Finite Group Databasebeta

← #14545283

Subgroups — #14545283

Order 2176.

532 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763761C211yesmaximal, characteristic
2#11763760C211yesmaximal, characteristic, complemented
3#11763759C211yesmaximal, characteristic, complemented
4#11763759C211yesmaximal, characteristic, complemented
5#11763759C211yesmaximal, characteristic, complemented
6#11763759C211yesmaximal, characteristic, complemented
7#11763758C211yesmaximal, characteristic, complemented
8#11763758C211yesmaximal, characteristic, complemented
9#11763757C211yesmaximal, characteristic
10#11763756C211yesmaximal, characteristic, complemented
11#11763751C211yesmaximal, characteristic, complemented
12C4⋊C4×#595C211yesmaximal, characteristic, complemented
13C22⋊C4×#595C211yesmaximal, characteristic, complemented
14C4×C22⋊#595C211yesmaximal, characteristic, complemented
15#123×D17C211yesmaximal, characteristic
16C23×#595C2211yescharacteristic
17C2×D4×D17C2211yescharacteristic
18C22×C4×D17C2211yescharacteristic
19C2×C22⋊#595C2211yescharacteristic
20C2×C22⋊#595C2211yescharacteristic
21C2×C22⋊#595C2211yescharacteristic
22C2×C22⋊#595C2211yescharacteristic
23C2×C22⋊#595C2211yescharacteristic
24C2×C22⋊#595C2211yescharacteristic
25C2×C22⋊#595C2211yescharacteristic
26C2×C4⋊#595C2211yescharacteristic
27C2×C4⋊#595C2211yescharacteristic
28C2×C4⋊#595C2211yescharacteristic
29C2×C4⋊#595C2211yescharacteristic
30C2×C4⋊#595C2211yescharacteristic
31C2×C4×#595C2211yescharacteristic
32C2×C4×#595C2211yescharacteristic
33C2×C4×#595C2211yescharacteristic
34C2×C4×#595C2211yescharacteristic
35C2×C4×#595C2211yescharacteristic
36C17×#123C411yescharacteristic, complemented
37#10587621C411yescharacteristic, complemented
38#10587615C411yescharacteristic, complemented
39#10587580C411yescharacteristic, complemented
40#10587580C411yescharacteristic, complemented
41C4⋊C4×D17C2211yescharacteristic
42C4⋊C4×D17C2211yescharacteristic
43#10587572C411yescharacteristic, complemented
44#10587569C411yescharacteristic, complemented
45#10587569C411yescharacteristic, complemented
46C22⋊C4×D17C2211yescharacteristic
47C22⋊C4×D17C2211yescharacteristic
48C22⋊C4×D17C2211yescharacteristic
49(C2×#595)⋊C4C2211yescharacteristic
50(C2×#595)⋊C4C2211yescharacteristic
51(C2×#595)⋊C4C2211yescharacteristic
52(C2×#595)⋊C4C2211yescharacteristic
53(C2×#595)⋊C4C2211yescharacteristic
54(C2×#595)⋊C4C2211yescharacteristic
55(C2×#595)⋊C4C2211yescharacteristic
56(C2×#595)⋊C4C2211yescharacteristic
57(C2×#595)⋊C4C2211yescharacteristic
58(C2×#595)⋊C4C2211yescharacteristic
59C23×D17C2311yescharacteristic
60C23×D17C2311yescharacteristic
61C22×#595—22no—
62C22×#595—41no—
