Finite Group Databasebeta

← C29×#22588 #20317488

Subgroups — C29×#22588 #20317488

Order 7424.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2924C211yesmaximal, characteristic, complemented
2C29×#2896C211yesmaximal, characteristic
3C29×#2880C211yesmaximal, characteristic
4C29×#1938C211yesmaximal, characteristic, complemented
5C29×#1937C211yesmaximal, characteristic, complemented
6C29×#1929C211yesmaximal, characteristic, complemented
7C29×#1929C211yesmaximal, characteristic, complemented
8C29×#1866C211yesmaximal, characteristic, complemented
9C29×#1866C211yesmaximal, characteristic, complemented
10C29×#1826C211yesmaximal, characteristic, complemented
11C29×#1811C211yesmaximal, characteristic, complemented
12C29×#1789C211yesmaximal, characteristic
13C29×#1765C211yesmaximal, characteristic, complemented
14C29×#1764C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C2×C29×#131C2211yescharacteristic
18C2×C29×#131C2211yescharacteristic
19C22×M16×C29C2211yescharacteristic
20C2×C29×#117C2211yescharacteristic
21C29×#433—21no—
22C29×#433—21no—
23C29×#432—21no—
24C29×#431—21no—
25C2×C29×#108C2211yescharacteristic, complemented
26C2×C29×#108C2211yescharacteristic, complemented
27C29×#424C2211yescharacteristic, complemented
28C29×#424C2211yescharacteristic, complemented
29C2×C29×#104C2211yescharacteristic
30C2×C29×#104C2211yescharacteristic
31C2×C29×#104C2211yescharacteristic
32C2×C29×#104C2211yescharacteristic
33C29×#419C411yescharacteristic, complemented
34C29×#419C411yescharacteristic, complemented
35C29×#418C411yescharacteristic, complemented
36C29×#418C411yescharacteristic, complemented
37C29×#417C411yescharacteristic, complemented
38C29×#417C411yescharacteristic, complemented
39C29×#417C411yescharacteristic, complemented
40C29×#417C411yescharacteristic, complemented
41C29×#416C2211yescharacteristic
42C29×#416C2211yescharacteristic
43C29×#416C2211yescharacteristic
44C29×#416C2211yescharacteristic
45C29×#408—21no—
46C29×#408—21no—
47C29×#408C2211yescharacteristic
48C29×#408C2211yescharacteristic
49C29×#407—21no—
50C29×#407C2211yescharacteristic
51C29×#407C2211yescharacteristic
52C2×C29×C22⋊C8—21no—
53C2×C29×C22⋊C8C2211yescharacteristic
54C29×#405C2211yescharacteristic, complemented
55C29×#405C2211yescharacteristic, complemented
56C2×C29×#97C2211yescharacteristic, complemented
57C2×C4×C8×C29C2211yescharacteristic, complemented
58C4×C22⋊C4×C29C2211yescharacteristic
59C29×#341C2211yescharacteristic, complemented
60C29×#341C2211yescharacteristic, complemented
61C29×#339C2211yescharacteristic, complemented
62C29×#339C2211yescharacteristic, complemented
63C29×#339C2211yescharacteristic, complemented
64C29×#339C2211yescharacteristic, complemented
65C29×#336C2211yescharacteristic, complemented
66C29×#336C2211yescharacteristic, complemented
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×#41×C29—22no—
70C2×#41×C29—22no—
71C2×#41×C29—41no—
72C2×#41×C29—41no—
73C2×#41×C29C2×C411yescharacteristic
74C2×#41×C29C2×C411yescharacteristic
75C2×#41×C29C2311yescharacteristic
76C2×#41×C29C2311yescharacteristic
77C22×Q8×C29C2×C411yescharacteristic
78C22×D4×C29—21no—
79C22×D4×C29C2×C411yescharacteristic
80C23×C4×C29—21no—
81C23×C4×C29C2311yescharacteristic
82C29×#131—22no—
83C29×#131—22no—
84C29×#131—41no—
