Finite Group Databasebeta

← C29×#23098 #20317998

Subgroups — C29×#23098 #20317998

Order 7424.

906 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#463C211yesmaximal, characteristic
2C29×#2367C211yesmaximal, characteristic, complemented
3C29×#2357C211yesmaximal, characteristic, complemented
4C29×#1970C211yesmaximal, characteristic
5C29×#1968C211yesmaximal, characteristic, complemented
6C29×#1958C211yesmaximal, characteristic, complemented
7C29×#1949C211yesmaximal, characteristic, complemented
8C29×#1928C211yesmaximal, characteristic, complemented
9C29×#1926C211yesmaximal, characteristic, complemented
10C29×#1880C211yesmaximal, characteristic, complemented
11C29×#1879C211yesmaximal, characteristic
12C8×C4⋊C4×C29C211yesmaximal, characteristic, complemented
13C4×C29×#103C211yesmaximal, characteristic, complemented
14C4×C29×#102C211yesmaximal, characteristic, complemented
15C4×C29×#102C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C22×D8×C29C2211yescharacteristic
18C2×C29×#124C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C2×C4×D4×C29C2211yescharacteristic
21C2×C4×D4×C29C2211yescharacteristic
22C29×#463C418yescomplemented
23C2×C29×#107C2211yescharacteristic
24C2×C29×#106C2211yescharacteristic
25C2×C29×C4⋊C8C2211yescharacteristic
26C2×C29×#103C2211yescharacteristic
27C2×C29×#103C2211yescharacteristic
28C2×C29×#103C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×#102C2211yescharacteristic
32C2×C29×#102C2211yescharacteristic
33C2×C29×#102C2211yescharacteristic
34C2×C4×C8×C29C2211yescharacteristic
35C2×C4×C8×C29C2211yescharacteristic
36C2×C4×C8×C29C2211yescharacteristic
37C29×#391C2211yescharacteristic
38C29×#390C2211yescharacteristic
39C29×#390C2211yescharacteristic
40C29×#390C2211yescharacteristic
41C29×#388—21no—
42C29×#388—21no—
43C29×#388—21no—
44C29×#388—21no—
45C29×#385—21no—
46C29×#382C2211yescharacteristic
47C29×#381—21no—
48C4×C4⋊C4×C29C2211yescharacteristic
49C4×C4⋊C4×C29C2211yescharacteristic
50C4×C4⋊C4×C29C2211yescharacteristic
51C4×C4⋊C4×C29C2211yescharacteristic
52C4×C22⋊C4×C29—21no—
53C4×C22⋊C4×C29—21no—
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C22×Q8×C29C2311yescharacteristic
61C22×D4×C29C2311yescharacteristic
62C22×D4×C29C2311yescharacteristic
63C23×C4×C29—21no—
64C23×C4×C29—21no—
65C2×SD16×C29—41no—
66C2×SD16×C29—41no—
67C2×SD16×C29C2×C414yescomplemented
68C2×D8×C29—41no—
69C2×D8×C29—41no—
70C2×D8×C29C2×C414yes—
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C29×#124—22no—
76C29×#124C2×C414yes—
77C4×Q8×C29—22no—
78C4×Q8×C29—41no—
79C4×D4×C29—22no—
80C4×D4×C29—22no—
81C4×D4×C29—41no—
82C4×D4×C29C2×C414yescomplemented
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29D411yescharacteristic
85C2×C4⋊C4×C29D411yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—21no—
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29—21no—
100C2×C22⋊C4×C29—21no—
101C2×C42×C29—21no—
102C2×C42×C29—21no—
103C2×C42×C29—21no—
104C2×C42×C29—21no—
105C2×C42×C29C2311yescharacteristic
106C2×C42×C29C2311yescharacteristic
107C2×C42×C29C2311yescharacteristic
108C29×#107—41no—
109C29×#106—41no—
110C29×C4⋊C8C2×C414yescomplemented
111C29×#103—22no—
112C29×#103—41no—
113C29×#103C2×C414yescomplemented
114C29×#102—22no—
115C29×#102—22no—
116C29×#102—22no—
117C29×#102—41no—
118C29×#102C2×C414yes—
119C4×C8×C29—22no—
120C4×C8×C29—41no—
121C4×C8×C29—41no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95—21no—
125C29×#95—21no—
126C29×#95—21no—
127C29×#95—21no—
128C29×#95—21no—
129C29×#95D411yescharacteristic
130C29×#95D411yescharacteristic
131C24×C29—21no—
132C24×C29—21no—
133C2×Q8×C29—21no—
134C2×Q8×C29—21no—
