Finite Group Databasebeta

← C29×#22887 #20317787

Subgroups — C29×#22887 #20317787

Order 7424.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3002C211yesmaximal, characteristic
2C2×C29×#444C211yesmaximal, characteristic, complemented
3C29×#2933C211yesmaximal, characteristic, complemented
4C2×C29×#421C211yesmaximal, characteristic, complemented
5C29×#2880C211yesmaximal, characteristic, complemented
6C29×#1974C211yesmaximal, characteristic, complemented
7C29×#1938C211yesmaximal, characteristic, complemented
8C29×#1929C211yesmaximal, characteristic, complemented
9C29×#1897C211yesmaximal, characteristic, complemented
10C29×#1876C211yesmaximal, characteristic, complemented
11C29×#1876C211yesmaximal, characteristic, complemented
12C29×#1866C211yesmaximal, characteristic, complemented
13C29×#1855C211yesmaximal, characteristic, complemented
14C29×#1764C211yesmaximal, characteristic, complemented
15C29×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C2×C29×#135C2211yescharacteristic
18C2×C29×#135C2211yescharacteristic
19C2×C29×#131C2211yescharacteristic
20C2×C29×#131C2211yescharacteristic
21C2×C29×#131C2211yescharacteristic, complemented
22C22×M16×C29C2211yescharacteristic
23C29×#525C2211yescharacteristic
24C2×C29×#117C2211yescharacteristic
25C29×#452C411yescharacteristic, complemented
26C29×#452C411yescharacteristic, complemented
27C29×#451C411yescharacteristic, complemented
28C29×#450C411yescharacteristic, complemented
29C29×#449C411yescharacteristic, complemented
30C29×#449C411yescharacteristic, complemented
31C29×#448C411yescharacteristic, complemented
32C29×#447C411yescharacteristic, complemented
33C29×#444—24no—
34C29×#436—21no—
35C29×#435—21no—
36C29×#435—21no—
37C8×D4×C29—21no—
38C2×C29×#108C2211yescharacteristic, complemented
39C2×C29×#108C2211yescharacteristic, complemented
40C29×#424C2211yescharacteristic, complemented
41C29×#421—24no—
42C2×C29×#104C2211yescharacteristic
43C2×C29×#104C2211yescharacteristic
44C2×C29×#104C2211yescharacteristic
45C2×C29×#104C2211yescharacteristic
46C2×C29×#104C2211yescharacteristic, complemented
47C2×C29×#104C2211yescharacteristic, complemented
48C29×#416C2211yescharacteristic
49C29×#416C2211yescharacteristic
50C29×#408—21no—
51C29×#408—21no—
52C29×#408C2211yescharacteristic
53C29×#408C2211yescharacteristic
54C29×#408C2211yescharacteristic, complemented
55C29×#407—21no—
56C29×#407C2211yescharacteristic
57C2×C29×C22⋊C8—21no—
58C2×C29×C22⋊C8C2211yescharacteristic
59C2×C29×C22⋊C8C2211yescharacteristic
60C29×#405C2211yescharacteristic, complemented
61C2×C29×#97C2211yescharacteristic, complemented
62C2×C4×C8×C29C2211yescharacteristic, complemented
63C29×#341C2211yescharacteristic, complemented
64C29×#341C2211yescharacteristic, complemented
65C29×#339C2211yescharacteristic, complemented
66C29×#339C2211yescharacteristic, complemented
67C29×#336C2211yescharacteristic, complemented
68C29×#336C2211yescharacteristic, complemented
69C2×#41×C29—21no—
70C2×#41×C29—21no—
71C2×#41×C29—22no—