85C29×#131—41no—
86C2×M16×C29—21no—
87C2×M16×C29—21no—
88C2×M16×C29—41no—
89C2×M16×C29—41no—
90C2×M16×C29C2×C411yescharacteristic
91C2×M16×C29C2×C411yescharacteristic
92C2×M16×C29C2×C411yescharacteristic
93C2×M16×C29C2×C411yescharacteristic
94C2×M16×C29C2311yescharacteristic
95C2×M16×C29C2311yescharacteristic
96C2×M16×C29C2311yescharacteristic
97C2×M16×C29C2311yescharacteristic
98C22×C8×C29—21no—
99C22×C8×C29—21no—
100C22×C8×C29C2311yescharacteristic
101C22×C8×C29C2311yescharacteristic
102C22×C8×C29C2311yescharacteristic
103C22×C8×C29C2311yescharacteristic
104C29×#117—21no—
105C29×#117—21no—
106C29×#117C2×C411yescharacteristic
107C29×#117C2×C411yescharacteristic
108C29×#117C2311yescharacteristic
109C29×#117C2311yescharacteristic
110C2×C4⋊C4×C29C2×C411yescharacteristic
111C2×C4⋊C4×C29C2×C411yescharacteristic
112C2×C22⋊C4×C29—21no—
113C2×C22⋊C4×C29—21no—
114C2×C42×C29—21no—
115C2×C42×C29C2311yescharacteristic
116C2×C42×C29C2311yescharacteristic
117C29×#108—41no—
118C29×#108—41no—
119C29×C4⋊C8—21no—
120C29×C4⋊C8—21no—
121C29×C4⋊C8—21no—
122C29×C4⋊C8—21no—
123C29×#104—22no—
124C29×#104—22no—
125C29×#104—41no—
126C29×#104—41no—
127C29×#103C2×C411yescharacteristic
128C29×#103C2×C411yescharacteristic
129C29×#103C2×C411yescharacteristic
130C29×#103C2×C411yescharacteristic
131C29×#103C2×C411yescharacteristic
132C29×#103C2×C411yescharacteristic
133C29×#103C2×C411yescharacteristic
134C29×#103C2×C411yescharacteristic
135C29×#102C2×C411yescharacteristic
136C29×#102C2×C411yescharacteristic
137C29×#102C2×C411yescharacteristic
138C29×#102C2×C411yescharacteristic
139C29×#102C2×C411yescharacteristic
140C29×#102C2×C411yescharacteristic
141C29×#102C2×C411yescharacteristic
142C29×#102C2×C411yescharacteristic
143C29×C22⋊C8—21no—
144C29×C22⋊C8—21no—
145C29×C22⋊C8—21no—
146C29×C22⋊C8—21no—
147C29×C22⋊C8—21no—
148C29×C22⋊C8—21no—
149C29×C22⋊C8—21no—
150C29×C22⋊C8—21no—
151C29×C22⋊C8D411yescharacteristic
152C29×C22⋊C8D411yescharacteristic
153C29×C22⋊C8D411yescharacteristic
154C29×C22⋊C8D411yescharacteristic
155C29×#97—21no—
156C29×#97—21no—
157C29×#97—41no—
158C4×C8×C29—21no—
159C4×C8×C29—21no—
160C4×C8×C29—41no—
161C29×#95—21no—
162C24×C29—21no—
163C24×C29#4111yescharacteristic
164#41×C29—21no—
165#41×C29—21no—
166#41×C29—22no—
167#41×C29—22no—
168#41×C29—21no—
169#41×C29—21no—
170#41×C29—21no—
171#41×C29—21no—
172#41×C29—42no—
173#41×C29—42no—
174#41×C29—41no—
175#41×C29—41no—
176#41×C29—42no—
177#41×C29—42no—
178#41×C29#4112yes—
179#41×C29#4112yes—
180C2×Q8×C29—21no—
181C2×Q8×C29—22no—
182C2×Q8×C29—41no—
183C2×Q8×C29C22×C411yescharacteristic
184C2×Q8×C29C22×C411yescharacteristic
185C2×D4×C29—21no—
186C2×D4×C29—22no—
187C2×D4×C29—21no—
188C2×D4×C29—21no—
189C2×D4×C29—21no—
190C2×D4×C29—21no—
191C2×D4×C29—41no—
192C2×D4×C29—42no—
193C2×D4×C29—42no—
194C2×D4×C29C22×C411yescharacteristic
195C2×D4×C29C22×C411yescharacteristic
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—21no—
209C22×C4×C29—42no—
210C22×C4×C29—42no—
211C22×C4×C29C22×C411yescharacteristic
212C22×C4×C29C22×C411yescharacteristic
213C22×C4×C29C2×D411yescharacteristic
214C22×C4×C29C2×D411yescharacteristic
215C22×C4×C29#4111yescharacteristic
216C22×C4×C29C2411yescharacteristic
217M16×C29—21no—
218M16×C29—21no—
219M16×C29—21no—
220M16×C29—21no—
221M16×C29—21no—
