented
51C2×C29×#104C2211yescharacteristic
52C2×C29×#104C2211yescharacteristic
53C2×C29×#104C2211yescharacteristic
54C2×C29×#104C2211yescharacteristic
55C2×C29×#104C2211yescharacteristic, complemented
56C2×C29×#104C2211yescharacteristic, complemented
57C29×#419C2211yescharacteristic, complemented
58C29×#417C2211yescharacteristic
59C29×#417C2211yescharacteristic
60C29×#417C2211yescharacteristic, complemented
61C2×C29×#101C2211yescharacteristic, complemented
62C2×C29×#101C2211yescharacteristic, complemented
63C2×C29×#100C2211yescharacteristic
64C2×C29×#100C2211yescharacteristic
65C4×M16×C29C2211yescharacteristic, complemented
66C29×#396—22no—
67C29×#391C2211yescharacteristic, complemented
68C29×#390C2211yescharacteristic
69C29×#388—22no—
70C4×C4⋊C4×C29C2211yescharacteristic, complemented
71C29×#339C2211yescharacteristic, complemented
72C29×#339C2211yescharacteristic, complemented
73C29×2−1+4—22no—
74C29×2−1+4—22no—
75C29×2−1+4—41no—
76C29×2−1+4—41no—
77C29×H(5,𝔽2)—22no—
78C29×H(5,𝔽2)—22no—
79C29×H(5,𝔽2)—41no—
80C29×H(5,𝔽2)—41no—
81C2×#41×C29—21no—
82C2×#41×C29—21no—
83C2×#41×C29—21no—
84C2×#41×C29—21no—
85C2×#41×C29—22no—
86C2×#41×C29C2311yescharacteristic
87C2×#41×C29C2311yescharacteristic
88C2×#41×C29C2311yescharacteristic
89C22×Q8×C29—21no—
90C22×Q8×C29—21no—
91C22×Q8×C29C2311yescharacteristic
92C22×Q8×C29C2311yescharacteristic
93C22×D4×C29—22no—
94C22×D4×C29—21no—
95C22×D4×C29—21no—
96C22×D4×C29C2311yescharacteristic
97C29×#137—22no—
98C29×#137—22no—
99C29×#137—22no—
100C29×#137—41no—
101C29×#137—41no—
102C29×#137D414yescomplemented
103C2×Q16×C29—21no—
104C2×Q16×C29—21no—
105C2×Q16×C29—21no—
106C2×SD16×C29—21no—
107C2×SD16×C29—21no—
108C2×SD16×C29—21no—
109C2×M16×C29C2311yescharacteristic
110C2×M16×C29C2311yescharacteristic
111C2×M16×C29C2311yescharacteristic
112C2×M16×C29C2311yescharacteristic
113C29×C4⋊Q8—21no—
114C29×C4⋊Q8—22no—
115C29×C4⋊Q8—41no—
116C29×C4⋊Q8D411yescharacteristic
117C29×#127—21no—
118C29×#127D411yescharacteristic
119C29×#124—22no—
120C29×#124—22no—
121C29×#124—21no—
122C29×#124—21no—
123C29×#124—22no—
124C29×#124—21no—
125C29×#124—21no—
126C29×#124—21no—
127C29×#124—21no—
128C29×#124—41no—
129C29×#124D411yescharacteristic
130C29×#124D411yescharacteristic
131C29×#123—22no—
132C29×#123—22no—
133C29×#123—22no—
134C29×C22⋊Q8—22no—
135C29×C22⋊Q8—22no—
136C29×C22⋊Q8—21no—
137C29×C22⋊Q8—21no—
138C29×#121—22no—
139C29×#121—22no—
140C29×#121—22no—
141C29×#121—22no—
142C29×#121—21no—
143C29×#121—21no—
144C29×#121—21no—
145C29×#121—21no—
146C29×#120—22no—
147C29×#120—22no—
148C29×#120—22no—
149C4×Q8×C29—21no—
150C4×Q8×C29—21no—
151C4×Q8×C29—21no—
152C4×Q8×C29—21no—
153C4×Q8×C29D411yescharacteristic
154C4×Q8×C29D411yescharacteristic
155C4×D4×C29—22no—
156C4×D4×C29—22no—
157C4×D4×C29—21no—
158C4×D4×C29—21no—
159C4×D4×C29—21no—
160C4×D4×C29—21no—
161C4×D4×C29D411yescharacteristic
162C4×D4×C29D411yescharacteristic