72C2×#41×C29—22no—
73C2×#41×C29—41no—
74C2×#41×C29—41no—
75C2×#41×C29C2×C411yescharacteristic
76C2×#41×C29C2×C411yescharacteristic
77C2×#41×C29C2311yescharacteristic
78C2×#41×C29C2311yescharacteristic
79C2×#41×C29C2311yescharacteristic
80C22×Q8×C29C2×C411yescharacteristic
81C22×D4×C29—21no—
82C22×D4×C29C2×C411yescharacteristic
83C23×C4×C29—21no—
84C23×C4×C29C2311yescharacteristic
85C29×#135—22no—
86C29×#135—22no—
87C29×#135—41no—
88C29×#135—41no—
89C2×Q16×C29C2×C411yescharacteristic
90C2×Q16×C29C2×C411yescharacteristic
91C2×SD16×C29C2×C411yescharacteristic
92C2×SD16×C29C2×C411yescharacteristic
93C2×SD16×C29C2×C411yescharacteristic
94C2×SD16×C29C2×C411yescharacteristic
95C2×D8×C29C2×C411yescharacteristic
96C2×D8×C29C2×C411yescharacteristic
97C29×#131—22no—
98C29×#131—22no—
99C29×#131—22no—
100C29×#131—41no—
101C29×#131—41no—
102C29×#131—41no—
103C2×M16×C29—21no—
104C2×M16×C29—21no—
105C2×M16×C29—21no—
106C2×M16×C29—21no—
107C2×M16×C29—22no—
108C2×M16×C29—41no—
109C2×M16×C29C2311yescharacteristic
110C2×M16×C29C2311yescharacteristic
111C2×M16×C29C2311yescharacteristic
112C2×M16×C29C2311yescharacteristic
113C22×C8×C29—21no—
114C22×C8×C29—21no—
115C22×C8×C29—21no—
116C22×C8×C29—21no—
117C22×C8×C29C2311yescharacteristic
118C22×C8×C29C2311yescharacteristic
119C22×C8×C29C2311yescharacteristic
120C22×C8×C29C2311yescharacteristic
121C29×#123—21no—
122C29×C22⋊Q8C2×C411yescharacteristic
123C29×C22⋊Q8C2×C411yescharacteristic
124C29×#121C2×C411yescharacteristic
125C29×#121C2×C411yescharacteristic
126C29×#120—21no—
127C4×D4×C29—21no—
128C4×D4×C29—21no—
129C29×#117—22no—
130C29×#117—41no—
131C29×#117C2311yescharacteristic
132C2×C4⋊C4×C29—21no—
133C2×C22⋊C4×C29—21no—
134C2×C42×C29C2311yescharacteristic
135C2×C42×C29C2311yescharacteristic
136C29×#108—22no—
137C29×#108—41no—
138C29×C4⋊C8—21no—
139C29×C4⋊C8—21no—
140C29×#104—22no—
141C29×#104—22no—
142C29×#104—22no—
143C29×#104—22no—
144C29×#104—41no—
145C29×#104D414yescomplemented
146C29×#103C2×C411yescharacteristic
147C29×#103C2×C411yescharacteristic
148C29×#103C2×C411yescharacteristic
149C29×#103C2×C411yescharacteristic
150C29×#102C2×C411yescharacteristic
151C29×#102C2×C411yescharacteristic
152C29×#102C2×C411yescharacteristic
153C29×#102C2×C411yescharacteristic
154C29×C22⋊C8—21no—
155C29×C22⋊C8—21no—
156C29×C22⋊C8—21no—
157C29×C22⋊C8—21no—
158C29×C22⋊C8—21no—
159C29×C22⋊C8—21no—
160C29×C22⋊C8—21no—
161C29×C22⋊C8—21no—
162C29×C22⋊C8C2×C411yescharacteristic
163C29×C22⋊C8C2×C411yescharacteristic
164C29×C22⋊C8C2×C411yescharacteristic
165C29×C22⋊C8C2×C411yescharacteristic
166C29×C22⋊C8D411yescharacteristic
167C29×C22⋊C8D411yescharacteristic
168C29×C22⋊C8D411yescharacteristic
169C29×C22⋊C8D411yescharacteristic
170C29×#97—21no—
171C29×#97—22no—
172C4×C8×C29—21no—
173C4×C8×C29—41no—
174C24×C29—21no—
175C24×C29#4111yescharacteristic
176#41×C29—21no—
177#41×C29—21no—
178#41×C29—22no—
179#41×C29—22no—
180#41×C29—21no—
181#41×C29—21no—
182#41×C29—21no—
183#41×C29—21no—
184#41×C29—21no—
185#41×C29—21no—
186#41×C29—21no—
