Finite Group Databasebeta

← C29×#22062 #20316962

Subgroups — C29×#22062 #20316962

Order 7424.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3002C211yesmaximal, characteristic
2C29×#2930C211yesmaximal, characteristic, complemented
3C29×#2879C211yesmaximal, characteristic, complemented
4C29×#1975C211yesmaximal, characteristic, complemented
5C29×#1974C211yesmaximal, characteristic, complemented
6C29×#1938C211yesmaximal, characteristic, complemented
7C29×#1937C211yesmaximal, characteristic, complemented
8C29×#1929C211yesmaximal, characteristic, complemented
9C29×#1929C211yesmaximal, characteristic, complemented
10C29×#1876C211yesmaximal, characteristic, complemented
11C29×#1876C211yesmaximal, characteristic, complemented
12C29×#1871C211yesmaximal, characteristic, complemented
13C29×#1855C211yesmaximal, characteristic, complemented
14C29×#1789C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C2×C29×#135C2211yescharacteristic
18C2×C29×#135C2211yescharacteristic
19C2×C29×#131C2211yescharacteristic, complemented
20C22×M16×C29C2211yescharacteristic
21C22×M16×C29C2211yescharacteristic
22C29×#525C2211yescharacteristic
23C29×#452C411yescharacteristic, complemented
24C29×#452C411yescharacteristic, complemented
25C29×#451C411yescharacteristic, complemented
26C29×#450C411yescharacteristic, complemented
27C29×#449C411yescharacteristic, complemented
28C29×#449C411yescharacteristic, complemented
29C29×#448C411yescharacteristic, complemented
30C29×#447C411yescharacteristic, complemented
31C29×#436—21no—
32C29×#436—21no—
33C29×#435—21no—
34C29×#435—21no—
35C2×C29×#108C2211yescharacteristic, complemented
36C2×C29×#108C2211yescharacteristic, complemented
37C29×#424C2211yescharacteristic, complemented
38C2×C29×#104C2211yescharacteristic
39C2×C29×#104C2211yescharacteristic
40C2×C29×#104C2211yescharacteristic
41C2×C29×#104C2211yescharacteristic
42C2×C29×#104C2211yescharacteristic, complemented
43C2×C29×#104C2211yescharacteristic, complemented
44C29×#416C2211yescharacteristic
45C29×#416C2211yescharacteristic
46C29×#408—21no—
47C29×#408—21no—
48C29×#408C2211yescharacteristic
49C29×#408C2211yescharacteristic
50C29×#408C2211yescharacteristic
51C29×#408C2211yescharacteristic
52C29×#408C2211yescharacteristic, complemented
53C29×#407—21no—
54C29×#407—21no—
55C29×#407C2211yescharacteristic
56C2×C29×C22⋊C8C2211yescharacteristic
57C29×#405C2211yescharacteristic, complemented
58C2×C29×#97C2211yescharacteristic, complemented
59C2×C4×C8×C29C2211yescharacteristic, complemented
60C4×C22⋊C4×C29C2211yescharacteristic
61C29×#341C2211yescharacteristic, complemented
62C29×#341C2211yescharacteristic, complemented
63C29×#339C2211yescharacteristic, complemented
64C29×#339C2211yescharacteristic, complemented
65C29×#336C2211yescharacteristic, complemented
66C29×#336C2211yescharacteristic, complemented
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×#41×C29—41no—
