Finite Group Databasebeta

← #28339898

Subgroups — #28339898

Order 13696.

788 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
1C2×#16812081C211yesmaximal, characteristic, complemented
2C2×#16812081C211yesmaximal, characteristic, complemented
3C2×#16812081C211yesmaximal, characteristic, complemented
4C2×D4×Dic107C211yesmaximal, characteristic, complemented
5C22×Dic107⋊C4C211yesmaximal, characteristic, complemented
6#20292550C211yesmaximal, characteristic, complemented
7#20292549C211yesmaximal, characteristic, complemented
8#20292542C211yesmaximal, characteristic, complemented
9#20292541C211yesmaximal, characteristic, complemented
10#20292527C211yesmaximal, characteristic, complemented
11#20292522C211yesmaximal, characteristic, complemented
12#20292507C211yesmaximal, characteristic, complemented
13#20292506C211yesmaximal, characteristic, complemented
14#20292485C211yesmaximal, characteristic, complemented
15C2×#121×C107C211yesmaximal, characteristic, complemented
16C22×C22⋊D107C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C22×C22⋊D107C2211yescharacteristic
19C23×Dic107C2211yescharacteristic
20C23×Dic107C2211yescharacteristic
21C23×Dic107C2211yescharacteristic
22#16812081—24no—
23#16812081—24no—
24#16812081—24no—
25D4×Dic107—24no—
26C2×C4⋊Dic107C2211yescharacteristic
27C2×Dic107⋊C4—24no—
28C2×Dic107⋊C4C2211yescharacteristic
29C2×Dic107⋊C4C2211yescharacteristic
30C2×Dic107⋊C4C2211yescharacteristic
31C2×Dic107⋊C4C2211yescharacteristic
32C2×Dic107⋊C4C2211yescharacteristic
33C2×Dic107⋊C4C2211yescharacteristic
34C2×C22⋊Dic107C2211yescharacteristic
35C2×C22⋊Dic107C2211yescharacteristic
36C2×C22⋊Dic107C2211yescharacteristic
37C2×C22⋊Dic107C2211yescharacteristic
38C2×C22⋊Dic107C2211yescharacteristic
39C2×C22⋊Dic107C2211yescharacteristic
40C2×(C2×D107)⋊C4C2211yescharacteristic
41C2×(C2×D107)⋊C4C2211yescharacteristic
42C2×(C2×D107)⋊C4C2211yescharacteristic
43C2×(C2×D107)⋊C4C2211yescharacteristic
44C2×C4×Dic107C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C107⋊#95C2211yescharacteristic
47C107⋊#95C2211yescharacteristic
48C107⋊#95C2211yescharacteristic
49C22×D4×C107C2211yescharacteristic
50C22×D4×C107C2211yescharacteristic
51C22×D4×C107C2211yescharacteristic
52C23×C4×C107C2211yescharacteristic
53#121×C107—24no—
54C2×C4⋊C4×C107C2211yescharacteristic
55C2×C22⋊C4×C107C2211yescharacteristic
56C2×C22⋊C4×C107C2211yescharacteristic
57C23×D107C2311yescharacteristic
58C2×C22⋊D107—22no—
59C2×C22⋊D107—22no—
60C2×C22⋊D107—22no—
61C2×C22⋊D107—22no—
62C2×C22⋊D107—22no—
63C2×C22⋊D107—22no—
64C2×C22⋊D107—22no—
65C2×C22⋊D107—22no—
66C2×C22⋊D107—41no—
67C22×Dic107—22no—
68C22×Dic107—22no—
69C22×Dic107—22no—
70C22×Dic107—22no—
71C22×Dic107—22no—
72C22×Dic107—22no—
73C22×Dic107—22no—
74C22×Dic107—41no—
75C22×Dic107D414yescomplemented
76C22×Dic107C2311yescharacteristic
77C22×Dic107C2311yescharacteristic
78C22×Dic107C2311yescharacteristic
79C22×Dic107C2311yescharacteristic
80C22×Dic107C2311yescharacteristic
81C22×Dic107C2311yescharacteristic
