Finite Group Databasebeta

← C29×#24403 #20319303

Subgroups — C29×#24403 #20319303

Order 7424.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#575C211yesmaximal, characteristic
2C2×C29×#473C211yesmaximal, characteristic, complemented
3C2×C29×#471C211yesmaximal, characteristic, complemented
4C29×#3007C211yesmaximal, characteristic, complemented
5C2×C29×#452C211yesmaximal, characteristic, complemented
6C29×#2880C211yesmaximal, characteristic, complemented
7C29×#2052C211yesmaximal, characteristic, complemented
8C29×#2051C211yesmaximal, characteristic, complemented
9C29×#2020C211yesmaximal, characteristic, complemented
10C29×#2019C211yesmaximal, characteristic, complemented
11C29×#1908C211yesmaximal, characteristic, complemented
12C29×#1907C211yesmaximal, characteristic, complemented
13C29×#1901C211yesmaximal, characteristic, complemented
14C29×#1855C211yesmaximal, characteristic, complemented
15C29×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C22×#41×C29C2211yescharacteristic
18C29×#575—24no—
19C29×#575—24no—
20C2×C29×#137—21no—
21C2×C29×#137C2211yescharacteristic
22C2×C29×#137C2211yescharacteristic
23C2×C29×#137C2211yescharacteristic
24C2×C29×#137C2211yescharacteristic
25C2×C29×AGL(1,ℤ/8)—21no—
26C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C29×#135—21no—
29C2×C29×#135—21no—
30C22×Q16×C29C2211yescharacteristic, complemented
31C22×SD16×C29C2211yescharacteristic, complemented
32C2×C29×#131C2211yescharacteristic
33C2×C29×#131C2211yescharacteristic
34C22×M16×C29C2211yescharacteristic
35C2×C29×C22⋊Q8C2211yescharacteristic
36C29×#473—24no—
37C29×#471—24no—
38C29×#452—21no—
39C29×#452—21no—
40C29×#452—21no—
41C29×#452—21no—
42C29×#452—21no—
43C29×#452—21no—
44C29×#451—21no—
45C29×#450—21no—
46C2×C29×#108C2211yescharacteristic, complemented
47C2×C29×#108C2211yescharacteristic, complemented
48C29×#417C2211yescharacteristic
49C29×#417C2211yescharacteristic
50C2×C29×#103C2211yescharacteristic, complemented
51C2×C29×#102C2211yescharacteristic, complemented
52C2×C29×#101C2211yescharacteristic, complemented
53C2×C29×#101C2211yescharacteristic, complemented
54C2×C29×#101C2211yescharacteristic, complemented
55C2×C29×#101C2211yescharacteristic, complemented
56C2×C29×#100C2211yescharacteristic, complemented
57C2×C29×#100C2211yescharacteristic, complemented
58C29×#408—21no—
59C29×#408—21no—
60C29×#408C2211yescharacteristic
61C29×#408C2211yescharacteristic
62C29×#407—21no—
63C29×#407C2211yescharacteristic
64C29×#407C2211yescharacteristic
65C2×C29×C22⋊C8—21no—
66C2×C29×C22⋊C8C2211yescharacteristic
67C29×#343C2211yescharacteristic, complemented
68C29×#343C2211yescharacteristic, complemented
69C29×#341C2211yescharacteristic, complemented
70C29×#341C2211yescharacteristic, complemented
71C2×#41×C29—21no—
72C2×#41×C29—21no—
73C2×#41×C29—22no—
74C2×#41×C29—22no—
75C2×#41×C29—22no—
