Finite Group Databasebeta

← C29×#24292 #20319192

Subgroups — C29×#24292 #20319192

Order 7424.

1324 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#577C211yesmaximal, characteristic, complemented
2C2×C29×#471C211yesmaximal, characteristic, complemented
3C29×#3061C211yesmaximal, characteristic, complemented
4C29×#3013C211yesmaximal, characteristic, complemented
5C29×#3012C211yesmaximal, characteristic, complemented
6C2×C29×#444C211yesmaximal, characteristic, complemented
7C29×#2052C211yesmaximal, characteristic, complemented
8C29×#2051C211yesmaximal, characteristic, complemented
9C29×#2007C211yesmaximal, characteristic, complemented
10C29×#2006C211yesmaximal, characteristic, complemented
11C29×#1975C211yesmaximal, characteristic, complemented
12C29×#1973C211yesmaximal, characteristic, complemented
13C29×#1816C211yesmaximal, characteristic, complemented
14C29×#1793C211yesmaximal, characteristic, complemented
15C29×#1792C211yesmaximal, characteristic, complemented
16C2×C29×2−1+4C2211yescharacteristic
17C2×C29×H(5,𝔽2)C2211yescharacteristic
18C29×#577—24no—
19C29×#577—24no—
20C2×C29×#137—21no—
21C2×C29×#137C2211yescharacteristic
22C2×C29×#137C2211yescharacteristic, complemented
23C2×C29×AGL(1,ℤ/8)—21no—
24C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C29×#135—21no—
27C2×C29×#135C2211yescharacteristic
28C2×C29×#135C2211yescharacteristic
29C22×SD16×C29—21no—
30C22×SD16×C29C2211yescharacteristic
31C2×C29×#131C2211yescharacteristic
32C2×C29×#131C2211yescharacteristic, complemented
33C29×#537C2211yescharacteristic
34C29×#537C2211yescharacteristic, complemented
35C29×#471—24no—
36C29×#468—21no—
37C29×#468—21no—
38C29×#467—21no—
39C29×#466—21no—
40C29×#452—21no—
41C29×#452—21no—
42C29×#451—21no—
43C29×#450—21no—
44C29×#449—21no—
45C29×#449—21no—
46C29×#448—21no—
47C29×#447—21no—
48C29×#444—24no—
49C2×C29×#108C2211yescharacteristic, complemented
50C2×C29×#108C2211yescharacteristic, complemented
51C2×C29×#107C2211yescharacteristic, complemented
52C2×C29×#104C2211yescharacteristic
53C2×C29×#104C2211yescharacteristic
54C2×C29×#104C2211yescharacteristic, complemented
55C2×C29×#104C2211yescharacteristic, complemented
56C29×#417C2211yescharacteristic
57C29×#417C2211yescharacteristic
58C29×#417C2211yescharacteristic
59C29×#417C2211yescharacteristic, complemented
60C2×C29×#103C2211yescharacteristic, complemented
61C2×C29×#102C2211yescharacteristic
62C2×C29×#101C2211yescharacteristic, complemented
63C2×C29×#100C2211yescharacteristic
64C29×#408C2211yescharacteristic
65C29×#408C2211yescharacteristic, complemented
66C2×C29×#97C2211yescharacteristic, complemented
67C29×#391C2211yescharacteristic, complemented
68C29×#390C2211yescharacteristic
69C29×#343C2211yescharacteristic, complemented
70C29×#343C2211yescharacteristic, complemented
71C29×2−1+4—22no—
72C29×2−1+4—22no—
73C29×2−1+4—22no—
74C29×2−1+4—41no—
75C29×H(5,𝔽2)—22no—
76C29×H(5,𝔽2)—22no—
77C29×H(5,𝔽2)—22no—
78C29×H(5,𝔽2)—41no—
79C2×#41×C29—21no—
80C2×#41×C29—21no—