163C29×#117—21no—
164C29×#117C2311yescharacteristic
165C2×C4⋊C4×C29—21no—
166C2×C4⋊C4×C29—22no—
167C2×C4⋊C4×C29—21no—
168C2×C4⋊C4×C29C2311yescharacteristic
169C2×C22⋊C4×C29—22no—
170C2×C22⋊C4×C29—22no—
171C2×C22⋊C4×C29—22no—
172C2×C22⋊C4×C29—22no—
173C2×C22⋊C4×C29D412yes—
174C2×C22⋊C4×C29D412yes—
175C2×C42×C29—21no—
176C2×C42×C29—21no—
177C2×C42×C29C2311yescharacteristic
178C2×C42×C29C2311yescharacteristic
179C2×C42×C29C2311yescharacteristic
180C29×#107—21no—
181C29×#106—21no—
182C29×C4⋊C8—21no—
183C29×C4⋊C8—21no—
184C29×#104—22no—
185C29×#104—22no—
186C29×#104—22no—
187C29×#104—22no—
188C29×#104—41no—
189C29×#104—41no—
190C29×#103—21no—
191C29×#103—21no—
192C29×#103—21no—
193C29×#103—21no—
194C29×#103—21no—
195C29×#102—21no—
196C29×#102—21no—
197C29×#102—21no—
198C29×#101—22no—
199C29×#101—41no—
200C29×#100—22no—
201C29×#100—41no—
202C29×#97—21no—
203C4×C8×C29—21no—
204C29×#95—21no—
205C29×#95—22no—
206C24×C29—22no—
207C24×C29C2×D412yes—
208#41×C29—21no—
209#41×C29—21no—
210#41×C29—21no—
211#41×C29—21no—
212#41×C29—21no—
213#41×C29—21no—
214#41×C29—21no—
215#41×C29—21no—
216#41×C29—21no—
217#41×C29—21no—
218#41×C29—42no—
219#41×C29—42no—
220#41×C29—44no—
221#41×C29—44no—
222#41×C29—42no—
223#41×C29—42no—
224#41×C29—42no—
225#41×C29—42no—
226#41×C29—42no—
227#41×C29—42no—
228#41×C29C2×D412yes—
229#41×C29#4112yes—
230C2×Q8×C29—22no—
231C2×Q8×C29—21no—
232C2×Q8×C29—21no—
233C2×Q8×C29—21no—
234C2×Q8×C29—21no—
235C2×Q8×C29—21no—
236C2×Q8×C29—21no—
237C2×Q8×C29—21no—
238C2×Q8×C29—21no—
239C2×Q8×C29—21no—
240C2×Q8×C29—21no—
241C2×Q8×C29—21no—
242C2×Q8×C29—42no—
243C2×Q8×C29—42no—
244C2×Q8×C29—42no—
245C2×Q8×C29—42no—
246C2×Q8×C29C2×D411yescharacteristic
247C2×Q8×C29C2×D412yes—
248C2×Q8×C29C2×D411yescharacteristic
249C2×Q8×C29C2×D411yescharacteristic
250C2×D4×C29—21no—
251C2×D4×C29—22no—
252C2×D4×C29—22no—
253C2×D4×C29—22no—
254C2×D4×C29—21no—
255C2×D4×C29—21no—
256C2×D4×C29—22no—
257C2×D4×C29—22no—
258C2×D4×C29—21no—
259C2×D4×C29—21no—
260C2×D4×C29—21no—
261C2×D4×C29—21no—
262C2×D4×C29—21no—
263C2×D4×C29—21no—
264C2×D4×C29—21no—
265C2×D4×C29—21no—
266C2×D4×C29—42no—
267C2×D4×C29—42no—
268C2×D4×C29—44no—
269C2×D4×C29—44no—
270C2×D4×C29—42no—
271C2×D4×C29—42no—
272C2×D4×C29C2×D411yescharacteristic
273C2×D4×C29C2×D411yescharacteristic
274C2×D4×C29C2×D411yescharacteristic
275C22×C4×C29—21no—
276C22×C4×C29—22no—
277C22×C4×C29—22no—
278C22×C4×C29—22no—
279C22×C4×C29—21no—
280C22×C4×C29—21no—
281C22×C4×C29—21no—
282C22×C4×C29—21no—
283C22×C4×C29—21no—
284C22×C4×C29—21no—
285C22×C4×C29—21no—
286C22×C4×C29—21no—
287C22×C4×C29C2×D412yes—
288C22×C4×C29C2×D411yescharacteristic
289C22×C4×C29C2×D411yescharacteristic
290C22×C4×C29C2411yescharacteristic
291Q16×C29—24no—
292Q16×C29—42no—
293Q16×C29—42no—
294SD16×C29—24no—
295SD16×C29—42no—
296SD16×C29—42no—
297M16×C29—21no—
298M16×C29—21no—
299M16×C29—21no—
300M16×C29—21no—