222M16×C29—21no—
223M16×C29—21no—
224M16×C29—21no—
225M16×C29—41no—
226M16×C29—41no—
227M16×C29—41no—
228M16×C29—41no—
229M16×C29—42no—
230M16×C29—42no—
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×C29—21no—
242C2×C8×C29—21no—
243C2×C8×C29—42no—
244C2×C8×C29—42no—
245C2×C8×C29C22×C411yescharacteristic
246C2×C8×C29C22×C411yescharacteristic
247C2×C8×C29C22×C411yescharacteristic
248C2×C8×C29C22×C411yescharacteristic
249C2×C8×C29C2×D411yescharacteristic
250C2×C8×C29C2×D411yescharacteristic
251C2×C8×C29C2×D411yescharacteristic
252C2×C8×C29C2×D411yescharacteristic
253C4⋊C4×C29—21no—
254C4⋊C4×C29—21no—
255C4⋊C4×C29C22×C411yescharacteristic
256C4⋊C4×C29C22×C411yescharacteristic
257C4⋊C4×C29C22×C411yescharacteristic
258C4⋊C4×C29C22×C411yescharacteristic
259C22⋊C4×C29—21no—
260C22⋊C4×C29—21no—
261C22⋊C4×C29—21no—
262C22⋊C4×C29—21no—
263C22⋊C4×C29—42no—
264C42×C29—21no—
265C42×C29—21no—
266C42×C29—21no—
267C42×C29—21no—
268C42×C29—21no—
269C42×C29—21no—
270C42×C29—21no—
271C42×C29—21no—
272#22588C2911yesmaximal, characteristic, direct product factor, Sylow
273C23×C29—21no—
274C23×C29—21no—
275C23×C29—21no—
276C23×C29—21no—
277C23×C29—41no—
278C23×C29—41no—
279C23×C29—42no—
280C23×C29—42no—
281C23×C29—81no—
282C23×C29C4×D411yescharacteristic
283C23×C29C4×D411yescharacteristic
284C23×C29C2×#4111yescharacteristic
285Q8×C29—21no—
286Q8×C29—21no—
287Q8×C29—21no—
288Q8×C29—42no—
289Q8×C29#11712yes—
290D4×C29—22no—
291D4×C29—22no—
292D4×C29—21no—
293D4×C29—21no—
294D4×C29—21no—
295D4×C29—42no—
296D4×C29—42no—
297D4×C29—42no—
298D4×C29—41no—
299D4×C29—41no—
300D4×C29#11712yes—
301C2×C4×C29—21no—
302C2×C4×C29—21no—
303C2×C4×C29—21no—
304C2×C4×C29—21no—
305C2×C4×C29—21no—
306C2×C4×C29—21no—
307C2×C4×C29—21no—
308C2×C4×C29—22no—
309C2×C4×C29—22no—
310C2×C4×C29—21no—
311C2×C4×C29—21no—
312C2×C4×C29—21no—
313C2×C4×C29—21no—
314C2×C4×C29—22no—
315C2×C4×C29—21no—
316C2×C4×C29—21no—
317C2×C4×C29—21no—
318C2×C4×C29—21no—
319C2×C4×C29—21no—
320C2×C4×C29—42no—
321C2×C4×C29—42no—
322C2×C4×C29—42no—
323C2×C4×C29—41no—
324C2×C4×C29—42no—
325C2×C4×C29—41no—
326C2×C4×C29—41no—
327C2×C4×C29—41no—
328C2×C4×C29—41no—
329C2×C4×C29—41no—
330C2×C4×C29—41no—
331C2×C4×C29—81no—
332C2×C4×C29C4×D411yescharacteristic
333C2×C4×C29C4×D411yescharacteristic
334C2×C4×C29C23×C411yescharacteristic
335C2×C4×C29C22×D411yescharacteristic
336C2×C4×C29C2×#4111yescharacteristic
337C2×C4×C29C2×#4111yescharacteristic
338C2×C4×C29H(5,𝔽2)11yescharacteristic
339C2×C4×C29H(5,𝔽2)11yescharacteristic
340C8×C29—21no—
341C8×C29—21no—
342C8×C29—21no—
343C8×C29—21no—
344C8×C29—21no—
345C8×C29—21no—
346C8×C29—21no—
347C8×C29—21no—
348C8×C29—41no—
349C8×C29—41no—
350C8×C29—41no—
351C8×C29—41no—
352#2924C2×C2911yescharacteristic, complemented
353#2896C2×C2911yescharacteristic
354#2880C2×C2911yescharacteristic
355#1938C2×C2911yescharacteristic, complemented
356#1937C2×C2911yescharacteristic, complemented
357#1929C2×C2911yescharacteristic, complemented
358#1929C2×C2911yescharacteristic, complemented
359#1866C2×C2911yescharacteristic, complemented
360#1866C2×C2911yescharacteristic, complemented
361#1826C2×C2911yescharacteristic, complemented
362#1811C2×C2911yescharacteristic, complemented
363#1789C2×C2911yescharacteristic
364#1765C2×C2911yescharacteristic, complemented