81C2×#41×C29—21no—
82C2×#41×C29—21no—
83C2×#41×C29—41no—
84C2×#41×C29C2311yescharacteristic
85C2×#41×C29C2311yescharacteristic
86C2×#41×C29C2311yescharacteristic
87C2×#41×C29C2311yescharacteristic
88C22×Q8×C29—21no—
89C22×Q8×C29—21no—
90C22×Q8×C29C2311yescharacteristic
91C22×D4×C29—21no—
92C22×D4×C29—21no—
93C22×D4×C29—41no—
94C22×D4×C29C2311yescharacteristic
95C29×#137—28no—
96C29×#137—22no—
97C29×#137—22no—
98C29×#137—22no—
99C29×#137—41no—
100C29×AGL(1,ℤ/8)—28no—
101C29×AGL(1,ℤ/8)—22no—
102C29×AGL(1,ℤ/8)—22no—
103C29×AGL(1,ℤ/8)—22no—
104C29×AGL(1,ℤ/8)—41no—
105C29×#135—28no—
106C29×#135—22no—
107C29×#135—22no—
108C29×#135—22no—
109C29×#135—22no—
110C2×Q16×C29—21no—
111C2×Q16×C29—21no—
112C2×Q16×C29D411yescharacteristic
113C2×Q16×C29D411yescharacteristic
114C2×SD16×C29—28no—
115C2×SD16×C29—21no—
116C2×SD16×C29—21no—
117C2×SD16×C29—21no—
118C2×SD16×C29—21no—
119C2×SD16×C29—21no—
120C2×SD16×C29—21no—
121C2×SD16×C29—22no—
122C2×SD16×C29D411yescharacteristic
123C2×SD16×C29D411yescharacteristic
124C2×SD16×C29D411yescharacteristic
125C2×SD16×C29D411yescharacteristic
126C2×SD16×C29D414yescomplemented
127C2×D8×C29—21no—
128C2×D8×C29—21no—
129C2×D8×C29D411yescharacteristic
130C2×D8×C29D411yescharacteristic
131C29×#131—22no—
132C29×#131—22no—
133C29×#131—22no—
134C29×#131D414yescomplemented
135C2×M16×C29—21no—
136C2×M16×C29—21no—
137C2×M16×C29C2311yescharacteristic
138C2×M16×C29C2311yescharacteristic
139C2×M16×C29C2311yescharacteristic
140C2×M16×C29C2311yescharacteristic
141C22×C8×C29—21no—
142C22×C8×C29—21no—
143C22×C8×C29C2311yescharacteristic
144C22×C8×C29C2311yescharacteristic
145C29×C22⋊Q8—21no—
146C29×C22⋊Q8—21no—
147C29×C22⋊Q8—21no—
148C29×C22⋊Q8—21no—
149C29×#121—21no—
150C29×#121—21no—
151C29×#121—21no—
152C29×#121—21no—
153C29×#121—41no—
154C29×#121—41no—
155C2×C4⋊C4×C29C2311yescharacteristic
156C2×C4⋊C4×C29C2311yescharacteristic
157C2×C22⋊C4×C29—41no—
158C2×C42×C29C2311yescharacteristic
159C29×#108—22no—
160C29×#108—22no—
161C29×#107—21no—
162C29×#107—21no—
163C29×#104—22no—
164C29×#104—22no—
165C29×#104—41no—
166C29×#104—41no—
167C29×#103—21no—
168C29×#103—21no—
169C29×#103—21no—
170C29×#103—21no—
171C29×#103—21no—
172C29×#103—21no—
173C29×#102—21no—
174C29×#102—21no—
175C29×#102—21no—
176C29×#102—21no—
177C29×#102—21no—
178C29×#102—21no—
179C29×#101—22no—
180C29×#100—22no—
181C29×C22⋊C8—21no—
182C29×C22⋊C8—21no—
183C29×C22⋊C8—21no—
184C29×C22⋊C8—21no—
185C29×#97—22no—
186C29×#95—41no—
187C24×C29—21no—
188C24×C29—41no—
189#41×C29—21no—
190#41×C29—21no—
191#41×C29—24no—
192#41×C29—24no—
193#41×C29—21no—
194#41×C29—21no—
195#41×C29—21no—
196#41×C29—21no—
197#41×C29—21no—
198#41×C29—21no—
199#41×C29—21no—
200#41×C29—21no—
201#41×C29—21no—
202#41×C29—21no—
203#41×C29—21no—
204#41×C29—21no—
205#41×C29—42no—
206#41×C29—44no—
207#41×C29—42no—
208#41×C29—42no—
209#41×C29—42no—
210#41×C29—44no—
211#41×C29—42no—
212#41×C29—42no—
213#41×C29C2×D412yes—
214#41×C29#4112yes—
215C2×Q8×C29—21no—
216C2×Q8×C29—24no—
