Finite Group Databasebeta

← C29×#33887 #20328787

Subgroups — C29×#33887 #20328787

Order 7424.

548 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3339C211yesmaximal, characteristic
2D4×Q16×C29C211yesmaximal, characteristic, complemented
3C29×#2245C211yesmaximal, characteristic, complemented
4C29×#2237C211yesmaximal, characteristic, complemented
5C29×#2236C211yesmaximal, characteristic, complemented
6C29×#2229C211yesmaximal, characteristic, complemented
7C29×#2220C211yesmaximal, characteristic, complemented
8C29×#2217C211yesmaximal, characteristic, complemented
9C29×#2208C211yesmaximal, characteristic, complemented
10C29×#2185C211yesmaximal, characteristic, complemented
11C29×#2185C211yesmaximal, characteristic, complemented
12C29×#2175C211yesmaximal, characteristic, complemented
13C29×#2168C211yesmaximal, characteristic, complemented
14C29×#2141C211yesmaximal, characteristic, complemented
15C2×C29×#358C211yesmaximal, characteristic, complemented
16C22×Q16×C29C2211yescharacteristic
17C22×Q16×C29C2211yescharacteristic
18C29×#553—21no—
19D4×Q8×C29—21no—
20C2×C29×SD32C2211yescharacteristic
21C2×C29×SD32C2211yescharacteristic
22C2×C29×SD32C2211yescharacteristic
23C2×C29×M32C2211yescharacteristic
24C22×C16×C29C2211yescharacteristic
25C29×#499C2211yescharacteristic
26C29×#494C2211yescharacteristic
27C29×#482—21no—
28C29×#481—21no—
29C29×#478—21no—
30C29×#467C2211yescharacteristic
31C29×#467C2211yescharacteristic
32C29×#466C2211yescharacteristic
33C29×#466C2211yescharacteristic
34C29×#462—21no—
35C29×#451—21no—
36C29×#451—21no—
37C4×Q16×C29C2211yescharacteristic
38C4×D8×C29C2211yescharacteristic
39C8×D4×C29C2211yescharacteristic
40C29×#427C2211yescharacteristic
41C2×C29×#107C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×#358C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#358C2211yescharacteristic
54C29×#358C2211yescharacteristic
55C29×#357C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×C22⋊C16C2211yescharacteristic
58C29×#346C2211yescharacteristic
59C22×Q8×C29—21no—
60C22×Q8×C29—21no—
61C2×Q16×C29—22no—
62C2×Q16×C29—22no—
63C2×Q16×C29—21no—
64C2×Q16×C29—21no—
65C2×Q16×C29—21no—
66C2×Q16×C29—41no—
67C2×Q16×C29—41no—
68C2×Q16×C29C2311yescharacteristic
69C2×Q16×C29C2311yescharacteristic
70C2×Q16×C29C2311yescharacteristic
71C2×D8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C29×C4⋊Q8—21no—
75C29×C4⋊Q8—41no—
76C29×#126—41no—
77C29×#125—21no—
78C29×#123—41no—
79C29×C22⋊Q8—21no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—41no—
82C29×C22⋊Q8—41no—
83C29×#121—21no—
84C29×#121—21no—
85C29×#121—41no—
86C4×Q8×C29—21no—
87C4×D4×C29—21no—
88C4×D4×C29—41no—
89C4×D4×C29—41no—
90C4×D4×C29D411yescharacteristic
91C29×#117—21no—
92C2×C4⋊C4×C29—21no—
93C29×SD32—22no—
94C29×SD32—41no—
95C29×SD32—41no—
96C29×M32—41no—
97C2×C16×C29—41no—
98C2×C16×C29C2311yescharacteristic
99C2×C16×C29C2311yescharacteristic
100C2×C16×C29C2311yescharacteristic
101C2×C16×C29C2311yescharacteristic
102C29×#107—21no—
103C29×#107C2311yescharacteristic
104C29×#107C2311yescharacteristic
105C29×#107C2311yescharacteristic
106C29×#107C2311yescharacteristic
107C29×#106—21no—
108C29×#106—21no—
109C29×C4⋊C8D411yescharacteristic
110C29×#103—21no—
111C29×#103—21no—