301M16×C29—21no—
302M16×C29—21no—
303M16×C29—21no—
304M16×C29C2×D412yes—
305C2×C8×C29—21no—
306C2×C8×C29—21no—
307C2×C8×C29—21no—
308C2×C8×C29—21no—
309C4⋊C4×C29—22no—
310C4⋊C4×C29—22no—
311C4⋊C4×C29—21no—
312C4⋊C4×C29—21no—
313C4⋊C4×C29—21no—
314C4⋊C4×C29—21no—
315C4⋊C4×C29—21no—
316C4⋊C4×C29—21no—
317C4⋊C4×C29—44no—
318C4⋊C4×C29—42no—
319C4⋊C4×C29—41no—
320C4⋊C4×C29—41no—
321C4⋊C4×C29C2×D411yescharacteristic
322C4⋊C4×C29C2×D411yescharacteristic
323C22⋊C4×C29—22no—
324C22⋊C4×C29—22no—
325C22⋊C4×C29—22no—
326C22⋊C4×C29—22no—
327C22⋊C4×C29—21no—
328C22⋊C4×C29—21no—
329C22⋊C4×C29—21no—
330C22⋊C4×C29—22no—
331C22⋊C4×C29—22no—
332C22⋊C4×C29—22no—
333C22⋊C4×C29—22no—
334C22⋊C4×C29—21no—
335C22⋊C4×C29—21no—
336C22⋊C4×C29—21no—
337C22⋊C4×C29—21no—
338C22⋊C4×C29—44no—
339C22⋊C4×C29—44no—
340C42×C29—21no—
341C42×C29—21no—
342C42×C29—21no—
343C42×C29—21no—
344C42×C29—21no—
345C42×C29—21no—
346C42×C29—21no—
347C42×C29—41no—
348C42×C29—41no—
349C42×C29C2×D411yescharacteristic
350C42×C29C2×D411yescharacteristic
351C42×C29C2×D411yescharacteristic
352C42×C29C2×D411yescharacteristic
353#24235C2911yesmaximal, characteristic, direct product factor, Sylow
354C23×C29—21no—
355C23×C29—22no—
356C23×C29—21no—
357C23×C29—21no—
358C23×C29—22no—
359C23×C29—22no—
360C23×C29—44no—
361C23×C29—42no—
362C23×C29—42no—
363C23×C29—82no—
364C23×C29—82no—
365C23×C29C22×D411yescharacteristic
366Q8×C29—21no—
367Q8×C29—22no—
368Q8×C29—22no—
369Q8×C29—21no—
370Q8×C29—21no—
371Q8×C29—21no—
372Q8×C29—21no—
373Q8×C29—44no—
374Q8×C29—41no—
375Q8×C29—41no—
376Q8×C29—41no—
377Q8×C29—41no—
378Q8×C29—41no—
379Q8×C29—41no—
380Q8×C29#12112yes—
381D4×C29—22no—
382D4×C29—22no—
383D4×C29—21no—
384D4×C29—21no—
385D4×C29—21no—
386D4×C29—21no—
387D4×C29—21no—
388D4×C29—44no—
389D4×C29—44no—
390D4×C29—44no—
391D4×C29—41no—
392D4×C29—41no—
393D4×C29—41no—
394D4×C29—41no—
395D4×C29—41no—
396D4×C29—41no—
397D4×C29—41no—
398D4×C29—41no—
399D4×C29—81no—
400D4×C29—81no—
401D4×C29—82no—
402D4×C29—82no—
403D4×C29#12112yes—
404C2×C4×C29—21no—
405C2×C4×C29—22no—
406C2×C4×C29—22no—
407C2×C4×C29—22no—
408C2×C4×C29—21no—
409C2×C4×C29—21no—
410C2×C4×C29—21no—
411C2×C4×C29—22no—
412C2×C4×C29—21no—
413C2×C4×C29—22no—
414C2×C4×C29—22no—
415C2×C4×C29—22no—
416C2×C4×C29—41no—
417C2×C4×C29—41no—
418C2×C4×C29—44no—
419C2×C4×C29—44no—
420C2×C4×C29—41no—
421C2×C4×C29—44no—
422C2×C4×C29—41no—
423C2×C4×C29—41no—
424C2×C4×C29—41no—
425C2×C4×C29—41no—
426C2×C4×C29—41no—
427C2×C4×C29—41no—
428C2×C4×C29—41no—
429C2×C4×C29—42no—
430C2×C4×C29—41no—
431C2×C4×C29—41no—
432C2×C4×C29—41no—
433C2×C4×C29—41no—
434C2×C4×C29—81no—
435C2×C4×C29—81no—
436C2×C4×C29#12011yescharacteristic
437C2×C4×C29#12011yescharacteristic
438C2×C4×C29#12011yescharacteristic
439C2×C4×C29#12011yescharacteristic
440C2×C4×C29C22×D411yescharacteristic
441C2×C4×C29C22×D411yescharacteristic
442C2×C4×C29C22×D411yescharacteristic