70C2×#41×C29—41no—
71C2×#41×C29—41no—
72C2×#41×C29—41no—
73C2×#41×C29C2×C411yescharacteristic
74C2×#41×C29C2×C411yescharacteristic
75C2×#41×C29C2311yescharacteristic
76C2×#41×C29C2311yescharacteristic
77C2×#41×C29C2311yescharacteristic
78C22×Q8×C29C2×C411yescharacteristic
79C22×D4×C29—21no—
80C22×D4×C29C2×C411yescharacteristic
81C23×C4×C29—21no—
82C23×C4×C29C2311yescharacteristic
83C29×#135—41no—
84C29×#135—41no—
85C29×#135—41no—
86C29×#135—41no—
87C2×Q16×C29C2×C411yescharacteristic
88C2×Q16×C29C2×C411yescharacteristic
89C2×SD16×C29C2×C411yescharacteristic
90C2×SD16×C29C2×C411yescharacteristic
91C2×SD16×C29C2×C411yescharacteristic
92C2×SD16×C29C2×C411yescharacteristic
93C2×D8×C29C2×C411yescharacteristic
94C2×D8×C29C2×C411yescharacteristic
95C29×#131—41no—
96C29×#131—41no—
97C2×M16×C29—21no—
98C2×M16×C29—21no—
99C2×M16×C29—41no—
100C2×M16×C29—41no—
101C2×M16×C29—41no—
102C2×M16×C29—41no—
103C2×M16×C29D411yescharacteristic
104C2×M16×C29D411yescharacteristic
105C2×M16×C29D411yescharacteristic
106C2×M16×C29D411yescharacteristic
107C2×M16×C29C2311yescharacteristic
108C2×M16×C29C2311yescharacteristic
109C2×M16×C29C2311yescharacteristic
110C2×M16×C29C2311yescharacteristic
111C22×C8×C29—21no—
112C22×C8×C29—21no—
113C22×C8×C29C2311yescharacteristic
114C22×C8×C29C2311yescharacteristic
115C22×C8×C29C2311yescharacteristic
116C22×C8×C29C2311yescharacteristic
117C29×#123—21no—
118C29×C22⋊Q8C2×C411yescharacteristic
119C29×C22⋊Q8C2×C411yescharacteristic
120C29×#121C2×C411yescharacteristic
121C29×#121C2×C411yescharacteristic
122C29×#120—21no—
123C4×D4×C29—21no—
124C4×D4×C29—21no—
125C29×#117C2311yescharacteristic
126C2×C22⋊C4×C29—21no—
127C2×C42×C29C2311yescharacteristic
128C2×C42×C29C2311yescharacteristic
129C29×#108—41no—
130C29×#108—41no—
131C29×C4⋊C8—21no—
132C29×C4⋊C8—21no—
133C29×#104—41no—
134C29×#104—41no—
135C29×#104—41no—
136C29×#104—41no—
137C29×#104—41no—
138C29×#104—41no—
139C29×#103C2×C411yescharacteristic
140C29×#103C2×C411yescharacteristic
141C29×#103C2×C411yescharacteristic
142C29×#103C2×C411yescharacteristic
143C29×#102C2×C411yescharacteristic
144C29×#102C2×C411yescharacteristic
145C29×#102C2×C411yescharacteristic
146C29×#102C2×C411yescharacteristic
147C29×C22⋊C8—21no—
148C29×C22⋊C8—21no—
149C29×C22⋊C8—21no—
150C29×C22⋊C8—21no—
151C29×C22⋊C8—21no—
152C29×C22⋊C8—21no—
153C29×C22⋊C8—21no—
154C29×C22⋊C8—21no—
155C29×C22⋊C8—21no—
156C29×C22⋊C8—21no—
157C29×C22⋊C8—21no—
158C29×C22⋊C8—21no—
159C29×C22⋊C8C2×C411yescharacteristic
160C29×C22⋊C8C2×C411yescharacteristic
161C29×C22⋊C8C2×C411yescharacteristic
162C29×C22⋊C8C2×C411yescharacteristic
163C29×#97—21no—
164C29×#97—41no—
165C4×C8×C29—21no—
166C4×C8×C29—41no—
167C29×#95—21no—
168C24×C29—21no—
169C24×C29#4111yescharacteristic
170#41×C29—21no—
171#41×C29—21no—
172#41×C29—21no—
173#41×C29—21no—
174#41×C29—21no—
175#41×C29—21no—
176#41×C29—21no—
177#41×C29—21no—
178#41×C29—21no—
179#41×C29—21no—
180#41×C29—21no—