112C29×#103—21no—
113C29×#102—21no—
114C29×#102—21no—
115C29×#102—21no—
116C29×C22⋊C8D411yescharacteristic
117C29×C22⋊C8D411yescharacteristic
118C4×C8×C29C2311yescharacteristic
119C2×Q8×C29—21no—
120C2×Q8×C29—21no—
121C2×Q8×C29—21no—
122C2×Q8×C29—42no—
123C2×Q8×C29—42no—
124C2×Q8×C29—41no—
125C2×Q8×C29—41no—
126C2×Q8×C29—81no—
127C2×Q8×C29—81no—
128C2×D4×C29—21no—
129C2×D4×C29—41no—
130C2×D4×C29—41no—
131C2×D4×C29D811yescharacteristic
132C22×C4×C29—41no—
133C22×C4×C29—41no—
134C22×C4×C29—41no—
135C22×C4×C29—41no—
136C22×C4×C29C2×D411yescharacteristic
137C22×C4×C29C2×D411yescharacteristic
138Q16×C29—21no—
139Q16×C29—21no—
140Q16×C29—21no—
141Q16×C29—21no—
142Q16×C29—21no—
143Q16×C29—42no—
144Q16×C29—42no—
145Q16×C29—81no—
146Q16×C29#4112yes—
147D8×C29—21no—
148D8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
151C2×C8×C29—21no—
152C2×C8×C29—21no—
153C2×C8×C29C2×D411yescharacteristic
154C2×C8×C29C2×D411yescharacteristic
155C2×C8×C29C2×D411yescharacteristic
156C2×C8×C29C2411yescharacteristic
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—41no—
162C4⋊C4×C29—41no—
163C4⋊C4×C29—41no—
164C4⋊C4×C29—41no—
165C4⋊C4×C29—41no—
166C4⋊C4×C29—41no—
167C4⋊C4×C29—41no—
168C4⋊C4×C29—41no—
169C4⋊C4×C29D811yescharacteristic
170C22⋊C4×C29—41no—
171C22⋊C4×C29—41no—
172C22⋊C4×C29—41no—
173C22⋊C4×C29—41no—
174C22⋊C4×C29—41no—
175C22⋊C4×C29—41no—
176C22⋊C4×C29D811yescharacteristic
177C22⋊C4×C29D811yescharacteristic
178C42×C29—41no—
179C42×C29—41no—
180C42×C29C2×D411yescharacteristic
181C16×C29—21no—
182C16×C29—21no—
183C16×C29—21no—
184C16×C29—21no—
185#33887C2911yesmaximal, characteristic, direct product factor, Sylow
186C23×C29—41no—
187C23×C29C2×D811yescharacteristic
188C23×C29C2×D811yescharacteristic
189Q8×C29—22no—
190Q8×C29—41no—
191Q8×C29—41no—
192Q8×C29—41no—
193Q8×C29—41no—
194Q8×C29—41no—
195Q8×C29—82no—
196Q8×C29—82no—
197D4×C29—22no—
198D4×C29—41no—
199D4×C29—41no—
200D4×C29—82no—
201D4×C29—161no—
202C2×C4×C29—21no—
203C2×C4×C29—21no—
204C2×C4×C29—21no—
205C2×C4×C29—21no—
206C2×C4×C29—41no—
207C2×C4×C29—41no—
208C2×C4×C29—41no—
209C2×C4×C29—41no—
210C2×C4×C29—41no—
211C2×C4×C29—41no—
212C2×C4×C29—41no—
213C2×C4×C29—82no—
214C2×C4×C29—82no—
215C2×C4×C29—161no—
216C2×C4×C29—161no—
217C2×C4×C29C2×D811yescharacteristic
218C2×C4×C29C2×D811yescharacteristic
219C2×C4×C29C2×D811yescharacteristic
220C2×C4×C29C2×D811yescharacteristic
221C2×C4×C29C22×D411yescharacteristic
222C8×C29—21no—
223C8×C29—21no—
224C8×C29—21no—
225C8×C29C2×#4111yescharacteristic
226C8×C29H(5,𝔽2)11yescharacteristic
227#3339C2×C2911yescharacteristic
228D4×Q16C2×C2911yescharacteristic, complemented
229#2245C2×C2911yescharacteristic, complemented
230#2237C2×C2911yescharacteristic, complemented
231#2236C2×C2911yescharacteristic, complemented
232#2229C2×C2911yescharacteristic, complemented
233#2220C2×C2911yescharacteristic, complemented
234#2217C2×C2911yescharacteristic, complemented
235#2208C2×C2911yescharacteristic, complemented
236#2185C2×C2911yescharacteristic, complemented
237#2185C2×C2911yescharacteristic, complemented
238#2175C2×C2911yescharacteristic, complemented
239#2168C2×C2911yescharacteristic, complemented
240#2141C2×C2911yescharacteristic, complemented