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29C22×C412yes—
139C2×D4×C29—21no—
140C2×D4×C29—21no—
141C2×D4×C29—21no—
142C2×D4×C29—21no—
143C2×D4×C29—21no—
144C2×D4×C29—21no—
145C2×D4×C29—21no—
146C2×D4×C29—21no—
147C2×D4×C29—21no—
148C2×D4×C29—21no—
149C2×D4×C29C22×C412yes—
150C2×D4×C29C22×C412yes—
151C22×C4×C29—21no—
152C22×C4×C29—21no—
153C22×C4×C29—21no—
154C22×C4×C29—24no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—21no—
158C22×C4×C29—42no—
159C22×C4×C29—42no—
160C22×C4×C29—81no—
161C22×C4×C29—81no—
162C22×C4×C29—81no—
163C22×C4×C29C2×D411yescharacteristic
164C22×C4×C29C2×D411yescharacteristic
165C22×C4×C29C2×D411yescharacteristic
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2411yescharacteristic
170SD16×C29—44no—
171D8×C29—44no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29C22×C412yes—
182C2×C8×C29C22×C412yes—
183C2×C8×C29#4112yes—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—42no—
195C4⋊C4×C29C22×C412yes—
196C4⋊C4×C29#4112yes—
197C22⋊C4×C29—24no—
198C22⋊C4×C29—24no—
199C22⋊C4×C29—24no—
200C22⋊C4×C29—42no—
201C22⋊C4×C29—42no—
202C22⋊C4×C29—42no—
203C22⋊C4×C29—42no—
204C22⋊C4×C29—81no—
205C22⋊C4×C29—81no—
206C22⋊C4×C29—81no—
207C42×C29—21no—
208C42×C29—21no—
209C42×C29—21no—
210C42×C29—21no—
211C42×C29—42no—
212C42×C29—81no—
213C42×C29—81no—
214C42×C29—81no—
215C42×C29C22×C412yes—
216C42×C29#4112yes—
217#23098C2911yesmaximal, characteristic, direct product factor, Sylow
218C23×C29—22no—
219C23×C29—22no—
220C23×C29—41no—
221C23×C29—41no—
222C23×C29—41no—
223C23×C29—41no—
224C23×C29—41no—
225C23×C29—41no—
226C23×C29—41no—
227C23×C29—41no—
228C23×C29—41no—
229C23×C29—41no—
230C23×C29—41no—
231C23×C29—41no—
232C23×C29C22×D411yescharacteristic
233Q8×C29—22no—
234Q8×C29—22no—
235Q8×C29—41no—
236Q8×C29—41no—
237D4×C29—22no—
238D4×C29—22no—
239D4×C29—22no—
240D4×C29—22no—
241D4×C29—41no—
242D4×C29—41no—
243D4×C29—41no—
244D4×C29—41no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—22no—
254C2×C4×C29—22no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—22no—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—41no—
267C2×C4×C29—41no—
268C2×C4×C29—41no—
269C2×C4×C29—41no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29—41no—
273C2×C4×C29—41no—
274C2×C4×C29—41no—
275C2×C4×C29—41no—
276C2×C4×C29—41no—
277C2×C4×C29—84no—
278C2×C4×C29—84no—
279C2×C4×C29C4×D412yes—
280C2×C4×C29C4×D412yes—
281C2×C4×C29#13512yes—
282C2×C4×C29#13512yes—
283C2×C4×C29C23×C411yescharacteristic
284C2×C4×C29C2×#4111yescharacteristic
285C2×C4×C29C2×#4111yescharacteristic
286C2×C4×C29C2×#4111yescharacteristic
287C2×C4×C29H(5,𝔽2)11yescharacteristic
288C2×C4×C29H(5,𝔽2)11yescharacteristic
289C8×C29—22no—
290C8×C29—22no—
291C8×C29—22no—
292C8×C29—41no—
293C2×#463C2×C2911yescharacteristic
294#2367C2×C2911yescharacteristic, complemented
295#2357C2×C2911yescharacteristic, complemented
296#1970C2×C2911yescharacteristic
297#1968C2×C2911yescharacteristic, complemented
298#1958C2×C2911yescharacteristic, complemented
299#1949C2×C2911yescharacteristic, complemented
300#1928C2×C2911yescharacteristic, complemented
301#1926C2×C2911yescharacteristic, complemented
302#1880C2×C2911yescharacteristic, complemented
303#1879C2×C2911yescharacteristic
304C8×C4⋊C4C2×C2911yescharacteristic, complemented
305C4×#103C2×C2911yescharacteristic, complemented
306C4×#102C2×C2911yescharacteristic, complemented
307C4×#102C2×C2911yescharacteristic, complemented
308C22×C29—42no—
309C22×C29—42no—
310C22×C29—42no—
311C22×C29—42no—
312C22×C29—42no—
313C22×C29—42no—
314C22×C29—81no—
315C22×C29—81no—
316C22×C29—81no—
317C22×C29—81no—
318C22×C29—81no—
319C22×C29—81no—