217C2×Q8×C29—21no—
218C2×Q8×C29—21no—
219C2×Q8×C29—21no—
220C2×Q8×C29—21no—
221C2×Q8×C29—41no—
222C2×Q8×C29—42no—
223C2×Q8×C29—42no—
224C2×Q8×C29—42no—
225C2×Q8×C29C2×D411yescharacteristic
226C2×Q8×C29C2×D411yescharacteristic
227C2×Q8×C29C2×D411yescharacteristic
228C2×Q8×C29C2×D412yes—
229C2×Q8×C29C2×D411yescharacteristic
230C2×D4×C29—21no—
231C2×D4×C29—24no—
232C2×D4×C29—21no—
233C2×D4×C29—21no—
234C2×D4×C29—21no—
235C2×D4×C29—21no—
236C2×D4×C29—21no—
237C2×D4×C29—21no—
238C2×D4×C29—21no—
239C2×D4×C29—21no—
240C2×D4×C29—42no—
241C2×D4×C29—41no—
242C2×D4×C29—41no—
243C2×D4×C29—42no—
244C2×D4×C29—44no—
245C2×D4×C29—44no—
246C2×D4×C29—41no—
247C2×D4×C29—42no—
248C2×D4×C29—41no—
249C2×D4×C29—41no—
250C2×D4×C29C2×D411yescharacteristic
251C2×D4×C29C2×D411yescharacteristic
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—41no—
264C22×C4×C29—41no—
265C22×C4×C29—41no—
266C22×C4×C29C2411yescharacteristic
267Q16×C29—24no—
268Q16×C29—22no—
269Q16×C29—22no—
270Q16×C29—42no—
271SD16×C29—24no—
272SD16×C29—24no—
273SD16×C29—22no—
274SD16×C29—22no—
275SD16×C29—22no—
276SD16×C29—24no—
277SD16×C29—24no—
278SD16×C29—22no—
279SD16×C29—42no—
280SD16×C29—42no—
281D8×C29—24no—
282D8×C29—22no—
283D8×C29—22no—
284D8×C29—42no—
285M16×C29—21no—
286M16×C29—24no—
287M16×C29—21no—
288M16×C29—21no—
289M16×C29—21no—
290M16×C29—21no—
291M16×C29—21no—
292M16×C29—21no—
293M16×C29—42no—
294M16×C29C2×D412yes—
295C2×C8×C29—21no—
296C2×C8×C29—21no—
297C2×C8×C29—21no—
298C2×C8×C29—24no—
299C2×C8×C29—21no—
300C2×C8×C29—21no—
301C2×C8×C29—21no—
302C2×C8×C29—42no—
303C2×C8×C29C2×D411yescharacteristic
304C2×C8×C29C2×D411yescharacteristic
305C2×C8×C29C2×D411yescharacteristic
306C2×C8×C29C2×D411yescharacteristic
307C2×C8×C29C2×D412yes—
308C2×C8×C29C2×D412yes—
309C4⋊C4×C29—21no—
310C4⋊C4×C29—21no—
311C4⋊C4×C29—21no—
312C4⋊C4×C29—21no—
313C4⋊C4×C29—41no—
314C4⋊C4×C29—41no—
315C22⋊C4×C29—41no—
316C22⋊C4×C29—41no—
317C22⋊C4×C29—41no—
318C22⋊C4×C29—41no—
319C22⋊C4×C29—82no—
320C42×C29—21no—
321C42×C29—21no—
322#24292C2911yesmaximal, characteristic, direct product factor, Sylow
323C23×C29—21no—
324C23×C29—21no—
325C23×C29—21no—
326C23×C29—21no—
327C23×C29—22no—
328C23×C29—44no—
329C23×C29—41no—
330C23×C29—41no—
331C23×C29—81no—
332C23×C29—81no—
333C23×C29—161no—
334C23×C29—161no—
335C23×C29H(5,𝔽2)11yescharacteristic
336Q8×C29—21no—
337Q8×C29—21no—
338Q8×C29—22no—
339Q8×C29—21no—
340Q8×C29—21no—
341Q8×C29—21no—
342Q8×C29—22no—
343Q8×C29—21no—
344Q8×C29—21no—
345Q8×C29—44no—
346Q8×C29—41no—
347Q8×C29—41no—
348Q8×C29#12112yes—
349D4×C29—22no—
350D4×C29—22no—
351D4×C29—21no—
352D4×C29—22no—
353D4×C29—21no—
354D4×C29—21no—
355D4×C29—21no—
356D4×C29—21no—
357D4×C29—22no—
358D4×C29—21no—
359D4×C29—21no—
360D4×C29—44no—
361D4×C29—44no—
362D4×C29—44no—
363D4×C29—41no—
364D4×C29—41no—
365D4×C29—41no—
366D4×C29—41no—
367D4×C29—41no—
368D4×C29—41no—
369D4×C29—41no—
370D4×C29—41no—
371D4×C29—161no—
372D4×C29—161no—
373D4×C29#12112yes—
374C2×C4×C29—21no—
