Finite Group Databasebeta

← C29×#16290 #20311190

Subgroups — C29×#16290 #20311190

Order 7424.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#396C211yesmaximal, characteristic, complemented
2C2×C29×#396C211yesmaximal, characteristic, complemented
3C2×C29×#394C211yesmaximal, characteristic, complemented
4C2×C29×#394C211yesmaximal, characteristic, complemented
5C2×C29×#394C211yesmaximal, characteristic, complemented
6C2×C29×#392C211yesmaximal, characteristic
7C2×C29×#390C211yesmaximal, characteristic, complemented
8C2×C29×#388C211yesmaximal, characteristic, complemented
9C29×#1444C211yesmaximal, characteristic, complemented
10C29×#1439C211yesmaximal, characteristic, complemented
11C29×#1439C211yesmaximal, characteristic, complemented
12C29×#1439C211yesmaximal, characteristic, complemented
13C29×#1438C211yesmaximal, characteristic, complemented
14C29×#1438C211yesmaximal, characteristic, complemented
15C29×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C29C2211yescharacteristic
17C23×D4×C29C2211yescharacteristic
18C23×D4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C4⋊C4×C29C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C22×C4⋊C4×C29C2211yescharacteristic
25C22×C22⋊C4×C29C2211yescharacteristic
26C22×C22⋊C4×C29C2211yescharacteristic
27C22×C22⋊C4×C29C2211yescharacteristic
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C22⋊C4×C29C2211yescharacteristic
30C22×C22⋊C4×C29C2211yescharacteristic
31C22×C22⋊C4×C29C2211yescharacteristic
32C22×C22⋊C4×C29C2211yescharacteristic
33C22×C22⋊C4×C29C2211yescharacteristic
34C22×C22⋊C4×C29C2211yescharacteristic
35C22×C22⋊C4×C29C2211yescharacteristic
36C22×C22⋊C4×C29C2211yescharacteristic
37C22×C22⋊C4×C29C2211yescharacteristic
38C22×C22⋊C4×C29C2211yescharacteristic
39C22×C22⋊C4×C29C2211yescharacteristic
40C22×C42×C29C2211yescharacteristic
41C29×#396—24no—
42C29×#396—24no—
43C29×#394—24no—
44C29×#394—24no—
45C29×#394—24no—
46C29×#392—24no—
47C29×#390—24no—
48C29×#388—24no—
49C2×C29×#95C2211yescharacteristic
50C2×C29×#95C2211yescharacteristic
51C2×C29×#95C2211yescharacteristic
52C2×C29×#95C2211yescharacteristic
53C2×C29×#95C2211yescharacteristic
54C2×C29×#95C2211yescharacteristic
55C2×C29×#95C2211yescharacteristic
56C2×C29×#95C2211yescharacteristic
57C2×C29×#95C2211yescharacteristic
58C2×C29×#95C2211yescharacteristic
59C25×C29C2311yescharacteristic
60C25×C29C2311yescharacteristic
61C25×C29C2311yescharacteristic
62C22×D4×C29—22no—
63C22×D4×C29—22no—
64C22×D4×C29—22no—
65C22×D4×C29—22no—
66C22×D4×C29—22no—
67C22×D4×C29—22no—
68C22×D4×C29—22no—
69C22×D4×C29—22no—
70C22×D4×C29—22no—
71C22×D4×C29—22no—
72C22×D4×C29—22no—
73C22×D4×C29—41no—
74C22×D4×C29—41no—
75C22×D4×C29—41no—
76C22×D4×C29—41no—
77C22×D4×C29—41no—
78C22×D4×C29—41no—
79C22×D4×C29—41no—
80C22×D4×C29—41no—
81C22×D4×C29—41no—
82C22×D4×C29—41no—