320C22×C29—81no—
321C22×C29—81no—
322C22×C29C2×C4×D411yescharacteristic
323C22×C29#54611yescharacteristic
324C22×C29#55011yescharacteristic
325C22×C29C2×#13511yescharacteristic
326C22×C29C2×#13511yescharacteristic
327C22×C29#57611yescharacteristic
328C22×C29#57711yescharacteristic
329C4×C29—22no—
330C4×C29—22no—
331C4×C29—22no—
332C4×C29—22no—
333C4×C29—42no—
334C4×C29—42no—
335C4×C29—41no—
336C4×C29—42no—
337C4×C29—41no—
338C4×C29—81no—
339C4×C29—81no—
340C4×C29—81no—
341C4×C29C4×#4111yescharacteristic
342C4×C29#51811yescharacteristic
343C4×C29#55311yescharacteristic
344C4×C29#55511yescharacteristic
345C22×SD16C22×C2911yescharacteristic
346C22×D8C22×C2911yescharacteristic
347C2×#124C22×C2911yescharacteristic
348C2×C4×Q8C22×C2911yescharacteristic
349C2×C4×D4C22×C2911yescharacteristic
350C2×C4×D4C22×C2911yescharacteristic
351#463C4×C2918yescomplemented
352C2×#107C22×C2911yescharacteristic
353C2×#106C22×C2911yescharacteristic
354C2×C4⋊C8C22×C2911yescharacteristic
355C2×#103C22×C2911yescharacteristic
356C2×#103C22×C2911yescharacteristic
357C2×#103C22×C2911yescharacteristic
358C2×#102C22×C2911yescharacteristic
359C2×#102C22×C2911yescharacteristic
360C2×#102C22×C2911yescharacteristic
361C2×#102C22×C2911yescharacteristic
362C2×#102C22×C2911yescharacteristic
363C2×C4×C8C22×C2911yescharacteristic
364C2×C4×C8C22×C2911yescharacteristic
365C2×C4×C8C22×C2911yescharacteristic
366#391C22×C2911yescharacteristic
367#390C22×C2911yescharacteristic
368#390C22×C2911yescharacteristic
369#390C22×C2911yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#385—21no—
375#382C22×C2911yescharacteristic
376#381—21no—
377C4×C4⋊C4C22×C2911yescharacteristic
378C4×C4⋊C4C22×C2911yescharacteristic
379C4×C4⋊C4C22×C2911yescharacteristic
380C4×C4⋊C4C22×C2911yescharacteristic
381C4×C22⋊C4—21no—
382C4×C22⋊C4—21no—
383#340C22×C2911yescharacteristic
384#340C22×C2911yescharacteristic
385#340C22×C2911yescharacteristic
386#340C22×C2911yescharacteristic
387#336C22×C2911yescharacteristic
388#336C22×C2911yescharacteristic
389C2×C29—82no—
390C2×C29—82no—
391C2×C29#236311yescharacteristic
392C2×C29C4×#13511yescharacteristic
393C2×C29#294611yescharacteristic
394C2×C29#329711yescharacteristic
395C2×C29#330111yescharacteristic
396C2×C29#339411yescharacteristic
397C2×C29#339611yescharacteristic
398C22×Q8C23×C2911yescharacteristic
399C22×D4C23×C2911yescharacteristic
400C22×D4C23×C2911yescharacteristic
401C23×C4—21no—
402C23×C4—21no—
403C2×SD16—41no—
404C2×SD16—41no—
405C2×SD16C2×C4×C2914yescomplemented
406C2×D8—41no—
407C2×D8—41no—
408C2×D8C2×C4×C2914yes—
409C22×C8C23×C2911yescharacteristic
410C22×C8C23×C2911yescharacteristic
411C22×C8C23×C2911yescharacteristic
412C22×C8C23×C2911yescharacteristic
413#124—22no—
414#124C2×C4×C2914yes—
415C4×Q8—22no—
416C4×Q8—41no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—41no—
420C4×D4C2×C4×C2914yescomplemented
421C2×C4⋊C4—21no—
422C2×C4⋊C4D4×C2911yescharacteristic
423C2×C4⋊C4D4×C2911yescharacteristic
424C2×C4⋊C4C23×C2911yescharacteristic
425C2×C4⋊C4C23×C2911yescharacteristic
426C2×C4⋊C4C23×C2911yescharacteristic
427C2×C4⋊C4C23×C2911yescharacteristic
428C2×C4⋊C4C23×C2911yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C2911yescharacteristic
444C2×C42C23×C2911yescharacteristic
445C2×C42C23×C2911yescharacteristic
446#107—41no—
447#106—41no—
448C4⋊C8C2×C4×C2914yescomplemented
449#103—22no—
450#103—41no—
451#103C2×C4×C2914yescomplemented
452#102—22no—
453#102—22no—
454#102—22no—
455#102—41no—
456#102C2×C4×C2914yes—
457C4×C8—22no—
458C4×C8—41no—
459C4×C8—41no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95D4×C2911yescharacteristic