443C2×C4×C29C2×#4111yescharacteristic
444C2×C4×C29H(5,𝔽2)11yescharacteristic
445C2×C4×C29H(5,𝔽2)11yescharacteristic
446C8×C29—22no—
447C8×C29—41no—
448C8×C29—41no—
449C8×C29—41no—
450#3500C2×C2911yescharacteristic
451#3037C2×C2911yescharacteristic, complemented
452C2×#456C2×C2911yescharacteristic, complemented
453C2×#455C2×C2911yescharacteristic, complemented
454C4×#137C2×C2911yescharacteristic, complemented
455#2545C2×C2911yescharacteristic, complemented
456#2038C2×C2911yescharacteristic, complemented
457#2037C2×C2911yescharacteristic, complemented
458#2005C2×C2911yescharacteristic, complemented
459#2004C2×C2911yescharacteristic, complemented
460#1980C2×C2911yescharacteristic, complemented
461#1967C2×C2911yescharacteristic, complemented
462#1806C2×C2911yescharacteristic, complemented
463#1793C2×C2911yescharacteristic, complemented
464#1792C2×C2911yescharacteristic, complemented
465C22×C29—21no—
466C22×C29—21no—
467C22×C29—22no—
468C22×C29—41no—
469C22×C29—41no—
470C22×C29—41no—
471C22×C29—41no—
472C22×C29—42no—
473C22×C29—41no—
474C22×C29—42no—
475C22×C29—41no—
476C22×C29—41no—
477C22×C29—42no—
478C22×C29—41no—
479C22×C29—82no—
480C22×C29—82no—
481C22×C29—164no—
482C22×C29C2×#12011yescharacteristic
483C22×C29D4211yescharacteristic
484C22×C29#54611yescharacteristic
485C4×C29—22no—
486C4×C29—21no—
487C4×C29—21no—
488C4×C29—21no—
489C4×C29—21no—
490C4×C29—42no—
491C4×C29—42no—
492C4×C29—41no—
493C4×C29—41no—
494C4×C29—42no—
495C4×C29—41no—
496C4×C29—41no—
497C4×C29—81no—
498C4×C29—81no—
499C4×C29C2×#12111yescharacteristic
500C4×C29#53511yescharacteristic
501C4×C29D4211yescharacteristic
502C4×C29#54611yescharacteristic
503C2×2−1+4C22×C2911yescharacteristic
504C2×H(5,𝔽2)C22×C2911yescharacteristic
505C2×#137C22×C2911yescharacteristic
506C2×#137C22×C2911yescharacteristic
507C2×#137C22×C2911yescharacteristic, complemented
508#548—21no—
509#548—21no—
510#546—21no—
511#546—21no—
512#546—22no—
513#546—22no—
514#536—21no—
515#536C22×C2911yescharacteristic
516#535—21no—
517#535C22×C2911yescharacteristic
518#532—21no—
519#532C22×C2911yescharacteristic
520C2×C4⋊Q8C22×C2911yescharacteristic, complemented
521C2×#124—21no—
522C2×#124C22×C2911yescharacteristic
523C2×#124C22×C2911yescharacteristic
524C4×#41C22×C2911yescharacteristic
525C2×C4×Q8C22×C2911yescharacteristic, complemented
526#464—21no—
527#464—21no—
528#462—21no—
529#460—21no—
530#456—24no—
531#455—24no—
532#441—21no—
533#440—21no—
534C4×Q16—21no—
535C4×SD16—21no—
536#428C22×C2911yescharacteristic, complemented
537#423C22×C2911yescharacteristic, complemented
538C2×#104C22×C2911yescharacteristic
539C2×#104C22×C2911yescharacteristic
540C2×#104C22×C2911yescharacteristic
541C2×#104C22×C2911yescharacteristic
542C2×#104C22×C2911yescharacteristic, complemented
543C2×#104C22×C2911yescharacteristic, complemented
544#419C22×C2911yescharacteristic, complemented
545#417C22×C2911yescharacteristic