83C23×C4×C29C2311yescharacteristic
84C23×C4×C29C2311yescharacteristic
85C23×C4×C29C2311yescharacteristic
86C23×C4×C29C2311yescharacteristic
87C23×C4×C29C2311yescharacteristic
88C23×C4×C29C2311yescharacteristic
89C23×C4×C29C2311yescharacteristic
90C23×C4×C29C2311yescharacteristic
91C23×C4×C29C2311yescharacteristic
92C23×C4×C29C2311yescharacteristic
93C23×C4×C29C2311yescharacteristic
94C23×C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29—22no—
96C2×C4⋊C4×C29—22no—
97C2×C4⋊C4×C29—22no—
98C2×C4⋊C4×C29—22no—
99C2×C4⋊C4×C29—22no—
100C2×C4⋊C4×C29—22no—
101C2×C4⋊C4×C29—22no—
102C2×C4⋊C4×C29—22no—
103C2×C4⋊C4×C29—22no—
104C2×C4⋊C4×C29—22no—
105C2×C4⋊C4×C29—22no—
106C2×C4⋊C4×C29—22no—
107C2×C4⋊C4×C29—41no—
108C2×C4⋊C4×C29—41no—
109C2×C4⋊C4×C29—41no—
110C2×C4⋊C4×C29—41no—
111C2×C4⋊C4×C29—41no—
112C2×C4⋊C4×C29—41no—
113C2×C22⋊C4×C29—22no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—22no—
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—22no—
119C2×C22⋊C4×C29—22no—
120C2×C22⋊C4×C29—22no—
121C2×C22⋊C4×C29—22no—
122C2×C22⋊C4×C29—22no—
123C2×C22⋊C4×C29—22no—
124C2×C22⋊C4×C29—22no—
125C2×C22⋊C4×C29—22no—
126C2×C22⋊C4×C29—22no—
127C2×C22⋊C4×C29—22no—
128C2×C22⋊C4×C29—22no—
129C2×C22⋊C4×C29—22no—
130C2×C22⋊C4×C29—22no—
131C2×C22⋊C4×C29—22no—
132C2×C22⋊C4×C29—22no—
133C2×C22⋊C4×C29—22no—
134C2×C22⋊C4×C29—22no—
135C2×C22⋊C4×C29—22no—
136C2×C22⋊C4×C29—22no—
137C2×C22⋊C4×C29—22no—
138C2×C22⋊C4×C29—22no—
139C2×C22⋊C4×C29—22no—
140C2×C22⋊C4×C29—41no—
141C2×C22⋊C4×C29—41no—
142C2×C22⋊C4×C29—41no—
143C2×C22⋊C4×C29—41no—
144C2×C22⋊C4×C29—41no—
145C2×C22⋊C4×C29—41no—
146C2×C22⋊C4×C29—41no—
147C2×C22⋊C4×C29—41no—
148C2×C22⋊C4×C29—41no—
149C2×C22⋊C4×C29—41no—
150C2×C22⋊C4×C29—41no—
151C2×C22⋊C4×C29—41no—
152C2×C22⋊C4×C29—41no—
153C2×C22⋊C4×C29—41no—
154C2×C22⋊C4×C29—41no—
155C2×C22⋊C4×C29—41no—
156C2×C22⋊C4×C29D414yes—
157C2×C22⋊C4×C29D414yescomplemented
158C2×C42×C29—22no—
159C2×C42×C29—22no—
160C2×C42×C29—41no—
161C29×#95—22no—
162C29×#95—22no—
163C29×#95—22no—
164C29×#95—22no—
165C29×#95—22no—
166C29×#95—41no—
167C29×#95—41no—
168C29×#95—41no—
169C29×#95D414yescomplemented
170C29×#95D414yescomplemented
171C24×C29—21no—
172C24×C29—21no—
173C24×C29—21no—
174C24×C29—21no—
175C24×C29—21no—
176C24×C29—21no—
177C24×C29—21no—
178C24×C29—21no—
179C24×C29—21no—
180C24×C29—21no—
181C24×C29—21no—
182C24×C29—21no—
183C24×C29—21no—
184C24×C29—21no—
185C24×C29—21no—
186C24×C29—21no—
187C24×C29—21no—
188C24×C29—21no—
189C24×C29—21no—
190C24×C29—21no—
191C24×C29—21no—
192C24×C29—21no—
193C24×C29—21no—
194C24×C29—21no—
195C24×C29—21no—
196C24×C29—21no—
197C24×C29—21no—
198C24×C29—21no—
199C24×C29—21no—
200C24×C29—21no—
201C24×C29—21no—
202C24×C29—21no—
203C24×C29—21no—
204C24×C29—21no—
205C24×C29—21no—
206C24×C29—21no—
207C24×C29—21no—
208C24×C29—21no—
209C24×C29—21no—
210C24×C29—21no—
211C24×C29—21no—