241C2×#358C2×C2911yescharacteristic, complemented
242C22×C29—21no—
243C22×C29—21no—
244C22×C29—21no—
245C22×C29—21no—
246C22×C29—21no—
247C22×C29—81no—
248C22×C29—81no—
249C22×C29—81no—
250C22×C29#51012yes—
251C22×C29C22×D811yescharacteristic
252C4×C29—21no—
253C4×C29—21no—
254C4×C29—21no—
255C4×C29—21no—
256C4×C29—42no—
257C4×C29—81no—
258C4×C29—81no—
259C4×C29—81no—
260C4×C29—81no—
261C4×C29—81no—
262C4×C29—81no—
263C4×C29#54611yescharacteristic
264C4×C29#57711yescharacteristic
265C22×Q16C22×C2911yescharacteristic
266C22×Q16C22×C2911yescharacteristic
267#553—21no—
268D4×Q8—21no—
269C2×SD32C22×C2911yescharacteristic
270C2×SD32C22×C2911yescharacteristic
271C2×SD32C22×C2911yescharacteristic
272C2×M32C22×C2911yescharacteristic
273C22×C16C22×C2911yescharacteristic
274#499C22×C2911yescharacteristic
275#494C22×C2911yescharacteristic
276#482—21no—
277#481—21no—
278#478—21no—
279#467C22×C2911yescharacteristic
280#467C22×C2911yescharacteristic
281#466C22×C2911yescharacteristic
282#466C22×C2911yescharacteristic
283#462—21no—
284#451—21no—
285#451—21no—
286C4×Q16C22×C2911yescharacteristic
287C4×D8C22×C2911yescharacteristic
288C8×D4C22×C2911yescharacteristic
289#427C22×C2911yescharacteristic
290C2×#107C22×C2911yescharacteristic
291#367C22×C2911yescharacteristic
292#366C22×C2911yescharacteristic
293#366C22×C2911yescharacteristic
294C4⋊C16C22×C2911yescharacteristic
295#358C22×C2911yescharacteristic
296#358C22×C2911yescharacteristic
297#358C22×C2911yescharacteristic
298#358C22×C2911yescharacteristic
299#358C22×C2911yescharacteristic
300#358C22×C2911yescharacteristic
301#358C22×C2911yescharacteristic
302#358C22×C2911yescharacteristic
303#358C22×C2911yescharacteristic
304#357C22×C2911yescharacteristic
305C22⋊C16C22×C2911yescharacteristic
306C22⋊C16C22×C2911yescharacteristic
307#346C22×C2911yescharacteristic
308C2×C29—22no—
309C2×C29—41no—
310C2×C29—161no—
311C2×C29#329411yescharacteristic
312C2×C29C2×#51011yescharacteristic
313C2×C29#341611yescharacteristic
314C22×Q8—21no—
315C22×Q8—21no—
316C2×Q16—22no—
317C2×Q16—22no—
318C2×Q16—21no—
319C2×Q16—21no—
320C2×Q16—21no—
321C2×Q16—41no—
322C2×Q16—41no—
323C2×Q16C23×C2911yescharacteristic
324C2×Q16C23×C2911yescharacteristic
325C2×Q16C23×C2911yescharacteristic
326C2×D8C23×C2911yescharacteristic
327C22×C8C23×C2911yescharacteristic
328C22×C8C23×C2911yescharacteristic
329C4⋊Q8—21no—
330C4⋊Q8—41no—
331#126—41no—
332#125—21no—
333#123—41no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—41no—
337C22⋊Q8—41no—
338#121—21no—
339#121—21no—
340#121—41no—
341C4×Q8—21no—
342C4×D4—21no—
343C4×D4—41no—
344C4×D4—41no—
345C4×D4D4×C2911yescharacteristic
346#117—21no—
347C2×C4⋊C4—21no—
348SD32—22no—
349SD32—41no—
350SD32—41no—
351M32—41no—
352C2×C16—41no—
353C2×C16C23×C2911yescharacteristic
354C2×C16C23×C2911yescharacteristic
355C2×C16C23×C2911yescharacteristic
356C2×C16C23×C2911yescharacteristic
357#107—21no—
358#107C23×C2911yescharacteristic
359#107C23×C2911yescharacteristic
360#107C23×C2911yescharacteristic
361#107C23×C2911yescharacteristic
362#106—21no—
363#106—21no—
364C4⋊C8D4×C2911yescharacteristic
365#103—21no—
366#103—21no—
367#103—21no—
368#102—21no—
369#102—21no—
370#102—21no—
371C22⋊C8D4×C2911yescharacteristic
372C22⋊C8D4×C2911yescharacteristic