365#1764C2×C2911yescharacteristic, complemented
366#1753C2×C2911yescharacteristic, complemented
367C22×C29—21no—
368C22×C29—21no—
369C22×C29—21no—
370C22×C29—21no—
371C22×C29—22no—
372C22×C29—21no—
373C22×C29—21no—
374C22×C29—21no—
375C22×C29—21no—
376C22×C29—41no—
377C22×C29—41no—
378C22×C29—41no—
379C22×C29—41no—
380C22×C29—41no—
381C22×C29—81no—
382C22×C29—81no—
383C22×C29—84no—
384C22×C29C2×C4×D411yescharacteristic
385C22×C29#55111yescharacteristic
386C22×C29#55111yescharacteristic
387C4×C29—21no—
388C4×C29—21no—
389C4×C29—22no—
390C4×C29—42no—
391C4×C29—41no—
392C4×C29—41no—
393C4×C29—41no—
394C4×C29—41no—
395C4×C29—41no—
396C4×C29—81no—
397C4×C29C2×#11711yescharacteristic
398C4×C29#51811yescharacteristic
399C4×C29#54611yescharacteristic
400C4×C29#54611yescharacteristic
401C22×#41C22×C2911yescharacteristic
402C2×#131C22×C2911yescharacteristic
403C2×#131C22×C2911yescharacteristic
404C22×M16C22×C2911yescharacteristic
405C2×#117C22×C2911yescharacteristic
406#433—21no—
407#433—21no—
408#432—21no—
409#431—21no—
410C2×#108C22×C2911yescharacteristic, complemented
411C2×#108C22×C2911yescharacteristic, complemented
412#424C22×C2911yescharacteristic, complemented
413#424C22×C2911yescharacteristic, complemented
414C2×#104C22×C2911yescharacteristic
415C2×#104C22×C2911yescharacteristic
416C2×#104C22×C2911yescharacteristic
417C2×#104C22×C2911yescharacteristic
418#419C4×C2911yescharacteristic, complemented
419#419C4×C2911yescharacteristic, complemented
420#418C4×C2911yescharacteristic, complemented
421#418C4×C2911yescharacteristic, complemented
422#417C4×C2911yescharacteristic, complemented
423#417C4×C2911yescharacteristic, complemented
424#417C4×C2911yescharacteristic, complemented
425#417C4×C2911yescharacteristic, complemented
426#416C22×C2911yescharacteristic
427#416C22×C2911yescharacteristic
428#416C22×C2911yescharacteristic
429#416C22×C2911yescharacteristic
430#408—21no—
431#408—21no—
432#408C22×C2911yescharacteristic
433#408C22×C2911yescharacteristic
434#407—21no—
435#407C22×C2911yescharacteristic
436#407C22×C2911yescharacteristic
437C2×C22⋊C8—21no—
438C2×C22⋊C8C22×C2911yescharacteristic
439#405C22×C2911yescharacteristic, complemented
440#405C22×C2911yescharacteristic, complemented
441C2×#97C22×C2911yescharacteristic, complemented
442C2×C4×C8C22×C2911yescharacteristic, complemented
443C4×C22⋊C4C22×C2911yescharacteristic
444#341C22×C2911yescharacteristic, complemented
445#341C22×C2911yescharacteristic, complemented
446#339C22×C2911yescharacteristic, complemented
447#339C22×C2911yescharacteristic, complemented
448#339C22×C2911yescharacteristic, complemented
449#339C22×C2911yescharacteristic, complemented
450#336C22×C2911yescharacteristic, complemented
451#336C22×C2911yescharacteristic, complemented
452C2×C29—21no—
453C2×C29—21no—
454C2×C29—41no—
455C2×C29—41no—
456C2×C29—42no—
457C2×C29—81no—
458C2×C29#234211yescharacteristic
459C2×C29#295511yescharacteristic
460C2×C29#295611yescharacteristic
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41C2×C4×C2911yescharacteristic
468C2×#41C2×C4×C2911yescharacteristic
469C2×#41C23×C2911yescharacteristic
470C2×#41C23×C2911yescharacteristic
471C22×Q8C2×C4×C2911yescharacteristic
472C22×D4—21no—
473C22×D4C2×C4×C2911yescharacteristic
474C23×C4—21no—