546#417C22×C2911yescharacteristic
547#417C22×C2911yescharacteristic, complemented
548C2×#101C22×C2911yescharacteristic, complemented
549C2×#101C22×C2911yescharacteristic, complemented
550C2×#100C22×C2911yescharacteristic
551C2×#100C22×C2911yescharacteristic
552C4×M16C22×C2911yescharacteristic, complemented
553#396—22no—
554#391C22×C2911yescharacteristic, complemented
555#390C22×C2911yescharacteristic
556#388—22no—
557C4×C4⋊C4C22×C2911yescharacteristic, complemented
558#339C22×C2911yescharacteristic, complemented
559#339C22×C2911yescharacteristic, complemented
560C2×C29—21no—
561C2×C29—21no—
562C2×C29—42no—
563C2×C29—81no—
564C2×C29—82no—
565C2×C29—81no—
566C2×C29#240811yescharacteristic
567C2×C29#301811yescharacteristic
568C2×C29#302211yescharacteristic
5692−1+4—22no—
5702−1+4—22no—
5712−1+4—41no—
5722−1+4—41no—
573H(5,𝔽2)—22no—
574H(5,𝔽2)—22no—
575H(5,𝔽2)—41no—
576H(5,𝔽2)—41no—
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—22no—
582C2×#41C23×C2911yescharacteristic
583C2×#41C23×C2911yescharacteristic
584C2×#41C23×C2911yescharacteristic
585C22×Q8—21no—
586C22×Q8—21no—
587C22×Q8C23×C2911yescharacteristic
588C22×Q8C23×C2911yescharacteristic
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4C23×C2911yescharacteristic
593#137—22no—
594#137—22no—
595#137—22no—
596#137—41no—
597#137—41no—
598#137D4×C2914yescomplemented
599C2×Q16—21no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×M16C23×C2911yescharacteristic
606C2×M16C23×C2911yescharacteristic
607C2×M16C23×C2911yescharacteristic
608C2×M16C23×C2911yescharacteristic
609C4⋊Q8—21no—
610C4⋊Q8—22no—
611C4⋊Q8—41no—
612C4⋊Q8D4×C2911yescharacteristic
613#127—21no—
614#127D4×C2911yescharacteristic
615#124—22no—
616#124—22no—
617#124—21no—
618#124—21no—
619#124—22no—
620#124—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—41no—
625#124D4×C2911yescharacteristic
626#124D4×C2911yescharacteristic
627#123—22no—
628#123—22no—
629#123—22no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—22no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#120—22no—
643#120—22no—
644#120—22no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—21no—
648C4×Q8—21no—
649C4×Q8D4×C2911yescharacteristic
650C4×Q8D4×C2911yescharacteristic
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4D4×C2911yescharacteristic
658C4×D4D4×C2911yescharacteristic
659#117—21no—
660#117C23×C2911yescharacteristic
661C2×C4⋊C4—21no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4C23×C2911yescharacteristic
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4D4×C2912yes—
670C2×C22⋊C4D4×C2912yes—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42C23×C2911yescharacteristic
674C2×C42C23×C2911yescharacteristic
675C2×C42C23×C2911yescharacteristic
676#107—21no—
677#106—21no—
678C4⋊C8—21no—
679C4⋊C8—21no—
680#104—22no—
681#104—22no—
682#104—22no—
683#104—22no—
684#104—41no—
685#104—41no—
686#103—21no—