63C22×#595—41no—
64C22×#595C2311yescharacteristic
65C22×#595C2311yescharacteristic
66C22×#595C2311yescharacteristic
67C22×#595C2311yescharacteristic
68C22×#595C2311yescharacteristic
69C22×#595C2311yescharacteristic
70C22×#595C2311yescharacteristic
71C22×#595C2311yescharacteristic
72C2×D4×C17C2×C411yescharacteristic
73C22×C4×C17C2×C411yescharacteristic, complemented
74C2×C22⋊D17C2×C411yescharacteristic
75C2×C22⋊D17C2×C411yescharacteristic
76C22×Dic17C2×C411yescharacteristic, complemented
77D4×D17—41no—
78D4×D17—41no—
79C2×D68C2×C411yescharacteristic
80C2×C4×D17—41no—
81C2×C4×D17—41no—
82C2×C4×D17C2×C411yescharacteristic, complemented
83C2×C4×D17C2×C411yescharacteristic, complemented
84C2×C4×D17C2311yescharacteristic
85C2×C4×D17C2311yescharacteristic
86C2×C4×D17C2311yescharacteristic
87C2×C4×D17C2311yescharacteristic
88C2×C4×D17C2311yescharacteristic
89C22⋊#595—22no—
90C22⋊#595—22no—
91C22⋊#595—22no—
92C22⋊#595—41no—
93C22⋊#595—41no—
94C22⋊#595—41no—
95C22⋊#595—41no—
96C4⋊#595—22no—
97C4⋊#595—41no—
98C4⋊#595—41no—
99C4⋊#595—41no—
100C4⋊#595—41no—
101C4×#595—22no—
102C4×#595—41no—
103C4×#595—41no—
104C4×#595—41no—
105C4×#595—41no—
106C4⋊C4×C17C2×C411yescharacteristic, complemented
107C4⋊C4×C17C2×C411yescharacteristic, complemented
108C22⋊C4×C17C2×C411yescharacteristic
109C22⋊C4×C17C2×C411yescharacteristic
110C22⋊C4×C17C2×C411yescharacteristic, complemented
111C22⋊Dic17C2×C411yescharacteristic
112C22⋊Dic17C2×C411yescharacteristic
113C22⋊Dic17C2×C411yescharacteristic, complemented
114#63227C2×C411yescharacteristic
115#63227C2×C411yescharacteristic
116#63227C2×C411yescharacteristic
117#63227C2×C411yescharacteristic
118#63227C2×C411yescharacteristic, complemented
119#63227C2×C411yescharacteristic, complemented
120C4⋊Dic17C2×C411yescharacteristic, complemented
121C4⋊Dic17C2×C411yescharacteristic, complemented
122#63225C2×C411yescharacteristic, complemented
123#63225C2×C411yescharacteristic, complemented
124#63225C2×C411yescharacteristic, complemented
125#63225C2×C411yescharacteristic, complemented
126C23×C17C22×C411yescharacteristic
127C23×C17C22×C411yescharacteristic
128C22×D17—21no—
129C22×D17—21no—
130C22×D17—21no—
131C22×D17—21no—
132C22×D17—21no—
133C22×D17—21no—
134C22×D17—21no—
135C22×D17—21no—
136C22×D17—21no—
137C22×D17—21no—
138C22×D17—21no—
139C22×D17—21no—
140C22×D17C22×C411yescharacteristic
141C22×D17C22×C411yescharacteristic
142C22×D17C2411yescharacteristic
143C2×#595—21no—
144C2×#595—21no—
145C2×#595—21no—
146C2×#595—21no—
147C2×#595—21no—
148C2×#595—21no—
149C2×#595—21no—
150C2×#595—21no—
151C2×#595—21no—
152C2×#595—21no—
153C2×#595—21no—
154C2×#595—21no—
155C2×#595—21no—