82C22×Dic107C2311yescharacteristic
83C4⋊Dic107—22no—
84Dic107⋊C4—22no—
85Dic107⋊C4—22no—
86Dic107⋊C4—22no—
87Dic107⋊C4—22no—
88Dic107⋊C4—22no—
89Dic107⋊C4D414yescomplemented
90C22⋊Dic107—22no—
91C22⋊Dic107—22no—
92C22⋊Dic107—22no—
93C22⋊Dic107—22no—
94C22⋊Dic107—22no—
95C22⋊Dic107—41no—
96(C2×D107)⋊C4—22no—
97(C2×D107)⋊C4—22no—
98(C2×D107)⋊C4—22no—
99(C2×D107)⋊C4—41no—
100C4×Dic107—22no—
101C24×C107C2311yescharacteristic
102C24×C107C2311yescharacteristic
103C24×C107C2311yescharacteristic
104C2×D4×C107—22no—
105C2×D4×C107—22no—
106C2×D4×C107—22no—
107C2×D4×C107—22no—
108C2×D4×C107—22no—
109C2×D4×C107—22no—
110C2×D4×C107—22no—
111C2×D4×C107—41no—
112C2×D4×C107D414yescomplemented
113C22×C4×C107—22no—
114C22×C4×C107—22no—
115C22×C4×C107—41no—
116C22×C4×C107C2311yescharacteristic
117C22×C4×C107C2311yescharacteristic
118C22×C4×C107C2311yescharacteristic
119C22×C4×C107C2311yescharacteristic
120C4⋊C4×C107—22no—
121C22⋊C4×C107—22no—
122C22⋊C4×C107—22no—
123C23×C107—21no—
124C23×C107—21no—
125C23×C107—21no—
126C23×C107—21no—
127C23×C107—21no—
128C23×C107—21no—
129C23×C107—21no—
130C23×C107—21no—
131C23×C107—21no—
132C23×C107—21no—
133C23×C107—21no—
134C23×C107—21no—
135C23×C107—21no—
136C23×C107—21no—
137C23×C107—21no—
138C23×C107—21no—
139C23×C107—21no—
140C23×C107C2×D412yes—
141C23×C107C2×D412yes—
142C23×C107C2×D412yes—
143C23×C107#4112yes—
144C23×C107C2411yescharacteristic
145C22×D107—21no—
146C22×D107—21no—
147C22×D107—21no—
148C22×D107—21no—
149C22×D107—21no—
150C22×D107—21no—
151C22×D107—21no—
152D4×C107—28no—
153D4×C107—44no—
154D4×C107—44no—
155C2×C4×C107—21no—
156C2×C4×C107—21no—
157C2×C4×C107—21no—
158C2×C4×C107—21no—
159C2×C4×C107—21no—
160C2×C4×C107—21no—
161C2×C4×C107—21no—
162C2×C4×C107—21no—
163C2×C4×C107—21no—
164C2×C4×C107—21no—
165C2×C4×C107—44no—
166C2×C4×C107C2×D412yes—
167C2×C4×C107C2×D412yes—
168C22⋊D107—44no—
169C22⋊D107—44no—
170C22⋊D107—44no—
171C2×Dic107—21no—
172C2×Dic107—21no—
173C2×Dic107—21no—
174C2×Dic107—21no—
175C2×Dic107—28no—
176C2×Dic107—21no—
177C2×Dic107—21no—
178C2×Dic107—21no—
179C2×Dic107—21no—
180C2×Dic107—21no—
181C2×Dic107—21no—
182C2×Dic107—21no—
183C2×Dic107—21no—
184C2×Dic107—21no—
185C2×Dic107—21no—
186C2×Dic107—21no—
187C2×Dic107—21no—
188C2×Dic107—44no—
189C2×Dic107—44no—
190C2×Dic107C2×D412yes—
191C2×Dic107C2×D412yes—
192C2×Dic107C2×D412yes—
193C2×Dic107C2×D412yes—
194C2×Dic107#4112yes—
195C22×C107—22no—
196C22×C107—22no—
197C22×C107—22no—
198C22×C107—22no—
199C22×C107—22no—
200C22×C107—22no—
201C22×C107—22no—
202C22×C107—22no—
203C22×C107—22no—
204C22×C107—41no—
205C22×C107—41no—
206C22×C107—41no—
207C22×C107—41no—
208C22×C107—41no—
209C22×C107—41no—
210C22×C107—41no—
211C22×C107—41no—
212C22×C107—41no—
213C22×C107—41no—
214C22×C107—41no—
215C22×C107#12114yescomplemented
216C22×C107C22×D411yescharacteristic
217C22×C107C22×D411yescharacteristic
218C22×C107C22×D411yescharacteristic
219C22×C107C2×#4111yescharacteristic
220C22×C107C2×#4111yescharacteristic
221C22×C107H(5,𝔽2)11yescharacteristic