181#41×C29—21no—
182#41×C29—41no—
183#41×C29—41no—
184#41×C29—41no—
185#41×C29—41no—
186#41×C29—42no—
187#41×C29—42no—
188#41×C29—42no—
189#41×C29—42no—
190C2×Q8×C29—21no—
191C2×Q8×C29—41no—
192C2×Q8×C29—41no—
193C2×Q8×C29C22×C411yescharacteristic
194C2×Q8×C29C22×C411yescharacteristic
195C2×Q8×C29C22×C411yescharacteristic
196C2×D4×C29—21no—
197C2×D4×C29—21no—
198C2×D4×C29—21no—
199C2×D4×C29—21no—
200C2×D4×C29—21no—
201C2×D4×C29—21no—
202C2×D4×C29—21no—
203C2×D4×C29—21no—
204C2×D4×C29—41no—
205C2×D4×C29—41no—
206C2×D4×C29—42no—
207C2×D4×C29—42no—
208C2×D4×C29C22×C411yescharacteristic
209C2×D4×C29C22×C411yescharacteristic
210C2×D4×C29C22×C411yescharacteristic
211C22×C4×C29—21no—
212C22×C4×C29—21no—
213C22×C4×C29—21no—
214C22×C4×C29—21no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—42no—
224C22×C4×C29—42no—
225C22×C4×C29C22×C411yescharacteristic
226C22×C4×C29C22×C411yescharacteristic
227C22×C4×C29C2×D411yescharacteristic
228C22×C4×C29C2×D411yescharacteristic
229C22×C4×C29#4111yescharacteristic
230C22×C4×C29C2411yescharacteristic
231Q16×C29—41no—
232Q16×C29—41no—
233SD16×C29—41no—
234SD16×C29—41no—
235SD16×C29—41no—
236SD16×C29—41no—
237D8×C29—41no—
238D8×C29—41no—
239M16×C29—21no—
240M16×C29—21no—
241M16×C29—21no—
242M16×C29—21no—
243M16×C29—21no—
244M16×C29—21no—
245M16×C29—21no—
246M16×C29—21no—
247M16×C29—41no—
248M16×C29—41no—
249M16×C29—41no—
250M16×C29—41no—
251M16×C29—42no—
252M16×C29—42no—
253C2×C8×C29—21no—
254C2×C8×C29—21no—
255C2×C8×C29—21no—
256C2×C8×C29—21no—
257C2×C8×C29—21no—
258C2×C8×C29—21no—
259C2×C8×C29—21no—
260C2×C8×C29—21no—
261C2×C8×C29—21no—
262C2×C8×C29—21no—
263C2×C8×C29—21no—
264C2×C8×C29—21no—
265C2×C8×C29—42no—
266C2×C8×C29—42no—
267C2×C8×C29C22×C411yescharacteristic
268C2×C8×C29C22×C411yescharacteristic
269C2×C8×C29C22×C411yescharacteristic
270C2×C8×C29C22×C411yescharacteristic
271C2×C8×C29C2×D411yescharacteristic
272C2×C8×C29C2×D411yescharacteristic
273C2×C8×C29C2×D411yescharacteristic
274C2×C8×C29C2×D411yescharacteristic
275C4⋊C4×C29—21no—
276C4⋊C4×C29—21no—
277C4⋊C4×C29C22×C411yescharacteristic
278C4⋊C4×C29C22×C411yescharacteristic
279C22⋊C4×C29—21no—
280C22⋊C4×C29—21no—
281C22⋊C4×C29—21no—
282C22⋊C4×C29—21no—
283C22⋊C4×C29—21no—
284C22⋊C4×C29—42no—
285C42×C29—21no—
286C42×C29—21no—
287C42×C29—21no—
288C42×C29—21no—
289C42×C29—21no—
290#22062C2911yesmaximal, characteristic, direct product factor, Sylow
291C23×C29—21no—
292C23×C29—21no—
293C23×C29—21no—
294C23×C29—21no—
295C23×C29—21no—
296C23×C29—41no—
297C23×C29—41no—
298C23×C29—42no—
299C23×C29—81no—
300C23×C29—81no—
301C23×C29C4×D411yescharacteristic
302C23×C29C4×D411yescharacteristic
303C23×C29C2×#4111yescharacteristic
304Q8×C29—21no—
305Q8×C29—21no—
306Q8×C29—21no—
307Q8×C29—21no—
308Q8×C29—21no—
309Q8×C29—21no—
310Q8×C29—42no—
311D4×C29—21no—
312D4×C29—21no—
313D4×C29—21no—
314D4×C29—21no—
315D4×C29—21no—
316D4×C29—21no—
317D4×C29—42no—