687#103—21no—
688#103—21no—
689#103—21no—
690#103—21no—
691#102—21no—
692#102—21no—
693#102—21no—
694#101—22no—
695#101—41no—
696#100—22no—
697#100—41no—
698#97—21no—
699C4×C8—21no—
700#95—21no—
701#95—22no—
702C29#2423511yescharacteristic, direct product factor, Sylow
703C24—22no—
704C24C2×D4×C2912yes—
705#41—21no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—21no—
715#41—42no—
716#41—42no—
717#41—44no—
718#41—44no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41—42no—
725#41C2×D4×C2912yes—
726#41#41×C2912yes—
727C2×Q8—22no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—42no—
740C2×Q8—42no—
741C2×Q8—42no—
742C2×Q8—42no—
743C2×Q8C2×D4×C2911yescharacteristic
744C2×Q8C2×D4×C2911yescharacteristic
745C2×Q8C2×D4×C2912yes—
746C2×Q8C2×D4×C2911yescharacteristic
747C2×D4—21no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—22no—
754C2×D4—22no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4C2×D4×C2911yescharacteristic
770C2×D4C2×D4×C2911yescharacteristic
771C2×D4C2×D4×C2911yescharacteristic
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4C2×D4×C2912yes—
785C22×C4C2×D4×C2911yescharacteristic
786C22×C4C2×D4×C2911yescharacteristic
787C22×C4C24×C2911yescharacteristic
788Q16—24no—
789Q16—42no—
790Q16—42no—
791SD16—24no—
792SD16—42no—
793SD16—42no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16C2×D4×C2912yes—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—44no—
815C4⋊C4—42no—
816C4⋊C4—41no—
817C4⋊C4—41no—
818C4⋊C4C2×D4×C2911yescharacteristic
819C4⋊C4C2×D4×C2911yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—22no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C42—21no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—21no—
844C42—41no—
845C42—41no—
846C42C2×D4×C2911yescharacteristic
847C42C2×D4×C2911yescharacteristic
848C42C2×D4×C2911yescharacteristic
849C42C2×D4×C2911yescharacteristic
850C23—21no—
851C23—22no—
852C23—21no—
853C23—21no—
854C23—22no—
855C23—22no—
856C23—44no—
857C23—42no—
858C23—42no—
859C23—82no—
860C23—82no—
861C23C22×D4×C2911yescharacteristic
862Q8—21no—
863Q8—22no—
864Q8—22no—
865Q8—21no—
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—44no—
870Q8—41no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875Q8—41no—
876Q8C29×#12112yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—21no—
883D4—21no—
884D4—44no—
885D4—44no—
886D4—44no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4C29×#12112yes—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4C29×#12011yescharacteristic
933C2×C4C29×#12011yescharacteristic
934C2×C4C29×#12011yescharacteristic
935C2×C4C29×#12011yescharacteristic
936C2×C4C22×D4×C2911yescharacteristic
937C2×C4C22×D4×C2911yescharacteristic
938C2×C4C22×D4×C2911yescharacteristic
939C2×C4C2×#41×C2911yescharacteristic
940C2×C4C29×H(5,𝔽2)11yescharacteristic
941C2×C4C29×H(5,𝔽2)11yescharacteristic