187#41×C29—21no—
188#41×C29—42no—
189#41×C29—42no—
190#41×C29—41no—
191#41×C29—41no—
192#41×C29—42no—
193#41×C29—42no—
194#41×C29C2×D412yes—
195#41×C29#4112yes—
196C2×Q8×C29—21no—
197C2×Q8×C29—22no—
198C2×Q8×C29—41no—
199C2×Q8×C29C22×C411yescharacteristic
200C2×Q8×C29C22×C411yescharacteristic
201C2×Q8×C29C22×C411yescharacteristic
202C2×D4×C29—21no—
203C2×D4×C29—22no—
204C2×D4×C29—21no—
205C2×D4×C29—21no—
206C2×D4×C29—21no—
207C2×D4×C29—21no—
208C2×D4×C29—21no—
209C2×D4×C29—21no—
210C2×D4×C29—21no—
211C2×D4×C29—41no—
212C2×D4×C29—42no—
213C2×D4×C29—42no—
214C2×D4×C29C22×C411yescharacteristic
215C2×D4×C29C22×C411yescharacteristic
216C2×D4×C29C22×C411yescharacteristic
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—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—21no—
227C22×C4×C29—21no—
228C22×C4×C29—21no—
229C22×C4×C29—42no—
230C22×C4×C29—42no—
231C22×C4×C29C22×C411yescharacteristic
232C22×C4×C29C22×C411yescharacteristic
233C22×C4×C29C2×D411yescharacteristic
234C22×C4×C29C2×D411yescharacteristic
235C22×C4×C29#4111yescharacteristic
236C22×C4×C29C2411yescharacteristic
237Q16×C29—22no—
238Q16×C29—41no—
239SD16×C29—22no—
240SD16×C29—22no—
241SD16×C29—41no—
242SD16×C29—41no—
243D8×C29—22no—
244D8×C29—41no—
245M16×C29—21no—
246M16×C29—21no—
247M16×C29—21no—
248M16×C29—21no—
249M16×C29—21no—
250M16×C29—21no—
251M16×C29—21no—
252M16×C29—42no—
253M16×C29—42no—
254M16×C29—42no—
255M16×C29—42no—
256M16×C29C2×D412yes—
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—21no—
266C2×C8×C29—21no—
267C2×C8×C29—21no—
268C2×C8×C29—21no—
269C2×C8×C29—42no—
270C2×C8×C29—42no—
271C2×C8×C29—42no—
272C2×C8×C29—42no—
273C2×C8×C29C22×C411yescharacteristic
274C2×C8×C29C22×C411yescharacteristic
275C2×C8×C29C22×C411yescharacteristic
276C2×C8×C29C22×C411yescharacteristic
277C2×C8×C29C2×D411yescharacteristic
278C2×C8×C29C2×D411yescharacteristic
279C2×C8×C29C2×D411yescharacteristic
280C2×C8×C29C2×D411yescharacteristic
281C4⋊C4×C29—21no—
282C4⋊C4×C29—21no—
283C4⋊C4×C29—42no—
284C4⋊C4×C29C22×C411yescharacteristic
285C4⋊C4×C29C22×C411yescharacteristic
286C22⋊C4×C29—21no—
287C22⋊C4×C29—21no—
288C22⋊C4×C29—21no—
289C22⋊C4×C29—21no—
290C22⋊C4×C29—21no—
291C22⋊C4×C29—42no—
292C42×C29—21no—
293C42×C29—21no—
294C42×C29—21no—
295C42×C29—21no—
296C42×C29C2×D412yes—
297#22887C2911yesmaximal, characteristic, direct product factor, Sylow
298C23×C29—21no—
299C23×C29—21no—
300C23×C29—21no—
301C23×C29—21no—
302C23×C29—21no—
303C23×C29—41no—
304C23×C29—41no—
305C23×C29—42no—
306C23×C29—42no—
307C23×C29—81no—
308C23×C29C4×D411yescharacteristic
309C23×C29C4×D411yescharacteristic
310C23×C29C2×#4111yescharacteristic
311Q8×C29—21no—
312Q8×C29—21no—
313Q8×C29—21no—
314Q8×C29—21no—
315Q8×C29—21no—
316Q8×C29—42no—
317Q8×C29C4×D412yes—
318D4×C29—22no—
319D4×C29—22no—
320D4×C29—21no—
321D4×C29—21no—
322D4×C29—21no—
323D4×C29—21no—
324D4×C29—21no—
325D4×C29—42no—
326D4×C29—42no—
327D4×C29—42no—
328D4×C29—42no—
329D4×C29—41no—
330D4×C29—41no—
331D4×C29—41no—