76C2×#41×C29—22no—
77C2×#41×C29—21no—
78C2×#41×C29—21no—
79C2×#41×C29—21no—
80C2×#41×C29—21no—
81C2×#41×C29—41no—
82C2×#41×C29—41no—
83C2×#41×C29—41no—
84C2×#41×C29—41no—
85C2×#41×C29D411yescharacteristic
86C2×#41×C29D411yescharacteristic
87C2×#41×C29C2311yescharacteristic
88C2×#41×C29C2311yescharacteristic
89C22×Q8×C29D411yescharacteristic
90C22×Q8×C29C2311yescharacteristic
91C22×Q8×C29C2311yescharacteristic
92C22×D4×C29—21no—
93C22×D4×C29—21no—
94C22×D4×C29D411yescharacteristic
95C22×D4×C29C2311yescharacteristic
96C23×C4×C29—21no—
97C23×C4×C29—21no—
98C23×C4×C29C2311yescharacteristic
99C29×#137—28no—
100C29×#137—22no—
101C29×#137—22no—
102C29×#137—22no—
103C29×#137—22no—
104C29×#137—22no—
105C29×#137—41no—
106C29×#137—41no—
107C29×#137D414yes—
108C29×AGL(1,ℤ/8)—28no—
109C29×AGL(1,ℤ/8)—22no—
110C29×AGL(1,ℤ/8)—22no—
111C29×AGL(1,ℤ/8)—22no—
112C29×AGL(1,ℤ/8)D414yes—
113C29×#135—28no—
114C29×#135—28no—
115C2×Q16×C29—21no—
116C2×Q16×C29—21no—
117C2×Q16×C29—21no—
118C2×Q16×C29—21no—
119C2×Q16×C29—22no—
120C2×Q16×C29—21no—
121C2×Q16×C29—21no—
122C2×Q16×C29—41no—
123C2×SD16×C29—21no—
124C2×SD16×C29—21no—
125C2×SD16×C29—21no—
126C2×SD16×C29—21no—
127C2×SD16×C29—21no—
128C2×SD16×C29—21no—
129C2×SD16×C29—22no—
130C2×SD16×C29—21no—
131C2×SD16×C29—21no—
132C2×SD16×C29—41no—
133C2×D8×C29—21no—
134C2×D8×C29—21no—
135C29×#131—22no—
136C29×#131—22no—
137C29×#131—41no—
138C29×#131—41no—
139C2×M16×C29—21no—
140C2×M16×C29—22no—
141C2×M16×C29—22no—
142C2×M16×C29—21no—
143C2×M16×C29—21no—
144C2×M16×C29C2311yescharacteristic
145C2×M16×C29C2311yescharacteristic
146C2×M16×C29C2311yescharacteristic
147C2×M16×C29C2311yescharacteristic
148C2×M16×C29C2311yescharacteristic
149C2×M16×C29C2311yescharacteristic
150C22×C8×C29—21no—
151C22×C8×C29—21no—
152C22×C8×C29—21no—
153C22×C8×C29C2311yescharacteristic
154C22×C8×C29C2311yescharacteristic
155C29×C22⋊Q8—21no—
156C29×C22⋊Q8—21no—
157C29×C22⋊Q8—21no—
158C29×C22⋊Q8—21no—
159C2×C4⋊C4×C29—21no—
160C2×C4⋊C4×C29C2311yescharacteristic
161C2×C22⋊C4×C29—21no—
162C29×#108—22no—
163C29×#108—22no—
164C29×#103—21no—
165C29×#103—21no—
166C29×#103—21no—
167C29×#103—21no—
168C29×#102—21no—
169C29×#102—21no—
170C29×#102—21no—
171C29×#102—21no—
172C29×#101—22no—
173C29×#101—22no—
174C29×#101—22no—
175C29×#101—41no—
176C29×#100—22no—
177C29×#100—41no—
178C29×C22⋊C8—21no—
179C29×C22⋊C8—21no—
180C29×C22⋊C8—21no—
181C29×C22⋊C8—21no—
182C29×C22⋊C8—21no—
183C29×C22⋊C8—21no—
184C29×C22⋊C8—21no—
185C29×C22⋊C8—21no—
186C29×C22⋊C8D411yescharacteristic
187C29×C22⋊C8D411yescharacteristic
188C29×C22⋊C8D411yescharacteristic
189C29×C22⋊C8D411yescharacteristic
190C24×C29—21no—
191C24×C29—21no—
192C24×C29#4111yescharacteristic
193#41×C29—21no—
194#41×C29—21no—
195#41×C29—24no—
196#41×C29—24no—
197#41×C29—22no—
198#41×C29—22no—
199#41×C29—21no—
200#41×C29—21no—
201#41×C29—21no—
202#41×C29—21no—
203#41×C29—42no—