212C24×C29—21no—
213C24×C29C2×D412yes—
214C24×C29C2×D412yes—
215C24×C29#4112yes—
216C24×C29C2411yescharacteristic
217C2×D4×C29—28no—
218C2×D4×C29—44no—
219C2×D4×C29—44no—
220C2×D4×C29—44no—
221C2×D4×C29—44no—
222C2×D4×C29—44no—
223C2×D4×C29—44no—
224C2×D4×C29—44no—
225C2×D4×C29—44no—
226C2×D4×C29—44no—
227C2×D4×C29—44no—
228C2×D4×C29—44no—
229C2×D4×C29—44no—
230C2×D4×C29—44no—
231C2×D4×C29—44no—
232C2×D4×C29—44no—
233C2×D4×C29—44no—
234C2×D4×C29—44no—
235C2×D4×C29—44no—
236C2×D4×C29—44no—
237C2×D4×C29—44no—
238C22×C4×C29—21no—
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—21no—
248C22×C4×C29—21no—
249C22×C4×C29—21no—
250C22×C4×C29—21no—
251C22×C4×C29—21no—
252C22×C4×C29—21no—
253C22×C4×C29—21no—
254C22×C4×C29—21no—
255C22×C4×C29—21no—
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—21no—
259C22×C4×C29—21no—
260C22×C4×C29—21no—
261C22×C4×C29—21no—
262C22×C4×C29—21no—
263C22×C4×C29—21no—
264C22×C4×C29—21no—
265C22×C4×C29—21no—
266C22×C4×C29—21no—
267C22×C4×C29—21no—
268C22×C4×C29—21no—
269C22×C4×C29—21no—
270C22×C4×C29—21no—
271C22×C4×C29—21no—
272C22×C4×C29—21no—
273C22×C4×C29—21no—
274C22×C4×C29—21no—
275C22×C4×C29—21no—
276C22×C4×C29—21no—
277C22×C4×C29—21no—
278C22×C4×C29—21no—
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×C29—21no—
288C22×C4×C29—21no—
289C22×C4×C29—21no—
290C22×C4×C29—21no—
291C22×C4×C29—21no—
292C22×C4×C29—21no—
293C22×C4×C29—21no—
294C22×C4×C29—21no—
295C22×C4×C29—21no—
296C22×C4×C29—21no—
297C22×C4×C29—21no—
298C22×C4×C29—21no—
299C22×C4×C29—21no—
300C22×C4×C29—21no—
301C22×C4×C29—21no—
302C22×C4×C29—21no—
303C22×C4×C29—21no—
304C22×C4×C29—21no—
305C22×C4×C29—21no—
306C22×C4×C29—21no—
307C22×C4×C29—21no—
308C22×C4×C29—21no—
309C22×C4×C29—21no—
310C22×C4×C29C2×D412yes—
311C22×C4×C29C2×D412yes—
312C22×C4×C29C2×D412yes—
313C22×C4×C29C2×D412yes—
314C22×C4×C29C2×D412yes—
315C22×C4×C29C2×D412yes—
316C22×C4×C29C2×D412yes—
317C22×C4×C29C2×D412yes—
318C22×C4×C29C2×D412yes—
319C22×C4×C29C2×D412yes—
320C22×C4×C29#4112yes—
321C22×C4×C29#4112yes—
322C4⋊C4×C29—44no—
323C4⋊C4×C29—44no—
324C4⋊C4×C29—44no—
325C4⋊C4×C29—44no—
326C4⋊C4×C29—44no—
327C4⋊C4×C29—44no—
328C22⋊C4×C29—28no—
329C22⋊C4×C29—44no—
330C22⋊C4×C29—44no—
331C22⋊C4×C29—44no—
332C22⋊C4×C29—44no—
333C22⋊C4×C29—44no—
334C22⋊C4×C29—44no—
335C22⋊C4×C29—44no—
336C22⋊C4×C29—44no—
337C22⋊C4×C29—44no—
338C22⋊C4×C29—44no—
339C22⋊C4×C29—44no—
340C22⋊C4×C29—44no—
341C22⋊C4×C29—44no—
342C22⋊C4×C29—44no—
343C42×C29—44no—
344#16290C2911yesmaximal, characteristic, direct product factor, Sylow
345C23×C29—22no—
346C23×C29—22no—
347C23×C29—22no—
348C23×C29—22no—
349C23×C29—22no—
350C23×C29—22no—
351C23×C29—22no—
352C23×C29—22no—
353C23×C29—22no—
354C23×C29—22no—
355C23×C29—22no—
356C23×C29—22no—
357C23×C29—22no—
358C23×C29—22no—
359C23×C29—22no—
360C23×C29—22no—
361C23×C29—22no—