318D4×C29—42no—
319D4×C29—42no—
320D4×C29—41no—
321D4×C29—41no—
322D4×C29—41no—
323D4×C29—41no—
324D4×C29—41no—
325D4×C29—41no—
326D4×C29—81no—
327D4×C29—81no—
328C2×C4×C29—21no—
329C2×C4×C29—21no—
330C2×C4×C29—21no—
331C2×C4×C29—21no—
332C2×C4×C29—21no—
333C2×C4×C29—21no—
334C2×C4×C29—21no—
335C2×C4×C29—21no—
336C2×C4×C29—21no—
337C2×C4×C29—21no—
338C2×C4×C29—22no—
339C2×C4×C29—21no—
340C2×C4×C29—21no—
341C2×C4×C29—21no—
342C2×C4×C29—21no—
343C2×C4×C29—21no—
344C2×C4×C29—42no—
345C2×C4×C29—42no—
346C2×C4×C29—41no—
347C2×C4×C29—42no—
348C2×C4×C29—41no—
349C2×C4×C29—41no—
350C2×C4×C29—41no—
351C2×C4×C29—41no—
352C2×C4×C29—41no—
353C2×C4×C29—41no—
354C2×C4×C29—41no—
355C2×C4×C29—41no—
356C2×C4×C29—41no—
357C2×C4×C29—41no—
358C2×C4×C29C4×D411yescharacteristic
359C2×C4×C29C4×D411yescharacteristic
360C2×C4×C29C23×C411yescharacteristic
361C2×C4×C29C22×D411yescharacteristic
362C2×C4×C29H(5,𝔽2)11yescharacteristic
363C2×C4×C29H(5,𝔽2)11yescharacteristic
364C2×C4×C29H(5,𝔽2)11yescharacteristic
365C2×C4×C29H(5,𝔽2)11yescharacteristic
366C8×C29—21no—
367C8×C29—21no—
368C8×C29—21no—
369C8×C29—21no—
370C8×C29—21no—
371C8×C29—21no—
372C8×C29—21no—
373C8×C29—21no—
374C8×C29—41no—
375C8×C29—41no—
376C8×C29—41no—
377C8×C29—41no—
378#3002C2×C2911yescharacteristic
379#2930C2×C2911yescharacteristic, complemented
380#2879C2×C2911yescharacteristic, complemented
381#1975C2×C2911yescharacteristic, complemented
382#1974C2×C2911yescharacteristic, complemented
383#1938C2×C2911yescharacteristic, complemented
384#1937C2×C2911yescharacteristic, complemented
385#1929C2×C2911yescharacteristic, complemented
386#1929C2×C2911yescharacteristic, complemented
387#1876C2×C2911yescharacteristic, complemented
388#1876C2×C2911yescharacteristic, complemented
389#1871C2×C2911yescharacteristic, complemented
390#1855C2×C2911yescharacteristic, complemented
391#1789C2×C2911yescharacteristic, complemented
392#1753C2×C2911yescharacteristic, complemented
393C22×C29—21no—
394C22×C29—21no—
395C22×C29—21no—
396C22×C29—21no—
397C22×C29—21no—
398C22×C29—21no—
399C22×C29—21no—
400C22×C29—21no—
401C22×C29—41no—
402C22×C29—41no—
403C22×C29—41no—
404C22×C29—41no—
405C22×C29—41no—
406C22×C29—41no—
407C22×C29—41no—
408C22×C29—41no—
409C22×C29—41no—
410C22×C29—81no—
411C22×C29—81no—
412C22×C29—84no—
413C22×C29C2×C4×D411yescharacteristic
414C22×C29#53811yescharacteristic
415C22×C29#53811yescharacteristic
416C4×C29—21no—
417C4×C29—21no—
418C4×C29—42no—
419C4×C29—41no—
420C4×C29—41no—
421C4×C29—41no—
422C4×C29—41no—
423C4×C29—41no—
424C4×C29—81no—
425C4×C29#51811yescharacteristic
426C4×C29#51811yescharacteristic
427C4×C29#53411yescharacteristic
428C4×C29#53511yescharacteristic
429C22×#41C22×C2911yescharacteristic
430C2×#135C22×C2911yescharacteristic
431C2×#135C22×C2911yescharacteristic
432C2×#131C22×C2911yescharacteristic, complemented
433C22×M16C22×C2911yescharacteristic
434C22×M16C22×C2911yescharacteristic