156C2×#595—21no—
157C2×#595—21no—
158C2×#595—21no—
159C2×#595—21no—
160C2×#595—21no—
161C2×#595—21no—
162C2×#595—21no—
163C2×#595—21no—
164C2×#595—21no—
165C2×#595—44no—
166C2×#595#4112yes—
167C2×#595#4112yes—
168D4×C17—41no—
169C2×C4×C17—41no—
170C2×C4×C17C22×C411yescharacteristic
171C2×C4×C17C22×C411yescharacteristic
172C2×C4×C17C22×C411yescharacteristic
173C2×C4×C17C22×C411yescharacteristic
174C2×C4×C17C22×C411yescharacteristic
175C22⋊D17—41no—
176C22⋊D17—41no—
177C2×Dic17—41no—
178C2×Dic17C22×C411yescharacteristic
179C2×Dic17C22×C411yescharacteristic
180C2×Dic17C22×C411yescharacteristic
181C2×Dic17C22×C411yescharacteristic
182C2×Dic17C22×C411yescharacteristic
183D68—41no—
184C4×D17—21no—
185C4×D17—21no—
186C4×D17—21no—
187C4×D17—21no—
188C4×D17—21no—
189C4×D17—21no—
190C4×D17—21no—
191C4×D17—21no—
192C4×D17—21no—
193C4×D17—21no—
194C4×D17—41no—
195C4×D17—41no—
196#2335—171nomaximal, Sylow
197C22×C17—21no—
198C22×C17—21no—
199C22×C17—21no—
200C22×C17—21no—
201C22×C17—21no—
202C22×C17—21no—
203C22×C17C23×C411yescharacteristic
204C2×D17—21no—
205C2×D17—21no—
206C2×D17—21no—
207C2×D17—21no—
208C2×D17—21no—
209C2×D17—21no—
210C2×D17—41no—
211C2×D17—41no—
212C2×D17—41no—
213C2×D17—41no—
214C2×D17—41no—
215C2×D17—41no—
216C2×D17—41no—
217C2×D17—41no—
218C2×D17C2×#4111yescharacteristic
219C2×D17C2×#4111yescharacteristic
220C2×D17H(5,𝔽2)11yescharacteristic
221C2×D17H(5,𝔽2)11yescharacteristic
222C2×D17H(5,𝔽2)11yescharacteristic
223C2×D172−1+411yescharacteristic
224#595—22no—
225#595—22no—
226#595—41no—
227#595—41no—
228#595—41no—
229#595—41no—
230#595—41no—
231#595—41no—
232C4×C17—21no—
233C4×C17—21no—
234C4×C17—21no—
235C4×C17—21no—
236C4×C17—21no—
237Dic17—21no—
238Dic17—21no—
239Dic17—21no—
240Dic17—21no—
241Dic17—21no—
242C2×#123—171no—
243#390—171no—
244#389—171no—
245#388—171no—
246#388—171no—
247#388—171no—
248#388—171no—
249#387—171no—
250#387—171no—
251#386—171no—
252#385—171no—
253#380—171no—
254C4×C4⋊C4—171no—
255C4×C22⋊C4—171no—
256C4×C22⋊C4—171no—
257C2×C17—41no—
258C2×C17—41no—
259C2×C17C4×#4111yescharacteristic
260C2×C17#51811yescharacteristic
261C2×C17#52011yescharacteristic
262D17—41no—
263D17—41no—
264D17#53811yescharacteristic
265D17#53911yescharacteristic
266D17#54011yescharacteristic
267D17#54211yescharacteristic
268C22×D4—171no—
269C23×C4—171no—
270C23×C4—171no—
271#123—171no—
272#123—171no—
273#123—171no—
274#123—171no—
275#123—171no—
276#123—171no—
277#123—171no—
278#123#59511yescharacteristic, complemented
279C2×C4⋊C4—171no—
280C2×C4⋊C4—171no—
281C2×C4⋊C4—171no—
282C2×C4⋊C4—171no—
283C2×C4⋊C4—171no—
284C2×C4⋊C4—171no—
285C2×C4⋊C4—171no—
286C2×C22⋊C4—171no—
287C2×C22⋊C4—171no—