362C23×C29—22no—
363C23×C29—22no—
364C23×C29—22no—
365C23×C29—22no—
366C23×C29—41no—
367C23×C29—41no—
368C23×C29—41no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—41no—
372C23×C29—41no—
373C23×C29—41no—
374C23×C29—41no—
375C23×C29—41no—
376C23×C29—41no—
377C23×C29—41no—
378C23×C29—41no—
379C23×C29—41no—
380C23×C29—41no—
381C23×C29—41no—
382C23×C29—41no—
383C23×C29—41no—
384C23×C29—41no—
385C23×C29—41no—
386C23×C29—41no—
387C23×C29—41no—
388C23×C29—41no—
389C23×C29—41no—
390C23×C29—41no—
391C23×C29—41no—
392C23×C29—41no—
393C23×C29—41no—
394C23×C29—41no—
395C23×C29—41no—
396C23×C29—41no—
397C23×C29—41no—
398C23×C29—41no—
399C23×C29—41no—
400C23×C29—41no—
401C23×C29—41no—
402C23×C29—41no—
403C23×C29—41no—
404C23×C29—41no—
405C23×C29—41no—
406C23×C29—41no—
407C23×C29—41no—
408C23×C29—41no—
409C23×C29—41no—
410C23×C29—41no—
411C23×C29—41no—
412C23×C29—41no—
413C23×C29—41no—
414C23×C29—41no—
415C23×C29—41no—
416C23×C29—41no—
417C23×C29—41no—
418C23×C29—41no—
419C23×C29—41no—
420C23×C29—41no—
421C23×C29—41no—
422C23×C29—41no—
423C23×C29—41no—
424C23×C29—41no—
425C23×C29—41no—
426C23×C29—41no—
427C23×C29—41no—
428C23×C29—41no—
429C23×C29—41no—
430C23×C29—41no—
431C23×C29—41no—
432C23×C29—41no—
433C23×C29—41no—
434C23×C29—41no—
435C23×C29—41no—
436C23×C29—41no—
437C23×C29—41no—
438C23×C29—41no—
439C23×C29—41no—
440C23×C29—41no—
441C23×C29—41no—
442C23×C29—41no—
443C23×C29—41no—
444C23×C29—41no—
445C23×C29—41no—
446C23×C29—41no—
447C23×C29—41no—
448C23×C29—41no—
449C23×C29—41no—
450C23×C29C22×D411yescharacteristic
451C23×C29C22×D411yescharacteristic
452C23×C29C22×D411yescharacteristic
453C23×C29C22×D411yescharacteristic
454C23×C29C2×#4111yescharacteristic
455C23×C29C2×#4111yescharacteristic
456C23×C29C2×#4111yescharacteristic
457C23×C29H(5,𝔽2)11yescharacteristic
458C23×C29H(5,𝔽2)11yescharacteristic
459C23×C29H(5,𝔽2)11yescharacteristic
460C23×C29H(5,𝔽2)11yescharacteristic
461C23×C29H(5,𝔽2)11yescharacteristic
462C23×C29H(5,𝔽2)11yescharacteristic
463C23×C292−1+411yescharacteristic
464C23×C292−1+411yescharacteristic
465D4×C29—416no—
466D4×C29—416no—
467D4×C29—416no—
468C2×C4×C29—22no—
469C2×C4×C29—22no—
470C2×C4×C29—22no—
471C2×C4×C29—22no—
472C2×C4×C29—22no—
473C2×C4×C29—22no—
474C2×C4×C29—22no—
475C2×C4×C29—22no—
476C2×C4×C29—22no—
477C2×C4×C29—22no—
478C2×C4×C29—22no—
479C2×C4×C29—22no—
480C2×C4×C29—22no—
481C2×C4×C29—22no—
482C2×C4×C29—22no—
483C2×C4×C29—22no—
484C2×C4×C29—22no—
485C2×C4×C29—22no—
486C2×C4×C29—22no—
487C2×C4×C29—22no—
488C2×C4×C29—22no—
489C2×C4×C29—22no—
490C2×C4×C29—22no—
491C2×C4×C29—22no—
492C2×C4×C29—22no—
493C2×C4×C29—22no—
494C2×C4×C29—22no—
495C2×C4×C29—22no—
496C2×C4×C29—22no—
497C2×C4×C29—22no—
498C2×C4×C29—22no—
499C2×C4×C29—22no—
500C2×C4×C29—22no—
501C2×C4×C29—41no—
502C2×C4×C29—41no—
503C2×C4×C29—41no—
504C2×C4×C29—41no—
505C2×C4×C29—41no—