332D4×C29—41no—
333D4×C29—81no—
334D4×C29C4×D412yes—
335C2×C4×C29—21no—
336C2×C4×C29—21no—
337C2×C4×C29—21no—
338C2×C4×C29—21no—
339C2×C4×C29—21no—
340C2×C4×C29—21no—
341C2×C4×C29—21no—
342C2×C4×C29—21no—
343C2×C4×C29—22no—
344C2×C4×C29—21no—
345C2×C4×C29—22no—
346C2×C4×C29—21no—
347C2×C4×C29—21no—
348C2×C4×C29—21no—
349C2×C4×C29—21no—
350C2×C4×C29—21no—
351C2×C4×C29—21no—
352C2×C4×C29—22no—
353C2×C4×C29—42no—
354C2×C4×C29—42no—
355C2×C4×C29—42no—
356C2×C4×C29—41no—
357C2×C4×C29—41no—
358C2×C4×C29—41no—
359C2×C4×C29—41no—
360C2×C4×C29—41no—
361C2×C4×C29—41no—
362C2×C4×C29—41no—
363C2×C4×C29—41no—
364C2×C4×C29—41no—
365C2×C4×C29C4×D411yescharacteristic
366C2×C4×C29C4×D411yescharacteristic
367C2×C4×C29C23×C411yescharacteristic
368C2×C4×C29C22×D411yescharacteristic
369C2×C4×C29C22×D411yescharacteristic
370C2×C4×C29C2×#4111yescharacteristic
371C2×C4×C29H(5,𝔽2)11yescharacteristic
372C2×C4×C29H(5,𝔽2)11yescharacteristic
373C8×C29—21no—
374C8×C29—21no—
375C8×C29—21no—
376C8×C29—21no—
377C8×C29—21no—
378C8×C29—21no—
379C8×C29—22no—
380C8×C29—21no—
381C8×C29—21no—
382C8×C29—41no—
383C8×C29—41no—
384C8×C29—41no—
385#3002C2×C2911yescharacteristic
386C2×#444C2×C2911yescharacteristic, complemented
387#2933C2×C2911yescharacteristic, complemented
388C2×#421C2×C2911yescharacteristic, complemented
389#2880C2×C2911yescharacteristic, complemented
390#1974C2×C2911yescharacteristic, complemented
391#1938C2×C2911yescharacteristic, complemented
392#1929C2×C2911yescharacteristic, complemented
393#1897C2×C2911yescharacteristic, complemented
394#1876C2×C2911yescharacteristic, complemented
395#1876C2×C2911yescharacteristic, complemented
396#1866C2×C2911yescharacteristic, complemented
397#1855C2×C2911yescharacteristic, complemented
398#1764C2×C2911yescharacteristic, complemented
399#1750C2×C2911yescharacteristic, complemented
400C22×C29—21no—
401C22×C29—21no—
402C22×C29—21no—
403C22×C29—21no—
404C22×C29—22no—
405C22×C29—21no—
406C22×C29—21no—
407C22×C29—21no—
408C22×C29—21no—
409C22×C29—41no—
410C22×C29—41no—
411C22×C29—41no—
412C22×C29—41no—
413C22×C29—41no—
414C22×C29—41no—
415C22×C29—41no—
416C22×C29—41no—
417C22×C29—81no—
418C22×C29—81no—
419C22×C29—84no—
420C22×C29C2×C4×D411yescharacteristic
421C22×C29#54611yescharacteristic
422C22×C29#55111yescharacteristic
423C4×C29—21no—
424C4×C29—21no—
425C4×C29—22no—
426C4×C29—42no—
427C4×C29—41no—
428C4×C29—41no—
429C4×C29—41no—
430C4×C29—41no—
431C4×C29—81no—
432C4×C29C2×C4×D411yescharacteristic
433C4×C29#51811yescharacteristic
434C4×C29D4211yescharacteristic
435C4×C29#54611yescharacteristic
436C22×#41C22×C2911yescharacteristic
437C2×#135C22×C2911yescharacteristic
438C2×#135C22×C2911yescharacteristic
439C2×#131C22×C2911yescharacteristic
440C2×#131C22×C2911yescharacteristic
441C2×#131C22×C2911yescharacteristic, complemented
442C22×M16C22×C2911yescharacteristic
443#525C22×C2911yescharacteristic
444C2×#117C22×C2911yescharacteristic
445#452C4×C2911yescharacteristic, complemented
446#452C4×C2911yescharacteristic, complemented