475C23×C4C23×C2911yescharacteristic
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—41no—
483C2×M16—41no—
484C2×M16C2×C4×C2911yescharacteristic
485C2×M16C2×C4×C2911yescharacteristic
486C2×M16C2×C4×C2911yescharacteristic
487C2×M16C2×C4×C2911yescharacteristic
488C2×M16C23×C2911yescharacteristic
489C2×M16C23×C2911yescharacteristic
490C2×M16C23×C2911yescharacteristic
491C2×M16C23×C2911yescharacteristic
492C22×C8—21no—
493C22×C8—21no—
494C22×C8C23×C2911yescharacteristic
495C22×C8C23×C2911yescharacteristic
496C22×C8C23×C2911yescharacteristic
497C22×C8C23×C2911yescharacteristic
498#117—21no—
499#117—21no—
500#117C2×C4×C2911yescharacteristic
501#117C2×C4×C2911yescharacteristic
502#117C23×C2911yescharacteristic
503#117C23×C2911yescharacteristic
504C2×C4⋊C4C2×C4×C2911yescharacteristic
505C2×C4⋊C4C2×C4×C2911yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C42—21no—
509C2×C42C23×C2911yescharacteristic
510C2×C42C23×C2911yescharacteristic
511#108—41no—
512#108—41no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517#104—22no—
518#104—22no—
519#104—41no—
520#104—41no—
521#103C2×C4×C2911yescharacteristic
522#103C2×C4×C2911yescharacteristic
523#103C2×C4×C2911yescharacteristic
524#103C2×C4×C2911yescharacteristic
525#103C2×C4×C2911yescharacteristic
526#103C2×C4×C2911yescharacteristic
527#103C2×C4×C2911yescharacteristic
528#103C2×C4×C2911yescharacteristic
529#102C2×C4×C2911yescharacteristic
530#102C2×C4×C2911yescharacteristic
531#102C2×C4×C2911yescharacteristic
532#102C2×C4×C2911yescharacteristic
533#102C2×C4×C2911yescharacteristic
534#102C2×C4×C2911yescharacteristic
535#102C2×C4×C2911yescharacteristic
536#102C2×C4×C2911yescharacteristic
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8D4×C2911yescharacteristic
546C22⋊C8D4×C2911yescharacteristic
547C22⋊C8D4×C2911yescharacteristic
548C22⋊C8D4×C2911yescharacteristic
549#97—21no—
550#97—21no—
551#97—41no—
552C4×C8—21no—
553C4×C8—21no—
554C4×C8—41no—
555#95—21no—
556C29#2258811yescharacteristic, direct product factor, Sylow
557C24—21no—
558C24#41×C2911yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#41×C2912yes—
574#41#41×C2912yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×C4×C2911yescharacteristic
579C2×Q8C22×C4×C2911yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×C4×C2911yescharacteristic
590C2×D4C22×C4×C2911yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C22×C4×C2911yescharacteristic
607C22×C4C22×C4×C2911yescharacteristic
608C22×C4C2×D4×C2911yescharacteristic
609C22×C4C2×D4×C2911yescharacteristic
610C22×C4#41×C2911yescharacteristic
611C22×C4C24×C2911yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—42no—
625M16—42no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8C22×C4×C2911yescharacteristic
641C2×C8C22×C4×C2911yescharacteristic
642C2×C8C22×C4×C2911yescharacteristic
643C2×C8C22×C4×C2911yescharacteristic
644C2×C8C2×D4×C2911yescharacteristic
645C2×C8C2×D4×C2911yescharacteristic
646C2×C8C2×D4×C2911yescharacteristic
647C2×C8C2×D4×C2911yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×C4×C2911yescharacteristic
651C4⋊C4C22×C4×C2911yescharacteristic
652C4⋊C4C22×C4×C2911yescharacteristic
653C4⋊C4C22×C4×C2911yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×D4×C2911yescharacteristic
677C23C4×D4×C2911yescharacteristic