204#41×C29—42no—
205#41×C29—41no—
206#41×C29—41no—
207#41×C29—42no—
208#41×C29—42no—
209#41×C29—42no—
210#41×C29—42no—
211#41×C29—42no—
212#41×C29—42no—
213#41×C29—42no—
214#41×C29—42no—
215#41×C29C2×D412yes—
216#41×C29C2×D412yes—
217C2×Q8×C29—21no—
218C2×Q8×C29—21no—
219C2×Q8×C29—22no—
220C2×Q8×C29—21no—
221C2×Q8×C29—21no—
222C2×Q8×C29—21no—
223C2×Q8×C29—21no—
224C2×Q8×C29—21no—
225C2×Q8×C29—21no—
226C2×Q8×C29—21no—
227C2×Q8×C29—21no—
228C2×Q8×C29—21no—
229C2×Q8×C29—21no—
230C2×Q8×C29—41no—
231C2×Q8×C29C2×D411yescharacteristic
232C2×Q8×C29C2×D412yes—
233C2×Q8×C29C2×D411yescharacteristic
234C2×D4×C29—21no—
235C2×D4×C29—22no—
236C2×D4×C29—21no—
237C2×D4×C29—21no—
238C2×D4×C29—21no—
239C2×D4×C29—21no—
240C2×D4×C29—21no—
241C2×D4×C29—21no—
242C2×D4×C29—21no—
243C2×D4×C29—21no—
244C2×D4×C29—21no—
245C2×D4×C29—41no—
246C2×D4×C29—42no—
247C2×D4×C29—42no—
248C2×D4×C29—42no—
249C2×D4×C29—42no—
250C2×D4×C29—41no—
251C2×D4×C29—41no—
252C2×D4×C29C2×D411yescharacteristic
253C2×D4×C29C2×D412yes—
254C2×D4×C29C2×D411yescharacteristic
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—42no—
268C22×C4×C29—42no—
269C22×C4×C29—42no—
270C22×C4×C29—42no—
271C22×C4×C29—41no—
272C22×C4×C29—41no—
273C22×C4×C29C2×D411yescharacteristic
274C22×C4×C29C2×D411yescharacteristic
275C22×C4×C29C2×D411yescharacteristic
276C22×C4×C29C2×D411yescharacteristic
277C22×C4×C29#4111yescharacteristic
278C22×C4×C29C2411yescharacteristic
279Q16×C29—24no—
280Q16×C29—24no—
281Q16×C29—42no—
282Q16×C29—42no—
283Q16×C29—42no—
284Q16×C29—42no—
285SD16×C29—24no—
286SD16×C29—24no—
287SD16×C29—24no—
288SD16×C29—24no—
289SD16×C29—42no—
290SD16×C29—42no—
291SD16×C29—42no—
292SD16×C29—42no—
293D8×C29—24no—
294D8×C29—24no—
295M16×C29—24no—
296M16×C29—21no—
297M16×C29—21no—
298M16×C29—21no—
299M16×C29—21no—
300M16×C29—21no—
301M16×C29—21no—
302M16×C29—21no—
303M16×C29—21no—
304M16×C29—21no—
305M16×C29—21no—
306M16×C29—42no—
307M16×C29—42no—
308M16×C29C2×D412yes—
309M16×C29C2×D412yes—
310C2×C8×C29—24no—
311C2×C8×C29—21no—
312C2×C8×C29—21no—
313C2×C8×C29—21no—
314C2×C8×C29—21no—
315C2×C8×C29—21no—
316C2×C8×C29—21no—
317C2×C8×C29—21no—
318C2×C8×C29—21no—
319C2×C8×C29—21no—
320C2×C8×C29—21no—
321C2×C8×C29—42no—
322C2×C8×C29—42no—
323C2×C8×C29C2×D411yescharacteristic
324C2×C8×C29C2×D411yescharacteristic
325C2×C8×C29C2×D411yescharacteristic
326C2×C8×C29C2×D411yescharacteristic
327C4⋊C4×C29—21no—
328C4⋊C4×C29—21no—
329C4⋊C4×C29—41no—
330C4⋊C4×C29—41no—
331C22⋊C4×C29—41no—
332C22⋊C4×C29—41no—
333#24403C2911yesmaximal, characteristic, direct product factor, Sylow
334C23×C29—21no—
335C23×C29—21no—
336C23×C29—21no—
337C23×C29—21no—
338C23×C29—22no—
339C23×C29—41no—
340C23×C29—41no—
341C23×C29—42no—
342C23×C29—42no—
343C23×C29—41no—
344C23×C29—41no—
345C23×C29—81no—
346C23×C29—81no—
347C23×C29—81no—
348C23×C29#12111yescharacteristic