447#451C4×C2911yescharacteristic, complemented
448#450C4×C2911yescharacteristic, complemented
449#449C4×C2911yescharacteristic, complemented
450#449C4×C2911yescharacteristic, complemented
451#448C4×C2911yescharacteristic, complemented
452#447C4×C2911yescharacteristic, complemented
453#444—24no—
454#436—21no—
455#435—21no—
456#435—21no—
457C8×D4—21no—
458C2×#108C22×C2911yescharacteristic, complemented
459C2×#108C22×C2911yescharacteristic, complemented
460#424C22×C2911yescharacteristic, complemented
461#421—24no—
462C2×#104C22×C2911yescharacteristic
463C2×#104C22×C2911yescharacteristic
464C2×#104C22×C2911yescharacteristic
465C2×#104C22×C2911yescharacteristic
466C2×#104C22×C2911yescharacteristic, complemented
467C2×#104C22×C2911yescharacteristic, complemented
468#416C22×C2911yescharacteristic
469#416C22×C2911yescharacteristic
470#408—21no—
471#408—21no—
472#408C22×C2911yescharacteristic
473#408C22×C2911yescharacteristic
474#408C22×C2911yescharacteristic, complemented
475#407—21no—
476#407C22×C2911yescharacteristic
477C2×C22⋊C8—21no—
478C2×C22⋊C8C22×C2911yescharacteristic
479C2×C22⋊C8C22×C2911yescharacteristic
480#405C22×C2911yescharacteristic, complemented
481C2×#97C22×C2911yescharacteristic, complemented
482C2×C4×C8C22×C2911yescharacteristic, complemented
483#341C22×C2911yescharacteristic, complemented
484#341C22×C2911yescharacteristic, complemented
485#339C22×C2911yescharacteristic, complemented
486#339C22×C2911yescharacteristic, complemented
487#336C22×C2911yescharacteristic, complemented
488#336C22×C2911yescharacteristic, complemented
489C2×C29—21no—
490C2×C29—21no—
491C2×C29—41no—
492C2×C29—41no—
493C2×C29—42no—
494C2×C29—81no—
495C2×C29—81no—
496C2×C29#235811yescharacteristic
497C2×C29#295511yescharacteristic
498C2×C29#295711yescharacteristic
499C2×#41—21no—
500C2×#41—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41C2×C4×C2911yescharacteristic
506C2×#41C2×C4×C2911yescharacteristic
507C2×#41C23×C2911yescharacteristic
508C2×#41C23×C2911yescharacteristic
509C2×#41C23×C2911yescharacteristic
510C22×Q8C2×C4×C2911yescharacteristic
511C22×D4—21no—
512C22×D4C2×C4×C2911yescharacteristic
513C23×C4—21no—
514C23×C4C23×C2911yescharacteristic
515#135—22no—
516#135—22no—
517#135—41no—
518#135—41no—
519C2×Q16C2×C4×C2911yescharacteristic
520C2×Q16C2×C4×C2911yescharacteristic
521C2×SD16C2×C4×C2911yescharacteristic
522C2×SD16C2×C4×C2911yescharacteristic
523C2×SD16C2×C4×C2911yescharacteristic
524C2×SD16C2×C4×C2911yescharacteristic
525C2×D8C2×C4×C2911yescharacteristic
526C2×D8C2×C4×C2911yescharacteristic
527#131—22no—
528#131—22no—
529#131—22no—
530#131—41no—
531#131—41no—
532#131—41no—
533C2×M16—21no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16C23×C2911yescharacteristic
540C2×M16C23×C2911yescharacteristic
541C2×M16C23×C2911yescharacteristic
542C2×M16C23×C2911yescharacteristic
543C22×C8—21no—
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8C23×C2911yescharacteristic
548C22×C8C23×C2911yescharacteristic