435#525C22×C2911yescharacteristic
436#452C4×C2911yescharacteristic, complemented
437#452C4×C2911yescharacteristic, complemented
438#451C4×C2911yescharacteristic, complemented
439#450C4×C2911yescharacteristic, complemented
440#449C4×C2911yescharacteristic, complemented
441#449C4×C2911yescharacteristic, complemented
442#448C4×C2911yescharacteristic, complemented
443#447C4×C2911yescharacteristic, complemented
444#436—21no—
445#436—21no—
446#435—21no—
447#435—21no—
448C2×#108C22×C2911yescharacteristic, complemented
449C2×#108C22×C2911yescharacteristic, complemented
450#424C22×C2911yescharacteristic, complemented
451C2×#104C22×C2911yescharacteristic
452C2×#104C22×C2911yescharacteristic
453C2×#104C22×C2911yescharacteristic
454C2×#104C22×C2911yescharacteristic
455C2×#104C22×C2911yescharacteristic, complemented
456C2×#104C22×C2911yescharacteristic, complemented
457#416C22×C2911yescharacteristic
458#416C22×C2911yescharacteristic
459#408—21no—
460#408—21no—
461#408C22×C2911yescharacteristic
462#408C22×C2911yescharacteristic
463#408C22×C2911yescharacteristic
464#408C22×C2911yescharacteristic
465#408C22×C2911yescharacteristic, complemented
466#407—21no—
467#407—21no—
468#407C22×C2911yescharacteristic
469C2×C22⋊C8C22×C2911yescharacteristic
470#405C22×C2911yescharacteristic, complemented
471C2×#97C22×C2911yescharacteristic, complemented
472C2×C4×C8C22×C2911yescharacteristic, complemented
473C4×C22⋊C4C22×C2911yescharacteristic
474#341C22×C2911yescharacteristic, complemented
475#341C22×C2911yescharacteristic, complemented
476#339C22×C2911yescharacteristic, complemented
477#339C22×C2911yescharacteristic, complemented
478#336C22×C2911yescharacteristic, complemented
479#336C22×C2911yescharacteristic, complemented
480C2×C29—21no—
481C2×C29—21no—
482C2×C29—41no—
483C2×C29—41no—
484C2×C29—81no—
485C2×C29—81no—
486C2×C29—81no—
487C2×C29#232111yescharacteristic
488C2×C29#295611yescharacteristic
489C2×C29#295711yescharacteristic
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C2×C4×C2911yescharacteristic
497C2×#41C2×C4×C2911yescharacteristic
498C2×#41C23×C2911yescharacteristic
499C2×#41C23×C2911yescharacteristic
500C2×#41C23×C2911yescharacteristic
501C22×Q8C2×C4×C2911yescharacteristic
502C22×D4—21no—
503C22×D4C2×C4×C2911yescharacteristic
504C23×C4—21no—
505C23×C4C23×C2911yescharacteristic
506#135—41no—
507#135—41no—
508#135—41no—
509#135—41no—
510C2×Q16C2×C4×C2911yescharacteristic
511C2×Q16C2×C4×C2911yescharacteristic
512C2×SD16C2×C4×C2911yescharacteristic
513C2×SD16C2×C4×C2911yescharacteristic
514C2×SD16C2×C4×C2911yescharacteristic
515C2×SD16C2×C4×C2911yescharacteristic
516C2×D8C2×C4×C2911yescharacteristic
517C2×D8C2×C4×C2911yescharacteristic
518#131—41no—
519#131—41no—
520C2×M16—21no—
521C2×M16—21no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16D4×C2911yescharacteristic
527C2×M16D4×C2911yescharacteristic
528C2×M16D4×C2911yescharacteristic