375C2×C4×C29—22no—
376C2×C4×C29—22no—
377C2×C4×C29—21no—
378C2×C4×C29—21no—
379C2×C4×C29—21no—
380C2×C4×C29—22no—
381C2×C4×C29—44no—
382C2×C4×C29—44no—
383C2×C4×C29—44no—
384C2×C4×C29—41no—
385C2×C4×C29—41no—
386C2×C4×C29—41no—
387C2×C4×C29—41no—
388C2×C4×C29—41no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—41no—
393C2×C4×C29—41no—
394C2×C4×C29—41no—
395C2×C4×C29—41no—
396C2×C4×C29—41no—
397C2×C4×C29—81no—
398C2×C4×C29—81no—
399C2×C4×C29C22×D411yescharacteristic
400C2×C4×C29C22×D411yescharacteristic
401C2×C4×C29C22×D411yescharacteristic
402C2×C4×C29C22×D411yescharacteristic
403C2×C4×C29C2×#4111yescharacteristic
404C2×C4×C29H(5,𝔽2)11yescharacteristic
405C8×C29—22no—
406C8×C29—21no—
407C8×C29—21no—
408C8×C29—41no—
409C8×C29—41no—
410C8×C29—41no—
411C8×C29#12012yes—
412C8×C29#12012yes—
413C2×#577C2×C2911yescharacteristic, complemented
414C2×#471C2×C2911yescharacteristic, complemented
415#3061C2×C2911yescharacteristic, complemented
416#3013C2×C2911yescharacteristic, complemented
417#3012C2×C2911yescharacteristic, complemented
418C2×#444C2×C2911yescharacteristic, complemented
419#2052C2×C2911yescharacteristic, complemented
420#2051C2×C2911yescharacteristic, complemented
421#2007C2×C2911yescharacteristic, complemented
422#2006C2×C2911yescharacteristic, complemented
423#1975C2×C2911yescharacteristic, complemented
424#1973C2×C2911yescharacteristic, complemented
425#1816C2×C2911yescharacteristic, complemented
426#1793C2×C2911yescharacteristic, complemented
427#1792C2×C2911yescharacteristic, complemented
428C22×C29—21no—
429C22×C29—21no—
430C22×C29—22no—
431C22×C29—41no—
432C22×C29—41no—
433C22×C29—41no—
434C22×C29—41no—
435C22×C29—42no—
436C22×C29—41no—
437C22×C29—41no—
438C22×C29—41no—
439C22×C29—41no—
440C22×C29—41no—
441C22×C29—41no—
442C22×C29—41no—
443C22×C29—82no—
444C22×C29—81no—
445C22×C29—81no—
446C22×C29—161no—
447C22×C29—164no—
448C22×C29#53511yescharacteristic
449C22×C29D4211yescharacteristic
450C22×C29#54611yescharacteristic
451C4×C29—22no—
452C4×C29—41no—
453C4×C29—41no—
454C4×C29—42no—
455C4×C29—41no—
456C4×C29—81no—
457C4×C29—81no—
458C4×C29—81no—
459C4×C29C2×#12011yescharacteristic
460C4×C29C2×#12111yescharacteristic
461C4×C29D4211yescharacteristic
462C4×C29#54611yescharacteristic
463C2×2−1+4C22×C2911yescharacteristic
464C2×H(5,𝔽2)C22×C2911yescharacteristic
465#577—24no—
466#577—24no—
467C2×#137—21no—
468C2×#137C22×C2911yescharacteristic
469C2×#137C22×C2911yescharacteristic, complemented
470C2×AGL(1,ℤ/8)—21no—
471C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
472C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
473C2×#135—21no—
474C2×#135C22×C2911yescharacteristic
475C2×#135C22×C2911yescharacteristic
476C22×SD16—21no—
477C22×SD16C22×C2911yescharacteristic
478C2×#131C22×C2911yescharacteristic
479C2×#131C22×C2911yescharacteristic, complemented
480#537C22×C2911yescharacteristic
481#537C22×C2911yescharacteristic, complemented
482#471—24no—
483#468—21no—
484#468—21no—
485#467—21no—