373C4×C8C23×C2911yescharacteristic
374C29#3388711yescharacteristic, direct product factor, Sylow
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—81no—
383C2×Q8—81no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4D8×C2911yescharacteristic
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4C2×D4×C2911yescharacteristic
393C22×C4C2×D4×C2911yescharacteristic
394Q16—21no—
395Q16—21no—
396Q16—21no—
397Q16—21no—
398Q16—21no—
399Q16—42no—
400Q16—42no—
401Q16—81no—
402Q16#41×C2912yes—
403D8—21no—
404D8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8C2×D4×C2911yescharacteristic
410C2×C8C2×D4×C2911yescharacteristic
411C2×C8C2×D4×C2911yescharacteristic
412C2×C8C24×C2911yescharacteristic
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4D8×C2911yescharacteristic
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4D8×C2911yescharacteristic
433C22⋊C4D8×C2911yescharacteristic
434C42—41no—
435C42—41no—
436C42C2×D4×C2911yescharacteristic
437C16—21no—
438C16—21no—
439C16—21no—
440C16—21no—
441C23—41no—
442C23C2×D8×C2911yescharacteristic
443C23C2×D8×C2911yescharacteristic
444Q8—22no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448Q8—41no—
449Q8—41no—
450Q8—82no—
451Q8—82no—
452D4—22no—
453D4—41no—
454D4—41no—
455D4—82no—
456D4—161no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—161no—
471C2×C4—161no—
472C2×C4C2×D8×C2911yescharacteristic
473C2×C4C2×D8×C2911yescharacteristic
474C2×C4C2×D8×C2911yescharacteristic
475C2×C4C2×D8×C2911yescharacteristic
476C2×C4C22×D4×C2911yescharacteristic
477C8—21no—
478C8—21no—
479C8—21no—
480C8C2×#41×C2911yescharacteristic
481C8C29×H(5,𝔽2)11yescharacteristic
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22C29×#51012yes—
491C22C22×D8×C2911yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—81no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4C29×#54611yescharacteristic
504C4C29×#57711yescharacteristic
505C2—22no—
506C2—41no—
507C2—161no—
508C2C29×#329411yescharacteristic
509C2C2×C29×#51011yescharacteristic
510C2C29×#341611yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#3339C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×D4×C29 ◁ C8×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×Q16×C29C2semidirect
3. C29×#2245C2semidirect
4. C29×#2237C2semidirect
5. C29×#2236C2semidirect
6. C29×#2229C2semidirect
7. C29×#2220C2semidirect
8. C29×#2217C2semidirect
9. C29×#2208C2semidirect
10. C29×#2185C2semidirect
11. C29×#2185C2semidirect
12. C29×#2175C2semidirect
13. C29×#2168C2semidirect
14. C29×#2141C2semidirect
15. C2×C29×#358C2semidirect
185. #33887C29direct (N × H)
228. D4×Q16C2×C29semidirect
229. #2245C2×C29semidirect
230. #2237C2×C29semidirect
231. #2236C2×C29semidirect
232. #2229C2×C29semidirect
233. #2220C2×C29semidirect
234. #2217C2×C29semidirect
235. #2208C2×C29semidirect
236. #2185C2×C29semidirect
237. #2185C2×C29semidirect
238. #2175C2×C29semidirect
239. #2168C2×C29semidirect
240. #2141C2×C29semidirect
241. C2×#358C2×C29semidirect
374. C29#33887direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33392
D4×Q16×C292
C29×#22452
C29×#22372
C29×#22362
C29×#22292
C29×#22202
C29×#22172
C29×#22082
C29×#21852
C29×#21752
C29×#21682
C29×#21412
C2×C29×#3582
#3388729