349C23×C29#12111yescharacteristic
350C23×C29C2×#4111yescharacteristic
351Q8×C29—21no—
352Q8×C29—21no—
353Q8×C29—22no—
354Q8×C29—21no—
355Q8×C29—22no—
356Q8×C29—42no—
357Q8×C29—41no—
358Q8×C29—41no—
359Q8×C29—41no—
360Q8×C29—41no—
361Q8×C29—41no—
362Q8×C29—41no—
363Q8×C29#12012yes—
364D4×C29—22no—
365D4×C29—22no—
366D4×C29—21no—
367D4×C29—22no—
368D4×C29—21no—
369D4×C29—21no—
370D4×C29—22no—
371D4×C29—42no—
372D4×C29—42no—
373D4×C29—42no—
374D4×C29—44no—
375D4×C29—44no—
376D4×C29—41no—
377D4×C29—41no—
378D4×C29—41no—
379D4×C29—41no—
380D4×C29#12012yes—
381C2×C4×C29—21no—
382C2×C4×C29—21no—
383C2×C4×C29—21no—
384C2×C4×C29—21no—
385C2×C4×C29—21no—
386C2×C4×C29—21no—
387C2×C4×C29—21no—
388C2×C4×C29—22no—
389C2×C4×C29—22no—
390C2×C4×C29—21no—
391C2×C4×C29—21no—
392C2×C4×C29—21no—
393C2×C4×C29—21no—
394C2×C4×C29—21no—
395C2×C4×C29—22no—
396C2×C4×C29—42no—
397C2×C4×C29—42no—
398C2×C4×C29—42no—
399C2×C4×C29—44no—
400C2×C4×C29—44no—
401C2×C4×C29—41no—
402C2×C4×C29—41no—
403C2×C4×C29—41no—
404C2×C4×C29—41no—
405C2×C4×C29—41no—
406C2×C4×C29—41no—
407C2×C4×C29—41no—
408C2×C4×C29—41no—
409C2×C4×C29—81no—
410C2×C4×C29#12111yescharacteristic
411C2×C4×C29#12111yescharacteristic
412C2×C4×C29C22×D411yescharacteristic
413C2×C4×C29C22×D411yescharacteristic
414C2×C4×C29C22×D411yescharacteristic
415C2×C4×C29C22×D411yescharacteristic
416C2×C4×C29H(5,𝔽2)11yescharacteristic
417C2×C4×C29H(5,𝔽2)11yescharacteristic
418C8×C29—22no—
419C8×C29—22no—
420C8×C29—21no—
421C8×C29—21no—
422C8×C29—21no—
423C8×C29—21no—
424C8×C29—41no—
425C8×C29—41no—
426C8×C29—41no—
427C8×C29—41no—
428C2×#575C2×C2911yescharacteristic
429C2×#473C2×C2911yescharacteristic, complemented
430C2×#471C2×C2911yescharacteristic, complemented
431#3007C2×C2911yescharacteristic, complemented
432C2×#452C2×C2911yescharacteristic, complemented
433#2880C2×C2911yescharacteristic, complemented
434#2052C2×C2911yescharacteristic, complemented
435#2051C2×C2911yescharacteristic, complemented
436#2020C2×C2911yescharacteristic, complemented
437#2019C2×C2911yescharacteristic, complemented
438#1908C2×C2911yescharacteristic, complemented
439#1907C2×C2911yescharacteristic, complemented
440#1901C2×C2911yescharacteristic, complemented
441#1855C2×C2911yescharacteristic, complemented
442#1785C2×C2911yescharacteristic, complemented
443C22×C29—21no—
444C22×C29—21no—
445C22×C29—21no—
446C22×C29—21no—
447C22×C29—22no—
448C22×C29—21no—
449C22×C29—21no—
450C22×C29—21no—
451C22×C29—21no—
452C22×C29—41no—
453C22×C29—41no—
454C22×C29—41no—
455C22×C29—42no—
456C22×C29—41no—
457C22×C29—41no—
458C22×C29—81no—
459C22×C29—81no—
460C22×C29—82no—
461C22×C29—82no—
462C22×C29—84no—
463C22×C29—81no—
464C22×C29—81no—
465C22×C29C2×#12111yescharacteristic
466C22×C29#54611yescharacteristic
467C22×C29#54611yescharacteristic
468C4×C29—21no—
469C4×C29—21no—
470C4×C29—22no—
471C4×C29—41no—
472C4×C29—42no—