529C2×M16D4×C2911yescharacteristic
530C2×M16C23×C2911yescharacteristic
531C2×M16C23×C2911yescharacteristic
532C2×M16C23×C2911yescharacteristic
533C2×M16C23×C2911yescharacteristic
534C22×C8—21no—
535C22×C8—21no—
536C22×C8C23×C2911yescharacteristic
537C22×C8C23×C2911yescharacteristic
538C22×C8C23×C2911yescharacteristic
539C22×C8C23×C2911yescharacteristic
540#123—21no—
541C22⋊Q8C2×C4×C2911yescharacteristic
542C22⋊Q8C2×C4×C2911yescharacteristic
543#121C2×C4×C2911yescharacteristic
544#121C2×C4×C2911yescharacteristic
545#120—21no—
546C4×D4—21no—
547C4×D4—21no—
548#117C23×C2911yescharacteristic
549C2×C22⋊C4—21no—
550C2×C42C23×C2911yescharacteristic
551C2×C42C23×C2911yescharacteristic
552#108—41no—
553#108—41no—
554C4⋊C8—21no—
555C4⋊C8—21no—
556#104—41no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#103C2×C4×C2911yescharacteristic
563#103C2×C4×C2911yescharacteristic
564#103C2×C4×C2911yescharacteristic
565#103C2×C4×C2911yescharacteristic
566#102C2×C4×C2911yescharacteristic
567#102C2×C4×C2911yescharacteristic
568#102C2×C4×C2911yescharacteristic
569#102C2×C4×C2911yescharacteristic
570C22⋊C8—21no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8C2×C4×C2911yescharacteristic
583C22⋊C8C2×C4×C2911yescharacteristic
584C22⋊C8C2×C4×C2911yescharacteristic
585C22⋊C8C2×C4×C2911yescharacteristic
586#97—21no—
587#97—41no—
588C4×C8—21no—
589C4×C8—41no—
590#95—21no—
591C29#2206211yescharacteristic, direct product factor, Sylow
592C24—21no—
593C24#41×C2911yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C2911yescharacteristic
618C2×Q8C22×C4×C2911yescharacteristic
619C2×Q8C22×C4×C2911yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C2911yescharacteristic
633C2×D4C22×C4×C2911yescharacteristic
634C2×D4C22×C4×C2911yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C2911yescharacteristic
650C22×C4C22×C4×C2911yescharacteristic
651C22×C4C2×D4×C2911yescharacteristic
652C22×C4C2×D4×C2911yescharacteristic
653C22×C4#41×C2911yescharacteristic
654C22×C4C24×C2911yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C2911yescharacteristic
692C2×C8C22×C4×C2911yescharacteristic
693C2×C8C22×C4×C2911yescharacteristic
694C2×C8C22×C4×C2911yescharacteristic
695C2×C8C2×D4×C2911yescharacteristic
696C2×C8C2×D4×C2911yescharacteristic
697C2×C8C2×D4×C2911yescharacteristic
698C2×C8C2×D4×C2911yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C2911yescharacteristic
702C4⋊C4C22×C4×C2911yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C2911yescharacteristic
725C23C4×D4×C2911yescharacteristic
726C23C2×#41×C2911yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C2911yescharacteristic
782C2×C4C4×D4×C2911yescharacteristic
783C2×C4C23×C4×C2911yescharacteristic
784C2×C4C22×D4×C2911yescharacteristic
785C2×C4C29×H(5,𝔽2)11yescharacteristic
786C2×C4C29×H(5,𝔽2)11yescharacteristic
787C2×C4C29×H(5,𝔽2)11yescharacteristic
788C2×C4C29×H(5,𝔽2)11yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C2911yescharacteristic