506C2×C4×C29—41no—
507C2×C4×C29—41no—
508C2×C4×C29—41no—
509C2×C4×C29—41no—
510C2×C4×C29—41no—
511C2×C4×C29—41no—
512C2×C4×C29—41no—
513C2×C4×C29—41no—
514C2×C4×C29—41no—
515C2×C4×C29—41no—
516C2×C4×C29—41no—
517C2×C4×C29—41no—
518C2×C4×C29—41no—
519C2×C4×C29—41no—
520C2×C4×C29—41no—
521C2×C4×C29—41no—
522C2×C4×C29—41no—
523C2×C4×C29—41no—
524C2×C4×C29—41no—
525C2×C4×C29—41no—
526C2×C4×C29—41no—
527C2×C4×C29—41no—
528C2×C4×C29—41no—
529C2×C4×C29—41no—
530C2×C4×C29—41no—
531C2×C4×C29—41no—
532C2×C4×C29—41no—
533C2×C4×C29—41no—
534C2×C4×C29—41no—
535C2×C4×C29—41no—
536C2×C4×C29—41no—
537C2×C4×C29—41no—
538C2×C4×C29—41no—
539C2×C4×C29—41no—
540C2×C4×C29—41no—
541C2×C4×C29—41no—
542C2×C4×C29—41no—
543C2×C4×C29—41no—
544C2×C4×C29—41no—
545C2×C4×C29—41no—
546C2×C4×C29—41no—
547C2×C4×C29—41no—
548C2×C4×C29—41no—
549C2×C4×C29—41no—
550C2×C4×C29—41no—
551C2×C4×C29#12114yes—
552C2×#396C2×C2911yescharacteristic, complemented
553C2×#396C2×C2911yescharacteristic, complemented
554C2×#394C2×C2911yescharacteristic, complemented
555C2×#394C2×C2911yescharacteristic, complemented
556C2×#394C2×C2911yescharacteristic, complemented
557C2×#392C2×C2911yescharacteristic
558C2×#390C2×C2911yescharacteristic, complemented
559C2×#388C2×C2911yescharacteristic, complemented
560#1444C2×C2911yescharacteristic, complemented
561#1439C2×C2911yescharacteristic, complemented
562#1439C2×C2911yescharacteristic, complemented
563#1439C2×C2911yescharacteristic, complemented
564#1438C2×C2911yescharacteristic, complemented
565#1438C2×C2911yescharacteristic, complemented
566#1436C2×C2911yescharacteristic, complemented
567C22×C29—42no—
568C22×C29—42no—
569C22×C29—42no—
570C22×C29—42no—
571C22×C29—42no—
572C22×C29—42no—
573C22×C29—42no—
574C22×C29—42no—
575C22×C29—42no—
576C22×C29—42no—
577C22×C29—42no—
578C22×C29—42no—
579C22×C29—42no—
580C22×C29—42no—
581C22×C29—42no—
582C22×C29—42no—
583C22×C29—42no—
584C22×C29—42no—
585C22×C29—42no—
586C22×C29—42no—
587C22×C29—42no—
588C22×C29—81no—
589C22×C29—81no—
590C22×C29—81no—
591C22×C29—81no—
592C22×C29—81no—
593C22×C29—81no—
594C22×C29—81no—
595C22×C29—81no—
596C22×C29—81no—
597C22×C29—81no—
598C22×C29—81no—
599C22×C29—81no—
600C22×C29—81no—
601C22×C29—81no—
602C22×C29—81no—
603C22×C29—81no—
604C22×C29—81no—
605C22×C29—81no—
606C22×C29—81no—
607C22×C29—81no—
608C22×C29—81no—
609C22×C29—81no—
610C22×C29—81no—
611C22×C29—81no—
612C22×C29C2×#12111yescharacteristic
613C22×C29#52511yescharacteristic
614C22×C29#53211yescharacteristic
615C22×C29#53411yescharacteristic
616C22×C29#53511yescharacteristic
617C22×C29#53511yescharacteristic
618C22×C29#53611yescharacteristic
619C22×C29#53711yescharacteristic
620C22×C29#53711yescharacteristic
621C22×C29#53711yescharacteristic
622C22×C29#53711yescharacteristic
623C22×C29#53811yescharacteristic
624C22×C29#53811yescharacteristic