222C22×C1072−1+411yescharacteristic
223C2×D107—41no—
224C2×D107—41no—
225C2×D107—41no—
226C2×D107—41no—
227C2×D107—41no—
228C2×D107—41no—
229C2×D107—41no—
230C4×C107—22no—
231C4×C107—22no—
232C4×C107—41no—
233C4×C107—41no—
234Dic107—22no—
235Dic107—22no—
236Dic107—41no—
237Dic107—41no—
238Dic107—41no—
239Dic107—41no—
240Dic107#12114yescomplemented
241C2×C107—24no—
242C2×C107—42no—
243C2×C107—81no—
244C2×C107C2×#12111yescharacteristic
245C2×C107C2×#12111yescharacteristic
246C2×C107#53711yescharacteristic
247C2×C107D4211yescharacteristic
248C2×C107#54711yescharacteristic
249C2×C107#54811yescharacteristic
250C2×C107#55311yescharacteristic
251D107—81no—
252#2416—1071nomaximal, Sylow
253C107#241611yescharacteristic, complemented, Sylow
254C2×#121—1071no—
255C2×#121—1071no—
256C2×#121—1071no—
257C2×#121D10711yescharacteristic, complemented
258C2×C4×D4—1071no—
259C22×C4⋊C4—1071no—
260#396—1071no—
261#396—1071no—
262#394—1071no—
263#394—1071no—
264#390—1071no—
265#389—1071no—
266#386—1071no—
267#386—1071no—
268#380—1071no—
269C22×D4—1071no—
270C22×D4—1071no—
271C22×D4—1071no—
272C22×D4C2×D10711yescharacteristic
273C22×D4C2×D10711yescharacteristic
274C22×D4C2×D10711yescharacteristic
275C23×C4—1071no—
276C23×C4—1071no—
277C23×C4—1071no—
278C23×C4C2×D10711yescharacteristic
279#121—24no—
280#121—2144no—
281#121—2144no—
282#121—2144no—
283C4×D4—2144no—
284C2×C4⋊C4—1071no—
285C2×C4⋊C4—1071no—
286C2×C4⋊C4—1071no—
287C2×C4⋊C4—1071no—
288C2×C4⋊C4—1071no—
289C2×C4⋊C4—1071no—
290C2×C4⋊C4—1071no—
291C2×C4⋊C4—2144no—
292C2×C4⋊C4C2×D10711yescharacteristic
293C2×C22⋊C4—1071no—
294C2×C22⋊C4—1071no—
295C2×C22⋊C4—1071no—
296C2×C22⋊C4—1071no—
297C2×C22⋊C4—1071no—
298C2×C22⋊C4—1071no—
299C2×C22⋊C4—1071no—
300C2×C22⋊C4—1071no—
301C2×C22⋊C4—1071no—
302C2×C22⋊C4—1071no—
303C2×C22⋊C4C2×D10711yescharacteristic
304C2×C22⋊C4C2×D10711yescharacteristic
305C2×C42—1071no—
306#95—1071no—
307#95—1071no—
308#95—1071no—
309#95—1071no—
310C24—1071no—
311C24C22×D10711yescharacteristic
312C24C22×D10711yescharacteristic
313C24C22×D10711yescharacteristic
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—41no—
322C2×D4—4281no—
323C2×D4—2142no—
324C2×D4—2142no—
325C2×D4—2142no—
326C2×D4—2142no—
327C2×D4—2142no—
328C2×D4—2142no—
329C2×D4—2142no—
330C2×D4—2142no—
331C2×D4C22⋊D10714yescomplemented
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4—1071no—
336C22×C4—1074no—
337C22×C4—1071no—
338C22×C4—1071no—
339C22×C4—1071no—
340C22×C4—1071no—
341C22×C4—1071no—
342C22×C4—1071no—
343C22×C4—4281no—
344C22×C4—2142no—
345C22×C4—2142no—
346C22×C4—2142no—
347C22×C4—2142no—
348C22×C4—2142no—
349C22×C4—2142no—
350C22×C4—2142no—
351C22×C4C22×D10711yescharacteristic
352C22×C4C22×D10711yescharacteristic
353C22×C4C22×D10711yescharacteristic
354C22×C4C22×D10711yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—1074no—
357C4⋊C4—2142no—
358C4⋊C4—2142no—
359C4⋊C4—2142no—
360C4⋊C4—2142no—
361C4⋊C4—2142no—
362C4⋊C4—2142no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—4281no—