822C22C29×#53811yescharacteristic
823C22C29×#53811yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4C29×#51811yescharacteristic
834C4C29×#51811yescharacteristic
835C4C29×#53411yescharacteristic
836C4C29×#53511yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C29×#232111yescharacteristic
845C2C29×#295611yescharacteristic
846C2C29×#295711yescharacteristic
subgroupG/H
centerC2×C4×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
socleC22×C29C2×C4×D4
prime radicalC29×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C22×M16×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2930C2semidirect
3. C29×#2879C2semidirect
4. C29×#1975C2semidirect
5. C29×#1974C2semidirect
6. C29×#1938C2semidirect
7. C29×#1937C2semidirect
8. C29×#1929C2semidirect
9. C29×#1929C2semidirect
10. C29×#1876C2semidirect
11. C29×#1876C2semidirect
12. C29×#1871C2semidirect
13. C29×#1855C2semidirect
14. C29×#1789C2semidirect
15. C29×#1753C2semidirect
19. C2×C29×#131C22semidirect
23. C29×#452C4semidirect
24. C29×#452C4semidirect
25. C29×#451C4semidirect
26. C29×#450C4semidirect
27. C29×#449C4semidirect
28. C29×#449C4semidirect
29. C29×#448C4semidirect
30. C29×#447C4semidirect
35. C2×C29×#108C22semidirect
36. C2×C29×#108C22semidirect
37. C29×#424C22semidirect
42. C2×C29×#104C22semidirect
43. C2×C29×#104C22semidirect
52. C29×#408C22semidirect
57. C29×#405C22semidirect
58. C2×C29×#97C22semidirect
59. C2×C4×C8×C29C22semidirect
61. C29×#341C22semidirect
62. C29×#341C22semidirect
63. C29×#339C22semidirect
64. C29×#339C22semidirect
65. C29×#336C22semidirect
66. C29×#336C22semidirect
290. #22062C29direct (N × H)
379. #2930C2×C29semidirect
380. #2879C2×C29semidirect
381. #1975C2×C29semidirect
382. #1974C2×C29semidirect
383. #1938C2×C29semidirect
384. #1937C2×C29semidirect
385. #1929C2×C29semidirect
386. #1929C2×C29semidirect
387. #1876C2×C29semidirect
388. #1876C2×C29semidirect
389. #1871C2×C29semidirect
390. #1855C2×C29semidirect
391. #1789C2×C29semidirect
392. #1753C2×C29semidirect
432. C2×#131C22×C29semidirect
436. #452C4×C29semidirect
437. #452C4×C29semidirect
438. #451C4×C29semidirect
439. #450C4×C29semidirect
440. #449C4×C29semidirect
441. #449C4×C29semidirect
442. #448C4×C29semidirect
443. #447C4×C29semidirect
448. C2×#108C22×C29semidirect
449. C2×#108C22×C29semidirect
450. #424C22×C29semidirect
455. C2×#104C22×C29semidirect
456. C2×#104C22×C29semidirect
465. #408C22×C29semidirect
470. #405C22×C29semidirect
471. C2×#97C22×C29semidirect
472. C2×C4×C8C22×C29semidirect
474. #341C22×C29semidirect
475. #341C22×C29semidirect
476. #339C22×C29semidirect
477. #339C22×C29semidirect
478. #336C22×C29semidirect
479. #336C22×C29semidirect
591. C29#22062direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30022
C29×#29302
C29×#28792
C29×#19752
C29×#19742
C29×#19382
C29×#19372
C29×#19292
C29×#18762
C29×#18712
C29×#18552
C29×#17892
C29×#17532
#2206229