625C22×C29#53811yescharacteristic
626C22×C29#53911yescharacteristic
627C22×C29#54011yescharacteristic
628C22×C29#54211yescharacteristic
629C22×C29#54211yescharacteristic
630C22×C29#54211yescharacteristic
631C22×C29D4211yescharacteristic
632C22×C29D4211yescharacteristic
633C22×C29D4211yescharacteristic
634C22×C29D4211yescharacteristic
635C22×C29D4211yescharacteristic
636C22×C29#54611yescharacteristic
637C22×C29#54611yescharacteristic
638C22×C29#54611yescharacteristic
639C22×C29#54711yescharacteristic
640C22×C29#54811yescharacteristic
641C22×C29#55011yescharacteristic
642C22×C29#55111yescharacteristic
643C22×C29#56011yescharacteristic
644C22×C29#56011yescharacteristic
645C22×C29#56211yescharacteristic
646C22×C29#56211yescharacteristic
647C4×C29—24no—
648C4×C29—42no—
649C4×C29—42no—
650C4×C29—42no—
651C4×C29—42no—
652C4×C29—42no—
653C4×C29—42no—
654C4×C29—42no—
655C4×C29—42no—
656C4×C29—42no—
657C4×C29—81no—
658C4×C29—81no—
659C23×D4C22×C2911yescharacteristic
660C23×D4C22×C2911yescharacteristic
661C23×D4C22×C2911yescharacteristic
662C22×C4⋊C4C22×C2911yescharacteristic
663C22×C4⋊C4C22×C2911yescharacteristic
664C22×C4⋊C4C22×C2911yescharacteristic
665C22×C4⋊C4C22×C2911yescharacteristic
666C22×C4⋊C4C22×C2911yescharacteristic
667C22×C4⋊C4C22×C2911yescharacteristic
668C22×C22⋊C4C22×C2911yescharacteristic
669C22×C22⋊C4C22×C2911yescharacteristic
670C22×C22⋊C4C22×C2911yescharacteristic
671C22×C22⋊C4C22×C2911yescharacteristic
672C22×C22⋊C4C22×C2911yescharacteristic
673C22×C22⋊C4C22×C2911yescharacteristic
674C22×C22⋊C4C22×C2911yescharacteristic
675C22×C22⋊C4C22×C2911yescharacteristic
676C22×C22⋊C4C22×C2911yescharacteristic
677C22×C22⋊C4C22×C2911yescharacteristic
678C22×C22⋊C4C22×C2911yescharacteristic
679C22×C22⋊C4C22×C2911yescharacteristic
680C22×C22⋊C4C22×C2911yescharacteristic
681C22×C22⋊C4C22×C2911yescharacteristic
682C22×C22⋊C4C22×C2911yescharacteristic
683C22×C42C22×C2911yescharacteristic
684#396—24no—
685#396—24no—
686#394—24no—
687#394—24no—
688#394—24no—
689#392—24no—
690#390—24no—
691#388—24no—
692C2×#95C22×C2911yescharacteristic
693C2×#95C22×C2911yescharacteristic
694C2×#95C22×C2911yescharacteristic
695C2×#95C22×C2911yescharacteristic
696C2×#95C22×C2911yescharacteristic
697C2×#95C22×C2911yescharacteristic
698C2×#95C22×C2911yescharacteristic
699C2×#95C22×C2911yescharacteristic
700C2×#95C22×C2911yescharacteristic
701C2×#95C22×C2911yescharacteristic
702C2×C29—82no—
703C2×C29—82no—
704C2×C29—82no—
705C2×C29#242411yescharacteristic
706C2×C29#242811yescharacteristic
707C2×C29#246111yescharacteristic
708C2×C29#262011yescharacteristic
709C2×C29#263011yescharacteristic
710C2×C29#266211yescharacteristic
711C2×C29#266911yescharacteristic
712C2×C29#267211yescharacteristic
713C2×C29#267511yescharacteristic
714C2×C29#267611yescharacteristic
715C2×C29#268111yescharacteristic
