Finite Group Databasebeta

← #28339919

Subgroups — #28339919

Order 13696.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812090C211yesmaximal, characteristic, complemented
2C2×D4×Dic107C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic107C211yesmaximal, characteristic, complemented
4#20292563C211yesmaximal, characteristic, complemented
5#20292552C211yesmaximal, characteristic, complemented
6#20292541C211yesmaximal, characteristic, complemented
7#20292541C211yesmaximal, characteristic, complemented
8#20292515C211yesmaximal, characteristic, complemented
9#20292515C211yesmaximal, characteristic, complemented
10#20292507C211yesmaximal, characteristic, complemented
11#20292507C211yesmaximal, characteristic, complemented
12#20292499C211yesmaximal, characteristic, complemented
13#20292485C211yesmaximal, characteristic, complemented
14#20292483C211yesmaximal, characteristic, complemented
15C2×#120×C107C211yesmaximal, characteristic
16C23×Dic107C2211yescharacteristic
17C23×Dic107C2211yescharacteristic
18C23×Dic107C2211yescharacteristic, complemented
19#16812090—24no—
20D4×Dic107—24no—
21C2×C4⋊Dic107C2211yescharacteristic, complemented
22C2×Dic107⋊C4C2211yescharacteristic, complemented
23C2×Dic107⋊C4C2211yescharacteristic, complemented
24C2×Dic107⋊C4C2211yescharacteristic, complemented
25C2×Dic107⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic107—24no—
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
32C2×C22⋊Dic107C2211yescharacteristic
33C2×C22⋊Dic107C2211yescharacteristic
34C2×C22⋊Dic107C2211yescharacteristic
35C2×C22⋊Dic107C2211yescharacteristic
36C2×C22⋊Dic107C2211yescharacteristic
37C2×C22⋊Dic107C2211yescharacteristic, complemented
38C2×C22⋊Dic107C2211yescharacteristic, complemented
39C2×C22⋊Dic107C2211yescharacteristic, complemented
40C2×C4×Dic107C2211yescharacteristic, complemented
41C107⋊#95C2211yescharacteristic, complemented
42C107⋊#95C2211yescharacteristic, complemented
43C107⋊#95C2211yescharacteristic, complemented
44C107⋊#95C2211yescharacteristic, complemented
45C107⋊#95C2211yescharacteristic, complemented
46C107⋊#95C2211yescharacteristic, complemented
47C25×C107C2211yescharacteristic
48C22×D4×C107C2211yescharacteristic
49C22×D4×C107C2211yescharacteristic
50C22×D4×C107C2211yescharacteristic
51#120×C107—24no—
52C2×C22⋊C4×C107C2211yescharacteristic
53C2×C22⋊C4×C107C2211yescharacteristic
54C2×C22⋊C4×C107C2211yescharacteristic
55C22×Dic107—22no—
56C22×Dic107—22no—
57C22×Dic107—22no—
58C22×Dic107—22no—
59C22×Dic107—22no—
60C22×Dic107—22no—
61C22×Dic107—41no—
62C22×Dic107—41no—
63C22×Dic107—41no—
64C22×Dic107C2311yescharacteristic
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67C22×Dic107C2311yescharacteristic
68C22×Dic107C2311yescharacteristic
69C22×Dic107C2311yescharacteristic
70C22×Dic107C2311yescharacteristic
71C22×Dic107C2311yescharacteristic
72C4⋊Dic107—22no—
73Dic107⋊C4—22no—
74Dic107⋊C4—22no—
75Dic107⋊C4—41no—
76Dic107⋊C4—41no—
77C22⋊Dic107—22no—
78C22⋊Dic107—22no—
79C22⋊Dic107—22no—
80C22⋊Dic107—22no—
81C22⋊Dic107—22no—
82C22⋊Dic107—22no—
83C22⋊Dic107—22no—
84C22⋊Dic107—22no—
85C22⋊Dic107—22no—
86C22⋊Dic107—41no—
87C22⋊Dic107—41no—
88C22⋊Dic107—41no—
89C22⋊Dic107D414yescomplemented
90C4×Dic107—22no—
91C24×C107—22no—
92C24×C107—22no—
93C24×C107—22no—