473C4×C29—81no—
474C4×C29—81no—
475C4×C29C2×#12011yescharacteristic
476C4×C29#53411yescharacteristic
477C4×C29D4211yescharacteristic
478C4×C29D4211yescharacteristic
479C22×#41C22×C2911yescharacteristic
480C22×#41C22×C2911yescharacteristic
481#575—24no—
482#575—24no—
483C2×#137—21no—
484C2×#137C22×C2911yescharacteristic
485C2×#137C22×C2911yescharacteristic
486C2×#137C22×C2911yescharacteristic
487C2×#137C22×C2911yescharacteristic
488C2×AGL(1,ℤ/8)—21no—
489C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
490C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
491C2×#135—21no—
492C2×#135—21no—
493C22×Q16C22×C2911yescharacteristic, complemented
494C22×SD16C22×C2911yescharacteristic, complemented
495C2×#131C22×C2911yescharacteristic
496C2×#131C22×C2911yescharacteristic
497C22×M16C22×C2911yescharacteristic
498C2×C22⋊Q8C22×C2911yescharacteristic
499#473—24no—
500#471—24no—
501#452—21no—
502#452—21no—
503#452—21no—
504#452—21no—
505#452—21no—
506#452—21no—
507#451—21no—
508#450—21no—
509C2×#108C22×C2911yescharacteristic, complemented
510C2×#108C22×C2911yescharacteristic, complemented
511#417C22×C2911yescharacteristic
512#417C22×C2911yescharacteristic
513C2×#103C22×C2911yescharacteristic, complemented
514C2×#102C22×C2911yescharacteristic, complemented
515C2×#101C22×C2911yescharacteristic, complemented
516C2×#101C22×C2911yescharacteristic, complemented
517C2×#101C22×C2911yescharacteristic, complemented
518C2×#101C22×C2911yescharacteristic, complemented
519C2×#100C22×C2911yescharacteristic, complemented
520C2×#100C22×C2911yescharacteristic, complemented
521#408—21no—
522#408—21no—
523#408C22×C2911yescharacteristic
524#408C22×C2911yescharacteristic
525#407—21no—
526#407C22×C2911yescharacteristic
527#407C22×C2911yescharacteristic
528C2×C22⋊C8—21no—
529C2×C22⋊C8C22×C2911yescharacteristic
530#343C22×C2911yescharacteristic, complemented
531#343C22×C2911yescharacteristic, complemented
532#341C22×C2911yescharacteristic, complemented
533#341C22×C2911yescharacteristic, complemented
534C2×C29—21no—
535C2×C29—21no—
536C2×C29—41no—
537C2×C29—41no—
538C2×C29—42no—
539C2×C29—81no—
540C2×C29—82no—
541C2×C29#241011yescharacteristic
542C2×C29#306711yescharacteristic
543C2×C29#306911yescharacteristic
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—41no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41D4×C2911yescharacteristic
559C2×#41D4×C2911yescharacteristic
560C2×#41C23×C2911yescharacteristic
561C2×#41C23×C2911yescharacteristic
562C22×Q8D4×C2911yescharacteristic
563C22×Q8C23×C2911yescharacteristic
564C22×Q8C23×C2911yescharacteristic
565C22×D4—21no—
566C22×D4—21no—
567C22×D4D4×C2911yescharacteristic
568C22×D4C23×C2911yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C2911yescharacteristic
572#137—28no—
573#137—22no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—22no—
578#137—41no—