716C2×C29#268211yescharacteristic
717C2×C29#268511yescharacteristic
718C2×C29#270511yescharacteristic
719C2×C29#282911yescharacteristic
720C25C23×C2911yescharacteristic
721C25C23×C2911yescharacteristic
722C25C23×C2911yescharacteristic
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C23×C4C23×C2911yescharacteristic
745C23×C4C23×C2911yescharacteristic
746C23×C4C23×C2911yescharacteristic
747C23×C4C23×C2911yescharacteristic
748C23×C4C23×C2911yescharacteristic
749C23×C4C23×C2911yescharacteristic
750C23×C4C23×C2911yescharacteristic
751C23×C4C23×C2911yescharacteristic
752C23×C4C23×C2911yescharacteristic
753C23×C4C23×C2911yescharacteristic
754C23×C4C23×C2911yescharacteristic
755C23×C4C23×C2911yescharacteristic
756C2×C4⋊C4—22no—
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—41no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4D4×C2914yes—
818C2×C22⋊C4D4×C2914yescomplemented
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—41no—
822#95—22no—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—41no—
828#95—41no—
829#95—41no—
830#95D4×C2914yescomplemented
831#95D4×C2914yescomplemented
832C29#1629011yescharacteristic, direct product factor, Sylow
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24C2×D4×C2912yes—
876C24C2×D4×C2912yes—
877C24#41×C2912yes—
878C24C24×C2911yescharacteristic
879C2×D4—28no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4C2×D4×C2912yes—
973C22×C4C2×D4×C2912yes—
974C22×C4C2×D4×C2912yes—
975C22×C4C2×D4×C2912yes—
976C22×C4C2×D4×C2912yes—
977C22×C4C2×D4×C2912yes—
978C22×C4C2×D4×C2912yes—
979C22×C4C2×D4×C2912yes—
980C22×C4C2×D4×C2912yes—
981C22×C4C2×D4×C2912yes—
982C22×C4#41×C2912yes—
983C22×C4#41×C2912yes—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C22⋊C4—28no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C42—44no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23C22×D4×C2911yescharacteristic
1112C23C22×D4×C2911yescharacteristic
1113C23C22×D4×C2911yescharacteristic
1114C23C22×D4×C2911yescharacteristic
1115C23C2×#41×C2911yescharacteristic
1116C23C2×#41×C2911yescharacteristic
1117C23C2×#41×C2911yescharacteristic
1118C23C29×H(5,𝔽2)11yescharacteristic
1119C23C29×H(5,𝔽2)11yescharacteristic
1120C23C29×H(5,𝔽2)11yescharacteristic
1121C23C29×H(5,𝔽2)11yescharacteristic
1122C23C29×H(5,𝔽2)11yescharacteristic
1123C23C29×H(5,𝔽2)11yescharacteristic
1124C23C29×2−1+411yescharacteristic
1125C23C29×2−1+411yescharacteristic
1126D4—416no—
1127D4—416no—
1128D4—416no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4C29×#12114yes—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×C29×#12111yescharacteristic
1259C22C29×#52511yescharacteristic
1260C22C29×#53211yescharacteristic
1261C22C29×#53411yescharacteristic
1262C22C29×#53511yescharacteristic
1263C22C29×#53511yescharacteristic
1264C22C29×#53611yescharacteristic
1265C22C29×#53711yescharacteristic