288C2×C22⋊C4—171no—
289C2×C22⋊C4—171no—
290C2×C22⋊C4—171no—
291C2×C22⋊C4—171no—
292C2×C22⋊C4—171no—
293C2×C22⋊C4—171no—
294C2×C22⋊C4—171no—
295C2×C22⋊C4—171no—
296C2×C42—171no—
297C2×C42—171no—
298C2×C42—171no—
299C2×C42—171no—
300C2×C42—171no—
301#95—171no—
302#95—171no—
303#95—171no—
304#95—171no—
305#95—171no—
306#95—171no—
307#95—171no—
308#95—171no—
309#95—171no—
310#95—171no—
311C17#233511yescharacteristic, complemented, Sylow
312C24—171no—
313C24—171no—
314C2×D4—171no—
315C2×D4—171no—
316C2×D4—171no—
317C2×D4—681no—
318C2×D4—681no—
319C2×D4C2×#59511yescharacteristic
320C22×C4—171no—
321C22×C4—171no—
322C22×C4—171no—
323C22×C4—171no—
324C22×C4—171no—
325C22×C4—171no—
326C22×C4—171no—
327C22×C4—171no—
328C22×C4—171no—
329C22×C4—171no—
330C22×C4—171no—
331C22×C4—171no—
332C22×C4—171no—
333C22×C4—171no—
334C22×C4—171no—
335C22×C4—171no—
336C22×C4—342no—
337C22×C4—681no—
338C22×C4—681no—
339C22×C4—681no—
340C22×C4—681no—
341C22×C4C2×#59511yescharacteristic, complemented
342C4⋊C4—171no—
343C4⋊C4—171no—
344C4⋊C4—171no—
345C4⋊C4—171no—
346C4⋊C4—171no—
347C4⋊C4—171no—
348C4⋊C4—342no—
349C4⋊C4—681no—
350C4⋊C4—681no—
351C4⋊C4—681no—
352C4⋊C4—681no—
353C4⋊C4C2×#59511yescharacteristic, complemented
354C4⋊C4C2×#59511yescharacteristic, complemented
355C22⋊C4—171no—
356C22⋊C4—171no—
357C22⋊C4—171no—
358C22⋊C4—171no—
359C22⋊C4—171no—
360C22⋊C4—171no—
361C22⋊C4—171no—
362C22⋊C4—171no—
363C22⋊C4—171no—
364C22⋊C4—342no—
365C22⋊C4—342no—
366C22⋊C4—342no—
367C22⋊C4—681no—
368C22⋊C4—681no—
369C22⋊C4—681no—
370C22⋊C4—681no—
371C22⋊C4C2×#59511yescharacteristic
372C22⋊C4C2×#59511yescharacteristic
373C22⋊C4C2×#59511yescharacteristic, complemented
374C42—342no—
375C42—681no—
376C42—681no—
377C42—681no—
378C42—681no—
379C23—171no—
380C23—171no—
381C23—171no—
382C23—341no—
383C23—341no—
384C23—341no—
385C23—341no—
386C23—341no—
387C23—341no—
388C23—341no—
389C23—341no—
390C23—341no—
391C23—341no—
392C23—341no—
393C23—341no—
394C23C22×#59511yescharacteristic
395C23C22×#59511yescharacteristic
396D4—41no—
397D4—681no—
398D4—681no—
399D4—681no—
400C2×C4—41no—
401C2×C4—172no—
402C2×C4—172no—
403C2×C4—171no—
404C2×C4—171no—
405C2×C4—171no—
406C2×C4—171no—
407C2×C4—171no—
408C2×C4—341no—
409C2×C4—341no—
410C2×C4—341no—
411C2×C4—341no—
412C2×C4—341no—
413C2×C4—341no—
414C2×C4—341no—
415C2×C4—341no—
416C2×C4—341no—
417C2×C4—341no—
418C2×C4—341no—
419C2×C4—341no—
420C2×C4—341no—
421C2×C4—341no—
422C2×C4—341no—
423C2×C4—341no—
424C2×C4—341no—
425C2×C4—341no—
426C2×C4—341no—
427C2×C4—341no—
428C2×C4—341no—
429C2×C4—341no—
430C2×C4—341no—
431C2×C4—341no—
432C2×C4—341no—
433C2×C4—341no—
434C2×C4—341no—
435C2×C4—341no—