579#137—41no—
580#137D4×C2914yes—
581AGL(1,ℤ/8)—28no—
582AGL(1,ℤ/8)—22no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)D4×C2914yes—
586#135—28no—
587#135—28no—
588C2×Q16—21no—
589C2×Q16—21no—
590C2×Q16—22no—
591C2×Q16—21no—
592C2×Q16—21no—
593C2×Q16—21no—
594C2×Q16—21no—
595C2×Q16—41no—
596C2×SD16—21no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—22no—
601C2×SD16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—41no—
606C2×D8—21no—
607C2×D8—21no—
608#131—22no—
609#131—22no—
610#131—41no—
611#131—41no—
612C2×M16—21no—
613C2×M16—22no—
614C2×M16—22no—
615C2×M16—21no—
616C2×M16—21no—
617C2×M16C23×C2911yescharacteristic
618C2×M16C23×C2911yescharacteristic
619C2×M16C23×C2911yescharacteristic
620C2×M16C23×C2911yescharacteristic
621C2×M16C23×C2911yescharacteristic
622C2×M16C23×C2911yescharacteristic
623C22×C8—21no—
624C22×C8—21no—
625C22×C8—21no—
626C22×C8C23×C2911yescharacteristic
627C22×C8C23×C2911yescharacteristic
628C22⋊Q8—21no—
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4C23×C2911yescharacteristic
634C2×C22⋊C4—21no—
635#108—22no—
636#108—22no—
637#103—21no—
638#103—21no—
639#103—21no—
640#103—21no—
641#102—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#101—22no—
646#101—22no—
647#101—22no—
648#101—41no—
649#100—22no—
650#100—41no—
651C22⋊C8—21no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8D4×C2911yescharacteristic
660C22⋊C8D4×C2911yescharacteristic
661C22⋊C8D4×C2911yescharacteristic
662C22⋊C8D4×C2911yescharacteristic
663C29#2440311yescharacteristic, direct product factor, Sylow
664C24—21no—
665C24—21no—
666C24#41×C2911yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×D4×C2912yes—
690#41C2×D4×C2912yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—41no—
705C2×Q8C2×D4×C2912yes—
706C2×Q8C2×D4×C2911yescharacteristic
707C2×Q8C2×D4×C2911yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×D4×C2912yes—
727C2×D4C2×D4×C2911yescharacteristic
728C2×D4C2×D4×C2911yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4C2×D4×C2911yescharacteristic
748C22×C4C2×D4×C2911yescharacteristic
749C22×C4C2×D4×C2911yescharacteristic
750C22×C4C2×D4×C2911yescharacteristic
751C22×C4#41×C2911yescharacteristic
752C22×C4C24×C2911yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758Q16—42no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766SD16—42no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—21no—
780M16—42no—
781M16—42no—
782M16C2×D4×C2912yes—
783M16C2×D4×C2912yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—42no—
796C2×C8—42no—
797C2×C8C2×D4×C2911yescharacteristic
798C2×C8C2×D4×C2911yescharacteristic
799C2×C8C2×D4×C2911yescharacteristic
800C2×C8C2×D4×C2911yescharacteristic
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23C29×#12111yescharacteristic
822C23C29×#12111yescharacteristic