1266C22C29×#53711yescharacteristic
1267C22C29×#53711yescharacteristic
1268C22C29×#53711yescharacteristic
1269C22C29×#53811yescharacteristic
1270C22C29×#53811yescharacteristic
1271C22C29×#53811yescharacteristic
1272C22C29×#53911yescharacteristic
1273C22C29×#54011yescharacteristic
1274C22C29×#54211yescharacteristic
1275C22C29×#54211yescharacteristic
1276C22C29×#54211yescharacteristic
1277C22D42×C2911yescharacteristic
1278C22D42×C2911yescharacteristic
1279C22D42×C2911yescharacteristic
1280C22D42×C2911yescharacteristic
1281C22D42×C2911yescharacteristic
1282C22C29×#54611yescharacteristic
1283C22C29×#54611yescharacteristic
1284C22C29×#54611yescharacteristic
1285C22C29×#54711yescharacteristic
1286C22C29×#54811yescharacteristic
1287C22C29×#55011yescharacteristic
1288C22C29×#55111yescharacteristic
1289C22C29×#56011yescharacteristic
1290C22C29×#56011yescharacteristic
1291C22C29×#56211yescharacteristic
1292C22C29×#56211yescharacteristic
1293C4—24no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—81no—
1304C4—81no—
1305C2—82no—
1306C2—82no—
1307C2—82no—
1308C2C29×#242411yescharacteristic
1309C2C29×#242811yescharacteristic
1310C2C29×#246111yescharacteristic
1311C2C29×#262011yescharacteristic
1312C2C29×#263011yescharacteristic
1313C2C29×#266211yescharacteristic
1314C2C29×#266911yescharacteristic
1315C2C29×#267211yescharacteristic
1316C2C29×#267511yescharacteristic
1317C2C29×#267611yescharacteristic
1318C2C29×#268111yescharacteristic
1319C2C29×#268211yescharacteristic
1320C2C29×#268511yescharacteristic
1321C2C29×#270511yescharacteristic
1322C2C29×#282911yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC2×C29×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#396C2semidirect
2. C2×C29×#396C2semidirect
3. C2×C29×#394C2semidirect
4. C2×C29×#394C2semidirect
5. C2×C29×#394C2semidirect
7. C2×C29×#390C2semidirect
8. C2×C29×#388C2semidirect
9. C29×#1444C2semidirect
10. C29×#1439C2semidirect
11. C29×#1439C2semidirect
12. C29×#1439C2semidirect
13. C29×#1438C2semidirect
14. C29×#1438C2semidirect
15. C29×#1436C2semidirect
157. C2×C22⋊C4×C29D4semidirect
169. C29×#95D4semidirect
170. C29×#95D4semidirect
344. #16290C29direct (N × H)
552. C2×#396C2×C29semidirect
553. C2×#396C2×C29semidirect
554. C2×#394C2×C29semidirect
555. C2×#394C2×C29semidirect
556. C2×#394C2×C29semidirect
558. C2×#390C2×C29semidirect
559. C2×#388C2×C29semidirect
560. #1444C2×C29semidirect
561. #1439C2×C29semidirect
562. #1439C2×C29semidirect
563. #1439C2×C29semidirect
564. #1438C2×C29semidirect
565. #1438C2×C29semidirect
566. #1436C2×C29semidirect
818. C2×C22⋊C4D4×C29semidirect
830. #95D4×C29semidirect
831. #95D4×C29semidirect
832. C29#16290direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3962
C2×C29×#3942
C2×C29×#3922
C2×C29×#3902
C2×C29×#3882
C29×#14442
C29×#14392
C29×#14382
C29×#14362
#1629029