549C22×C8C23×C2911yescharacteristic
550C22×C8C23×C2911yescharacteristic
551#123—21no—
552C22⋊Q8C2×C4×C2911yescharacteristic
553C22⋊Q8C2×C4×C2911yescharacteristic
554#121C2×C4×C2911yescharacteristic
555#121C2×C4×C2911yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117—22no—
560#117—41no—
561#117C23×C2911yescharacteristic
562C2×C4⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C42C23×C2911yescharacteristic
565C2×C42C23×C2911yescharacteristic
566#108—22no—
567#108—41no—
568C4⋊C8—21no—
569C4⋊C8—21no—
570#104—22no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—41no—
575#104D4×C2914yescomplemented
576#103C2×C4×C2911yescharacteristic
577#103C2×C4×C2911yescharacteristic
578#103C2×C4×C2911yescharacteristic
579#103C2×C4×C2911yescharacteristic
580#102C2×C4×C2911yescharacteristic
581#102C2×C4×C2911yescharacteristic
582#102C2×C4×C2911yescharacteristic
583#102C2×C4×C2911yescharacteristic
584C22⋊C8—21no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8C2×C4×C2911yescharacteristic
593C22⋊C8C2×C4×C2911yescharacteristic
594C22⋊C8C2×C4×C2911yescharacteristic
595C22⋊C8C2×C4×C2911yescharacteristic
596C22⋊C8D4×C2911yescharacteristic
597C22⋊C8D4×C2911yescharacteristic
598C22⋊C8D4×C2911yescharacteristic
599C22⋊C8D4×C2911yescharacteristic
600#97—21no—
601#97—22no—
602C4×C8—21no—
603C4×C8—41no—
604C29#2288711yescharacteristic, direct product factor, Sylow
605C24—21no—
606C24#41×C2911yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C2912yes—
626#41#41×C2912yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C2911yescharacteristic
631C2×Q8C22×C4×C2911yescharacteristic
632C2×Q8C22×C4×C2911yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C2911yescharacteristic
646C2×D4C22×C4×C2911yescharacteristic
647C2×D4C22×C4×C2911yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C2911yescharacteristic
663C22×C4C22×C4×C2911yescharacteristic
664C22×C4C2×D4×C2911yescharacteristic
665C22×C4C2×D4×C2911yescharacteristic
666C22×C4#41×C2911yescharacteristic
667C22×C4C24×C2911yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C2912yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C2911yescharacteristic
705C2×C8C22×C4×C2911yescharacteristic
706C2×C8C22×C4×C2911yescharacteristic
707C2×C8C22×C4×C2911yescharacteristic
708C2×C8C2×D4×C2911yescharacteristic
709C2×C8C2×D4×C2911yescharacteristic
710C2×C8C2×D4×C2911yescharacteristic
711C2×C8C2×D4×C2911yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C2911yescharacteristic
716C4⋊C4C22×C4×C2911yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C2912yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C2911yescharacteristic
739C23C4×D4×C2911yescharacteristic
740C23C2×#41×C2911yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C2912yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C2912yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C2911yescharacteristic
796C2×C4C4×D4×C2911yescharacteristic
797C2×C4C23×C4×C2911yescharacteristic
798C2×C4C22×D4×C2911yescharacteristic
799C2×C4C22×D4×C2911yescharacteristic