486#466—21no—
487#452—21no—
488#452—21no—
489#451—21no—
490#450—21no—
491#449—21no—
492#449—21no—
493#448—21no—
494#447—21no—
495#444—24no—
496C2×#108C22×C2911yescharacteristic, complemented
497C2×#108C22×C2911yescharacteristic, complemented
498C2×#107C22×C2911yescharacteristic, complemented
499C2×#104C22×C2911yescharacteristic
500C2×#104C22×C2911yescharacteristic
501C2×#104C22×C2911yescharacteristic, complemented
502C2×#104C22×C2911yescharacteristic, complemented
503#417C22×C2911yescharacteristic
504#417C22×C2911yescharacteristic
505#417C22×C2911yescharacteristic
506#417C22×C2911yescharacteristic, complemented
507C2×#103C22×C2911yescharacteristic, complemented
508C2×#102C22×C2911yescharacteristic
509C2×#101C22×C2911yescharacteristic, complemented
510C2×#100C22×C2911yescharacteristic
511#408C22×C2911yescharacteristic
512#408C22×C2911yescharacteristic, complemented
513C2×#97C22×C2911yescharacteristic, complemented
514#391C22×C2911yescharacteristic, complemented
515#390C22×C2911yescharacteristic
516#343C22×C2911yescharacteristic, complemented
517#343C22×C2911yescharacteristic, complemented
518C2×C29—21no—
519C2×C29—21no—
520C2×C29—42no—
521C2×C29—81no—
522C2×C29—81no—
523C2×C29—81no—
524C2×C29—82no—
525C2×C29#240811yescharacteristic
526C2×C29#328811yescharacteristic
527C2×C29#328911yescharacteristic
5282−1+4—22no—
5292−1+4—22no—
5302−1+4—22no—
5312−1+4—41no—
532H(5,𝔽2)—22no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—41no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—41no—
541C2×#41C23×C2911yescharacteristic
542C2×#41C23×C2911yescharacteristic
543C2×#41C23×C2911yescharacteristic
544C2×#41C23×C2911yescharacteristic
545C22×Q8—21no—
546C22×Q8—21no—
547C22×Q8C23×C2911yescharacteristic
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4C23×C2911yescharacteristic
552#137—28no—
553#137—22no—
554#137—22no—
555#137—22no—
556#137—41no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—41no—
562#135—28no—
563#135—22no—
564#135—22no—
565#135—22no—
566#135—22no—
567C2×Q16—21no—
568C2×Q16—21no—
569C2×Q16D4×C2911yescharacteristic
570C2×Q16D4×C2911yescharacteristic
571C2×SD16—28no—
572C2×SD16—21no—
573C2×SD16—21no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—22no—
579C2×SD16D4×C2911yescharacteristic
580C2×SD16D4×C2911yescharacteristic
581C2×SD16D4×C2911yescharacteristic
582C2×SD16D4×C2911yescharacteristic
583C2×SD16D4×C2914yescomplemented
584C2×D8—21no—
585C2×D8—21no—
586C2×D8D4×C2911yescharacteristic
587C2×D8D4×C2911yescharacteristic
588#131—22no—
589#131—22no—
590#131—22no—
591#131D4×C2914yescomplemented
592C2×M16—21no—
593C2×M16—21no—
594C2×M16C23×C2911yescharacteristic
595C2×M16C23×C2911yescharacteristic
596C2×M16C23×C2911yescharacteristic
597C2×M16C23×C2911yescharacteristic
598C22×C8—21no—
599C22×C8—21no—
600C22×C8C23×C2911yescharacteristic
601C22×C8C23×C2911yescharacteristic
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121—41no—
611#121—41no—
612C2×C4⋊C4C23×C2911yescharacteristic