823C23C2×#41×C2911yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8C29×#12012yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4C29×#12012yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4C29×#12111yescharacteristic
884C2×C4C29×#12111yescharacteristic
885C2×C4C22×D4×C2911yescharacteristic
886C2×C4C22×D4×C2911yescharacteristic
887C2×C4C22×D4×C2911yescharacteristic
888C2×C4C22×D4×C2911yescharacteristic
889C2×C4C29×H(5,𝔽2)11yescharacteristic
890C2×C4C29×H(5,𝔽2)11yescharacteristic
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×C29×#12111yescharacteristic
924C22C29×#54611yescharacteristic
925C22C29×#54611yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×C29×#12011yescharacteristic
934C4C29×#53411yescharacteristic
935C4D42×C2911yescharacteristic
936C4D42×C2911yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C29×#241011yescharacteristic
945C2C29×#306711yescharacteristic
946C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#473C2semidirect
3. C2×C29×#471C2semidirect
4. C29×#3007C2semidirect
5. C2×C29×#452C2semidirect
6. C29×#2880C2semidirect
7. C29×#2052C2semidirect
8. C29×#2051C2semidirect
9. C29×#2020C2semidirect
10. C29×#2019C2semidirect
11. C29×#1908C2semidirect
12. C29×#1907C2semidirect
13. C29×#1901C2semidirect
14. C29×#1855C2semidirect
15. C29×#1785C2semidirect
30. C22×Q16×C29C22semidirect
31. C22×SD16×C29C22semidirect
46. C2×C29×#108C22semidirect
47. C2×C29×#108C22semidirect
50. C2×C29×#103C22semidirect
51. C2×C29×#102C22semidirect
52. C2×C29×#101C22semidirect
53. C2×C29×#101C22semidirect
54. C2×C29×#101C22semidirect
55. C2×C29×#101C22semidirect
56. C2×C29×#100C22semidirect
57. C2×C29×#100C22semidirect
67. C29×#343C22semidirect
68. C29×#343C22semidirect
69. C29×#341C22semidirect
70. C29×#341C22semidirect
333. #24403C29direct (N × H)
429. C2×#473C2×C29semidirect
430. C2×#471C2×C29semidirect
431. #3007C2×C29semidirect
432. C2×#452C2×C29semidirect
433. #2880C2×C29semidirect
434. #2052C2×C29semidirect
435. #2051C2×C29semidirect
436. #2020C2×C29semidirect
437. #2019C2×C29semidirect
438. #1908C2×C29semidirect
439. #1907C2×C29semidirect
440. #1901C2×C29semidirect
441. #1855C2×C29semidirect
442. #1785C2×C29semidirect
493. C22×Q16C22×C29semidirect
494. C22×SD16C22×C29semidirect
509. C2×#108C22×C29semidirect
510. C2×#108C22×C29semidirect
513. C2×#103C22×C29semidirect
514. C2×#102C22×C29semidirect
515. C2×#101C22×C29semidirect
516. C2×#101C22×C29semidirect
517. C2×#101C22×C29semidirect
518. C2×#101C22×C29semidirect
519. C2×#100C22×C29semidirect
520. C2×#100C22×C29semidirect
530. #343C22×C29semidirect
531. #343C22×C29semidirect
532. #341C22×C29semidirect
533. #341C22×C29semidirect
663. C29#24403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5752
C2×C29×#4732
C2×C29×#4712
C29×#30072
C2×C29×#4522
C29×#28802
C29×#20522
C29×#20512
C29×#20202
C29×#20192
C29×#19082
C29×#19072
C29×#19012
C29×#18552
C29×#17852
#2440329