366C22⋊C4—4281no—
367C22⋊C4—2142no—
368C22⋊C4—2142no—
369C22⋊C4—2142no—
370C22⋊C4—2142no—
371C22⋊C4—2142no—
372C22⋊C4—2142no—
373C22⋊C4—2142no—
374C22⋊C4—2142no—
375C42—2142no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—2141no—
394C23—2141no—
395C23—2141no—
396C23—2141no—
397C23—2141no—
398C23—2141no—
399C23—2141no—
400C23D4×D10712yes—
401C23C2×C22⋊D10712yes—
402C23C2×C22⋊D10712yes—
403C23#1313381712yes—
404C23C23×D10711yescharacteristic
405D4—28no—
406D4—44no—
407D4—44no—
408D4—4284no—
409D4—4284no—
410D4—4284no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—44no—
422C2×C4—1072no—
423C2×C4—1072no—
424C2×C4—1072no—
425C2×C4—1072no—
426C2×C4—1072no—
427C2×C4—4284no—
428C2×C4—4284no—
429C2×C4—2148no—
430C2×C4—2141no—
431C2×C4—2141no—
432C2×C4—2141no—
433C2×C4—2141no—
434C2×C4—2141no—
435C2×C4—2141no—
436C2×C4—2141no—
437C2×C4—2141no—
438C2×C4—2141no—
439C2×C4—2141no—
440C2×C4—2141no—
441C2×C4—2141no—
442C2×C4—2141no—
443C2×C4—2141no—
444C2×C4—2141no—
445C2×C4—2141no—
446C2×C4D4×D10712yes—
447C2×C4C2×C22⋊D10712yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—4281no—
469C22—4281no—
470C22—4281no—
471C22—4281no—
472C22—4281no—
473C22—4281no—
474C22—4281no—
475C22#1681208114yescomplemented
476C22C2×D4×D10711yescharacteristic
477C22C2×D4×D10711yescharacteristic
478C22C22×C22⋊D10711yescharacteristic
479C22#41×D10711yescharacteristic
480C22C2×#1313381711yescharacteristic
481C22#1681215411yescharacteristic
482C22#1681215611yescharacteristic
483C4—22no—
484C4—22no—
485C4—41no—
486C4—41no—
487C4—1074no—
488C4—4281no—
489C4—4281no—
490C4—4281no—
491C4—4281no—
492C4—2142no—
493C4—2142no—
494C2—24no—
495C2—42no—
496C2—81no—
497C2—8561no—
498C2#121×D10711yescharacteristic
499C2C2×#1681208111yescharacteristic
500C2#2029320411yescharacteristic
501C2D4×C22⋊D10711yescharacteristic
502C2#2029327611yescharacteristic
503C2#2029328311yescharacteristic
504C2#2029332011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
FittingC2×#121×C107C2
hypercenterC2×#121D107
hypocenterC107#2416
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16812081C2semidirect
2. C2×#16812081C2semidirect
3. C2×#16812081C2semidirect
4. C2×D4×Dic107C2semidirect
5. C22×Dic107⋊C4C2semidirect
6. #20292550C2semidirect
7. #20292549C2semidirect
8. #20292542C2semidirect
9. #20292541C2semidirect
10. #20292527C2semidirect
11. #20292522C2semidirect
12. #20292507C2semidirect
13. #20292506C2semidirect
14. #20292485C2semidirect
15. C2×#121×C107C2semidirect
75. C22×Dic107D4semidirect
89. Dic107⋊C4D4semidirect
112. C2×D4×C107D4semidirect
215. C22×C107#121semidirect
240. Dic107#121semidirect
253. C107#2416semidirect
257. C2×#121D107semidirect
331. C2×D4C22⋊D107semidirect
475. C22#16812081semidirect

Maximal subgroups

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

subgroupindex
C2×#168120812
C2×D4×Dic1072
C22×Dic107⋊C42
#202925502
#202925492
#202925422
#202925412
#202925272
#202925222
#202925072
#202925062
#202924852
C2×#121×C1072
#2416107