613C2×C4⋊C4C23×C2911yescharacteristic
614C2×C22⋊C4—41no—
615C2×C42C23×C2911yescharacteristic
616#108—22no—
617#108—22no—
618#107—21no—
619#107—21no—
620#104—22no—
621#104—22no—
622#104—41no—
623#104—41no—
624#103—21no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#102—21no—
631#102—21no—
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#101—22no—
637#100—22no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640C22⋊C8—21no—
641C22⋊C8—21no—
642#97—22no—
643#95—41no—
644C29#2429211yescharacteristic, direct product factor, Sylow
645C24—21no—
646C24—41no—
647#41—21no—
648#41—21no—
649#41—24no—
650#41—24no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—21no—
663#41—42no—
664#41—44no—
665#41—42no—
666#41—42no—
667#41—42no—
668#41—44no—
669#41—42no—
670#41—42no—
671#41C2×D4×C2912yes—
672#41#41×C2912yes—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—41no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8C2×D4×C2912yes—
684C2×Q8C2×D4×C2911yescharacteristic
685C2×Q8C2×D4×C2911yescharacteristic
686C2×Q8C2×D4×C2911yescharacteristic
687C2×Q8C2×D4×C2911yescharacteristic
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4C2×D4×C2912yes—
709C2×D4C2×D4×C2911yescharacteristic
710C2×D4C2×D4×C2911yescharacteristic
711C2×D4C2×D4×C2911yescharacteristic
712C2×D4C2×D4×C2911yescharacteristic
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C24×C2911yescharacteristic
725Q16—24no—
726Q16—22no—
727Q16—22no—
728Q16—42no—
729SD16—24no—
730SD16—24no—
731SD16—22no—
732SD16—22no—
733SD16—22no—
734SD16—24no—
735SD16—24no—
736SD16—22no—
737SD16—42no—
738SD16—42no—
739D8—24no—
740D8—22no—
741D8—22no—
742D8—42no—
743M16—21no—
744M16—24no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—42no—
752M16C2×D4×C2912yes—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—24no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C2911yescharacteristic
762C2×C8C2×D4×C2911yescharacteristic
763C2×C8C2×D4×C2912yes—
764C2×C8C2×D4×C2911yescharacteristic
765C2×C8C2×D4×C2911yescharacteristic
766C2×C8C2×D4×C2912yes—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—41no—
772C4⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—41no—
776C22⋊C4—41no—
777C22⋊C4—82no—
778C42—21no—
779C42—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—44no—
786C23—41no—
787C23—41no—
788C23—81no—
789C23—81no—
790C23—161no—
791C23—161no—
792C23C29×H(5,𝔽2)11yescharacteristic
793Q8—21no—
794Q8—21no—
795Q8—22no—
796Q8—21no—
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—21no—
802Q8—44no—
803Q8—41no—
804Q8—41no—
805Q8C29×#12112yes—
806D4—22no—
807D4—22no—
808D4—21no—
809D4—22no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—21no—
814D4—22no—
815D4—21no—
816D4—21no—
817D4—44no—
818D4—44no—
819D4—44no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—161no—
829D4—161no—
830D4C29×#12112yes—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4C22×D4×C2911yescharacteristic
857C2×C4C22×D4×C2911yescharacteristic