468#95D4×C2911yescharacteristic
469C29#2309811yescharacteristic, direct product factor, Sylow
470C24—21no—
471C24—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C22×C4×C2912yes—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C22×C4×C2912yes—
489C2×D4C22×C4×C2912yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C2×D4×C2911yescharacteristic
503C22×C4C2×D4×C2911yescharacteristic
504C22×C4C2×D4×C2911yescharacteristic
505C22×C4C2×D4×C2911yescharacteristic
506C22×C4C2×D4×C2911yescharacteristic
507C22×C4C2×D4×C2911yescharacteristic
508C22×C4C24×C2911yescharacteristic
509SD16—44no—
510D8—44no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C22×C4×C2912yes—
521C2×C8C22×C4×C2912yes—
522C2×C8#41×C2912yes—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4C22×C4×C2912yes—
535C4⋊C4#41×C2912yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—81no—
552C42—81no—
553C42—81no—
554C42C22×C4×C2912yes—
555C42#41×C2912yes—
556C23—22no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23C22×D4×C2911yescharacteristic
571Q8—22no—
572Q8—22no—
573Q8—41no—
574Q8—41no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—84no—
616C2×C4—84no—
617C2×C4C4×D4×C2912yes—
618C2×C4C4×D4×C2912yes—
619C2×C4C29×#13512yes—
620C2×C4C29×#13512yes—
621C2×C4C23×C4×C2911yescharacteristic
622C2×C4C2×#41×C2911yescharacteristic
623C2×C4C2×#41×C2911yescharacteristic
624C2×C4C2×#41×C2911yescharacteristic
625C2×C4C29×H(5,𝔽2)11yescharacteristic
626C2×C4C29×H(5,𝔽2)11yescharacteristic
627C8—22no—
628C8—22no—
629C8—22no—
630C8—41no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22C2×C4×D4×C2911yescharacteristic
646C22C29×#54611yescharacteristic
647C22C29×#55011yescharacteristic
648C22C2×C29×#13511yescharacteristic
649C22C2×C29×#13511yescharacteristic
650C22C29×#57611yescharacteristic
651C22C29×#57711yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—42no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4C4×#41×C2911yescharacteristic
665C4C29×#51811yescharacteristic
666C4C29×#55311yescharacteristic
667C4C29×#55511yescharacteristic
668C2—82no—
669C2—82no—
670C2C29×#236311yescharacteristic
671C2C4×C29×#13511yescharacteristic
672C2C29×#294611yescharacteristic
673C2C29×#329711yescharacteristic
674C2C29×#330111yescharacteristic
675C2C29×#339411yescharacteristic
676C2C29×#339611yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
prime radicalC22×D8×C29C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2367C2semidirect
3. C29×#2357C2semidirect
5. C29×#1968C2semidirect
6. C29×#1958C2semidirect
7. C29×#1949C2semidirect
8. C29×#1928C2semidirect
9. C29×#1926C2semidirect
10. C29×#1880C2semidirect
12. C8×C4⋊C4×C29C2semidirect
13. C4×C29×#103C2semidirect
14. C4×C29×#102C2semidirect
15. C4×C29×#102C2semidirect
22. C29×#463C4semidirect
67. C2×SD16×C29C2×C4semidirect
82. C4×D4×C29C2×C4semidirect
110. C29×C4⋊C8C2×C4semidirect
113. C29×#103C2×C4semidirect
217. #23098C29direct (N × H)
294. #2367C2×C29semidirect
295. #2357C2×C29semidirect
297. #1968C2×C29semidirect
298. #1958C2×C29semidirect
299. #1949C2×C29semidirect
300. #1928C2×C29semidirect
301. #1926C2×C29semidirect
302. #1880C2×C29semidirect
304. C8×C4⋊C4C2×C29semidirect
305. C4×#103C2×C29semidirect
306. C4×#102C2×C29semidirect
307. C4×#102C2×C29semidirect
351. #463C4×C29semidirect
405. C2×SD16C2×C4×C29semidirect
420. C4×D4C2×C4×C29semidirect
448. C4⋊C8C2×C4×C29semidirect
451. #103C2×C4×C29semidirect
469. C29#23098direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4632
C29×#23672
C29×#23572
C29×#19702
C29×#19682
C29×#19582
C29×#19492
C29×#19282
C29×#19262
C29×#18802
C29×#18792
C8×C4⋊C4×C292
C4×C29×#1032
C4×C29×#1022
#2309829