800C2×C4C2×#41×C2911yescharacteristic
801C2×C4C29×H(5,𝔽2)11yescharacteristic
802C2×C4C29×H(5,𝔽2)11yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C2911yescharacteristic
836C22C29×#54611yescharacteristic
837C22C29×#55111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C2911yescharacteristic
848C4C29×#51811yescharacteristic
849C4D42×C2911yescharacteristic
850C4C29×#54611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C29×#235811yescharacteristic
859C2C29×#295511yescharacteristic
860C2C29×#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 ◁ C2×C29×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#444C2semidirect
3. C29×#2933C2semidirect
4. C2×C29×#421C2semidirect
5. C29×#2880C2semidirect
6. C29×#1974C2semidirect
7. C29×#1938C2semidirect
8. C29×#1929C2semidirect
9. C29×#1897C2semidirect
10. C29×#1876C2semidirect
11. C29×#1876C2semidirect
12. C29×#1866C2semidirect
13. C29×#1855C2semidirect
14. C29×#1764C2semidirect
15. C29×#1750C2semidirect
21. C2×C29×#131C22semidirect
25. C29×#452C4semidirect
26. C29×#452C4semidirect
27. C29×#451C4semidirect
28. C29×#450C4semidirect
29. C29×#449C4semidirect
30. C29×#449C4semidirect
31. C29×#448C4semidirect
32. C29×#447C4semidirect
38. C2×C29×#108C22semidirect
39. C2×C29×#108C22semidirect
40. C29×#424C22semidirect
46. C2×C29×#104C22semidirect
47. C2×C29×#104C22semidirect
54. C29×#408C22semidirect
60. C29×#405C22semidirect
61. C2×C29×#97C22semidirect
62. C2×C4×C8×C29C22semidirect
63. C29×#341C22semidirect
64. C29×#341C22semidirect
65. C29×#339C22semidirect
66. C29×#339C22semidirect
67. C29×#336C22semidirect
68. C29×#336C22semidirect
145. C29×#104D4semidirect
297. #22887C29direct (N × H)
386. C2×#444C2×C29semidirect
387. #2933C2×C29semidirect
388. C2×#421C2×C29semidirect
389. #2880C2×C29semidirect
390. #1974C2×C29semidirect
391. #1938C2×C29semidirect
392. #1929C2×C29semidirect
393. #1897C2×C29semidirect
394. #1876C2×C29semidirect
395. #1876C2×C29semidirect
396. #1866C2×C29semidirect
397. #1855C2×C29semidirect
398. #1764C2×C29semidirect
399. #1750C2×C29semidirect
441. C2×#131C22×C29semidirect
445. #452C4×C29semidirect
446. #452C4×C29semidirect
447. #451C4×C29semidirect
448. #450C4×C29semidirect
449. #449C4×C29semidirect
450. #449C4×C29semidirect
451. #448C4×C29semidirect
452. #447C4×C29semidirect
458. C2×#108C22×C29semidirect
459. C2×#108C22×C29semidirect
460. #424C22×C29semidirect
466. C2×#104C22×C29semidirect
467. C2×#104C22×C29semidirect
474. #408C22×C29semidirect
480. #405C22×C29semidirect
481. C2×#97C22×C29semidirect
482. C2×C4×C8C22×C29semidirect
483. #341C22×C29semidirect
484. #341C22×C29semidirect
485. #339C22×C29semidirect
486. #339C22×C29semidirect
487. #336C22×C29semidirect
488. #336C22×C29semidirect
575. #104D4×C29semidirect
604. C29#22887direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30022
C2×C29×#4442
C29×#29332
C2×C29×#4212
C29×#28802
C29×#19742
C29×#19382
C29×#19292
C29×#18972
C29×#18762
C29×#18662
C29×#18552
C29×#17642
C29×#17502
#2288729