858C2×C4C22×D4×C2911yescharacteristic
859C2×C4C22×D4×C2911yescharacteristic
860C2×C4C2×#41×C2911yescharacteristic
861C2×C4C29×H(5,𝔽2)11yescharacteristic
862C8—22no—
863C8—21no—
864C8—21no—
865C8—41no—
866C8—41no—
867C8—41no—
868C8C29×#12012yes—
869C8C29×#12012yes—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—161no—
889C22—164no—
890C22C29×#53511yescharacteristic
891C22D42×C2911yescharacteristic
892C22C29×#54611yescharacteristic
893C4—22no—
894C4—41no—
895C4—41no—
896C4—42no—
897C4—41no—
898C4—81no—
899C4—81no—
900C4—81no—
901C4C2×C29×#12011yescharacteristic
902C4C2×C29×#12111yescharacteristic
903C4D42×C2911yescharacteristic
904C4C29×#54611yescharacteristic
905C2—21no—
906C2—21no—
907C2—42no—
908C2—81no—
909C2—81no—
910C2—81no—
911C2—82no—
912C2C29×#240811yescharacteristic
913C2C29×#328811yescharacteristic
914C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#577C2semidirect
2. C2×C29×#471C2semidirect
3. C29×#3061C2semidirect
4. C29×#3013C2semidirect
5. C29×#3012C2semidirect
6. C2×C29×#444C2semidirect
7. C29×#2052C2semidirect
8. C29×#2051C2semidirect
9. C29×#2007C2semidirect
10. C29×#2006C2semidirect
11. C29×#1975C2semidirect
12. C29×#1973C2semidirect
13. C29×#1816C2semidirect
14. C29×#1793C2semidirect
15. C29×#1792C2semidirect
22. C2×C29×#137C22semidirect
32. C2×C29×#131C22semidirect
34. C29×#537C22semidirect
49. C2×C29×#108C22semidirect
50. C2×C29×#108C22semidirect
51. C2×C29×#107C22semidirect
54. C2×C29×#104C22semidirect
55. C2×C29×#104C22semidirect
59. C29×#417C22semidirect
60. C2×C29×#103C22semidirect
62. C2×C29×#101C22semidirect
65. C29×#408C22semidirect
66. C2×C29×#97C22semidirect
67. C29×#391C22semidirect
69. C29×#343C22semidirect
70. C29×#343C22semidirect
126. C2×SD16×C29D4semidirect
134. C29×#131D4semidirect
322. #24292C29direct (N × H)
413. C2×#577C2×C29semidirect
414. C2×#471C2×C29semidirect
415. #3061C2×C29semidirect
416. #3013C2×C29semidirect
417. #3012C2×C29semidirect
418. C2×#444C2×C29semidirect
419. #2052C2×C29semidirect
420. #2051C2×C29semidirect
421. #2007C2×C29semidirect
422. #2006C2×C29semidirect
423. #1975C2×C29semidirect
424. #1973C2×C29semidirect
425. #1816C2×C29semidirect
426. #1793C2×C29semidirect
427. #1792C2×C29semidirect
469. C2×#137C22×C29semidirect
479. C2×#131C22×C29semidirect
481. #537C22×C29semidirect
496. C2×#108C22×C29semidirect
497. C2×#108C22×C29semidirect
498. C2×#107C22×C29semidirect
501. C2×#104C22×C29semidirect
502. C2×#104C22×C29semidirect
506. #417C22×C29semidirect
507. C2×#103C22×C29semidirect
509. C2×#101C22×C29semidirect
512. #408C22×C29semidirect
513. C2×#97C22×C29semidirect
514. #391C22×C29semidirect
516. #343C22×C29semidirect
517. #343C22×C29semidirect
583. C2×SD16D4×C29semidirect
591. #131D4×C29semidirect
644. C29#24292direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5772
C2×C29×#4712
C29×#30612
C29×#30132
C29×#30122
C2×C29×#4442
C29×#20522
C29×#20512
C29×#20072
C29×#20062
C29×#19752
C29×#19732
C29×#18162
C29×#17932
C29×#17922
#2429229