942C8—22no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—22no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—42no—
953C22—41no—
954C22—41no—
955C22—42no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—42no—
960C22—82no—
961C22—82no—
962C22—164no—
963C22C2×C29×#12011yescharacteristic
964C22D42×C2911yescharacteristic
965C22C29×#54611yescharacteristic
966C4—21no—
967C4—21no—
968C4—21no—
969C4—21no—
970C4—22no—
971C4—42no—
972C4—41no—
973C4—41no—
974C4—42no—
975C4—41no—
976C4—41no—
977C4—42no—
978C4—81no—
979C4—81no—
980C4C2×C29×#12111yescharacteristic
981C4C29×#53511yescharacteristic
982C4D42×C2911yescharacteristic
983C4C29×#54611yescharacteristic
984C2—21no—
985C2—21no—
986C2—42no—
987C2—82no—
988C2—81no—
989C2—81no—
990C2C29×#240811yescharacteristic
991C2C29×#301811yescharacteristic
992C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3500C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3037C2semidirect
3. C2×C29×#456C2semidirect
4. C2×C29×#455C2semidirect
5. C4×C29×#137C2semidirect
6. C29×#2545C2semidirect
7. C29×#2038C2semidirect
8. C29×#2037C2semidirect
9. C29×#2005C2semidirect
10. C29×#2004C2semidirect
11. C29×#1980C2semidirect
12. C29×#1967C2semidirect
13. C29×#1806C2semidirect
14. C29×#1793C2semidirect
15. C29×#1792C2semidirect
20. C2×C29×#137C22semidirect
33. C2×C29×C4⋊Q8C22semidirect
38. C2×C4×Q8×C29C22semidirect
49. C29×#428C22semidirect
50. C29×#423C22semidirect
55. C2×C29×#104C22semidirect
56. C2×C29×#104C22semidirect
57. C29×#419C22semidirect
60. C29×#417C22semidirect
61. C2×C29×#101C22semidirect
62. C2×C29×#101C22semidirect
65. C4×M16×C29C22semidirect
67. C29×#391C22semidirect
70. C4×C4⋊C4×C29C22semidirect
71. C29×#339C22semidirect
72. C29×#339C22semidirect
102. C29×#137D4semidirect
353. #24235C29direct (N × H)
451. #3037C2×C29semidirect
452. C2×#456C2×C29semidirect
453. C2×#455C2×C29semidirect
454. C4×#137C2×C29semidirect
455. #2545C2×C29semidirect
456. #2038C2×C29semidirect
457. #2037C2×C29semidirect
458. #2005C2×C29semidirect
459. #2004C2×C29semidirect
460. #1980C2×C29semidirect
461. #1967C2×C29semidirect
462. #1806C2×C29semidirect
463. #1793C2×C29semidirect
464. #1792C2×C29semidirect
507. C2×#137C22×C29semidirect
520. C2×C4⋊Q8C22×C29semidirect
525. C2×C4×Q8C22×C29semidirect
536. #428C22×C29semidirect
537. #423C22×C29semidirect
542. C2×#104C22×C29semidirect
543. C2×#104C22×C29semidirect
544. #419C22×C29semidirect
547. #417C22×C29semidirect
548. C2×#101C22×C29semidirect
549. C2×#101C22×C29semidirect
552. C4×M16C22×C29semidirect
554. #391C22×C29semidirect
557. C4×C4⋊C4C22×C29semidirect
558. #339C22×C29semidirect
559. #339C22×C29semidirect
598. #137D4×C29semidirect
702. C29#24235direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35002
C29×#30372
C2×C29×#4562
C2×C29×#4552
C4×C29×#1372
C29×#25452
C29×#20382
C29×#20372
C29×#20052
C29×#20042
C29×#19802
C29×#19672
C29×#18062
C29×#17932
C29×#17922
#2423529