678C23C2×#41×C2911yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8C29×#11712yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4C29×#11712yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4C4×D4×C2911yescharacteristic
727C2×C4C4×D4×C2911yescharacteristic
728C2×C4C23×C4×C2911yescharacteristic
729C2×C4C22×D4×C2911yescharacteristic
730C2×C4C2×#41×C2911yescharacteristic
731C2×C4C2×#41×C2911yescharacteristic
732C2×C4C29×H(5,𝔽2)11yescharacteristic
733C2×C4C29×H(5,𝔽2)11yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×D4×C2911yescharacteristic
764C22C29×#55111yescharacteristic
765C22C29×#55111yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×C29×#11711yescharacteristic
777C4C29×#51811yescharacteristic
778C4C29×#54611yescharacteristic
779C4C29×#54611yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2C29×#234211yescharacteristic
787C2C29×#295511yescharacteristic
788C2C29×#295611yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
socleC22×C29C2×C4×D4
prime radicalC22×#41×C29C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C29×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2924C2semidirect
4. C29×#1938C2semidirect
5. C29×#1937C2semidirect
6. C29×#1929C2semidirect
7. C29×#1929C2semidirect
8. C29×#1866C2semidirect
9. C29×#1866C2semidirect
10. C29×#1826C2semidirect
11. C29×#1811C2semidirect
13. C29×#1765C2semidirect
14. C29×#1764C2semidirect
15. C29×#1753C2semidirect
25. C2×C29×#108C22semidirect
26. C2×C29×#108C22semidirect
27. C29×#424C22semidirect
28. C29×#424C22semidirect
33. C29×#419C4semidirect
34. C29×#419C4semidirect
35. C29×#418C4semidirect
36. C29×#418C4semidirect
37. C29×#417C4semidirect
38. C29×#417C4semidirect
39. C29×#417C4semidirect
40. C29×#417C4semidirect
54. C29×#405C22semidirect
55. C29×#405C22semidirect
56. C2×C29×#97C22semidirect
57. C2×C4×C8×C29C22semidirect
59. C29×#341C22semidirect
60. C29×#341C22semidirect
61. C29×#339C22semidirect
62. C29×#339C22semidirect
63. C29×#339C22semidirect
64. C29×#339C22semidirect
65. C29×#336C22semidirect
66. C29×#336C22semidirect
272. #22588C29direct (N × H)
352. #2924C2×C29semidirect
355. #1938C2×C29semidirect
356. #1937C2×C29semidirect
357. #1929C2×C29semidirect
358. #1929C2×C29semidirect
359. #1866C2×C29semidirect
360. #1866C2×C29semidirect
361. #1826C2×C29semidirect
362. #1811C2×C29semidirect
364. #1765C2×C29semidirect
365. #1764C2×C29semidirect
366. #1753C2×C29semidirect
410. C2×#108C22×C29semidirect
411. C2×#108C22×C29semidirect
412. #424C22×C29semidirect
413. #424C22×C29semidirect
418. #419C4×C29semidirect
419. #419C4×C29semidirect
420. #418C4×C29semidirect
421. #418C4×C29semidirect
422. #417C4×C29semidirect
423. #417C4×C29semidirect
424. #417C4×C29semidirect
425. #417C4×C29semidirect
439. #405C22×C29semidirect
440. #405C22×C29semidirect
441. C2×#97C22×C29semidirect
442. C2×C4×C8C22×C29semidirect
444. #341C22×C29semidirect
445. #341C22×C29semidirect
446. #339C22×C29semidirect
447. #339C22×C29semidirect
448. #339C22×C29semidirect
449. #339C22×C29semidirect
450. #336C22×C29semidirect
451. #336C22×C29semidirect
556. C29#22588direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#29242
C29×#28962
C29×#28802
C29×#19382
C29×#19372
C29×#19292
C29×#18662
C29×#18262
C29×#18112
C29×#17892
C29×#17652
C29×#17642
C29×#17532
#2258829