436C2×C4—341no—
437C2×C4—341no—
438C2×C4—341no—
439C2×C4—341no—
440C2×C4—681no—
441C2×C4—681no—
442C2×C4—681no—
443C2×C4—684no—
444C2×C4C22×#59511yescharacteristic
445C2×C4C22×#59511yescharacteristic
446C2×C4C22×#59511yescharacteristic
447C2×C4C22×#59511yescharacteristic
448C2×C4C22×#59511yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—171no—
456C22—171no—
457C22—171no—
458C22—171no—
459C22—171no—
460C22—171no—
461C22—341no—
462C22—341no—
463C22—341no—
464C22—341no—
465C22—341no—
466C22—341no—
467C22—681no—
468C22—681no—
469C22—681no—
470C22—681no—
471C22—681no—
472C22—681no—
473C22—681no—
474C22—681no—
475C22C23×#59511yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—342no—
482C4—342no—
483C4—341no—
484C4—341no—
485C4—341no—
486C4—341no—
487C4—341no—
488C4—681no—
489C4—681no—
490C4—681no—
491C4—681no—
492C4—681no—
493C4—681no—
494C2—41no—
495C2—41no—
496C2—171no—
497C2—171no—
498C2—171no—
499C2—171no—
500C2—681no—
501C2—681no—
502C2#41×#59511yescharacteristic
503C2#1176387611yescharacteristic
504C2#1176387811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#595
commutator, socleC22×C17C23×C4
FittingC17×#123C4
prime radicalC2×D4×D17C22
cosocleC22×D17C24
hypercenter#123#595
hypocenterC17#2335
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #11763760C2semidirect
3. #11763759C2semidirect
4. #11763759C2semidirect
5. #11763759C2semidirect
6. #11763759C2semidirect
7. #11763758C2semidirect
8. #11763758C2semidirect
10. #11763756C2semidirect
11. #11763751C2semidirect
12. C4⋊C4×#595C2semidirect
13. C22⋊C4×#595C2semidirect
14. C4×C22⋊#595C2semidirect
36. C17×#123C4semidirect
37. #10587621C4semidirect
38. #10587615C4semidirect
39. #10587580C4semidirect
40. #10587580C4semidirect
43. #10587572C4semidirect
44. #10587569C4semidirect
45. #10587569C4semidirect
73. C22×C4×C17C2×C4semidirect
76. C22×Dic17C2×C4semidirect
82. C2×C4×D17C2×C4semidirect
83. C2×C4×D17C2×C4semidirect
106. C4⋊C4×C17C2×C4semidirect
107. C4⋊C4×C17C2×C4semidirect
110. C22⋊C4×C17C2×C4semidirect
113. C22⋊Dic17C2×C4semidirect
118. #63227C2×C4semidirect
119. #63227C2×C4semidirect
120. C4⋊Dic17C2×C4semidirect
121. C4⋊Dic17C2×C4semidirect
122. #63225C2×C4semidirect
123. #63225C2×C4semidirect
124. #63225C2×C4semidirect
125. #63225C2×C4semidirect
278. #123#595semidirect
311. C17#2335semidirect
341. C22×C4C2×#595semidirect
353. C4⋊C4C2×#595semidirect
354. C4⋊C4C2×#595semidirect
373. C22⋊C4C2×#595semidirect

Maximal subgroups

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

subgroupindex
#117637612
#117637602
#117637592
#117637582
#117637572
#117637562
#117637512
C4⋊C4×#5952
C22⋊C4×#5952
C4×C22⋊#5952
#123×D172
#233517