94C24×C107—22no—
95C24×C107—22no—
96C24×C107—41no—
97C24×C107—41no—
98C24×C107C2311yescharacteristic
99C24×C107C2311yescharacteristic
100C24×C107C2311yescharacteristic
101C24×C107C2311yescharacteristic
102C2×D4×C107—22no—
103C2×D4×C107—22no—
104C2×D4×C107—22no—
105C2×D4×C107—22no—
106C2×D4×C107—22no—
107C2×D4×C107—22no—
108C2×D4×C107—41no—
109C2×D4×C107—41no—
110C2×D4×C107D414yes—
111C22×C4×C107C2311yescharacteristic
112C22×C4×C107C2311yescharacteristic
113C22×C4×C107C2311yescharacteristic
114C22⋊C4×C107—22no—
115C22⋊C4×C107—22no—
116C22⋊C4×C107—22no—
117C23×C107—21no—
118C23×C107—21no—
119C23×C107—21no—
120C23×C107—21no—
121C23×C107—28no—
122C23×C107—21no—
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×C107—44no—
141C23×C107—44no—
142C23×C107—44no—
143C23×C107—44no—
144C23×C107—44no—
145C23×C107—44no—
146C23×C107C2×D412yes—
147C23×C107C2×D412yes—
148C23×C107C2×D412yes—
149C23×C107#4112yes—
150C23×C107#4112yes—
151C23×C107#4112yes—
152C23×C107C2411yescharacteristic
153D4×C107—28no—
154D4×C107—44no—
155D4×C107—44no—
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×C107C2×D412yes—
165C2×Dic107—21no—
166C2×Dic107—21no—
167C2×Dic107—21no—
168C2×Dic107—21no—
169C2×Dic107—21no—
170C2×Dic107—21no—
171C2×Dic107—21no—
172C2×Dic107—21no—
173C2×Dic107—21no—
174C2×Dic107—21no—
175C2×Dic107—21no—
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—44no—
188C2×Dic107—44no—
189C2×Dic107—44no—
190C2×Dic107C2×D412yes—
191C2×Dic107C2×D412yes—
192C22×C107—22no—
193C22×C107—22no—
194C22×C107—22no—
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—22no—
205C22×C107—22no—
206C22×C107—22no—
207C22×C107—416no—
208C22×C107—41no—
209C22×C107—41no—
210C22×C107—41no—
211C22×C107—41no—
212C22×C107—41no—
213C22×C107—41no—
214C22×C107—41no—
215C22×C107—41no—
216C22×C107—41no—
217C22×C107—41no—
218C22×C107—41no—
219C22×C107—41no—
220C22×C107#12314yescomplemented
221C22×C107C22×D411yescharacteristic
222C22×C107C22×D411yescharacteristic
223C22×C107C2×#4111yescharacteristic
224C22×C107C2×#4111yescharacteristic
225C22×C107C2×#4111yescharacteristic
226C22×C107H(5,𝔽2)11yescharacteristic
227C22×C107H(5,𝔽2)11yescharacteristic
228C4×C107—22no—
229C4×C107—41no—
230C4×C107—41no—
231Dic107—22no—
232Dic107—22no—
233Dic107—41no—
234Dic107—41no—
235Dic107—41no—
236Dic107—41no—
237Dic107—41no—
238Dic107—41no—
239C2×C107—24no—
240C2×C107—42no—
241C2×C107—42no—
242C2×C107—42no—
243C2×C107C2×#12311yescharacteristic
244C2×C107#52511yescharacteristic
245C2×C107#53811yescharacteristic
246C2×C107D4211yescharacteristic
247C2×C107#54611yescharacteristic
248C2×C107#54611yescharacteristic
249C2×C107#55111yescharacteristic
250#2418—1071nomaximal, Sylow
251C107#241811yescharacteristic, complemented, Sylow
252C2×#123—1071no—
253C2×#120D10711yescharacteristic
254C2×C4×D4—1071no—
255C22×C22⋊C4—1071no—
256#399—1071no—
257#397—1071no—
258#394—1071no—
259#394—1071no—
260#388—1071no—
261#388—1071no—
262#386—1071no—
263#386—1071no—
264#385—1071no—
265#380—1071no—
266#379—1071no—
267C25C2×D10711yescharacteristic
268C22×D4C2×D10711yescharacteristic
269C22×D4C2×D10711yescharacteristic
270C22×D4C2×D10711yescharacteristic
271C23×C4—1071no—
272C23×C4—1071no—
273C23×C4—1071no—
274#123—2144no—
275#120—24no—
276C4×D4—2144no—
277C2×C4⋊C4—1071no—
278C2×C4⋊C4—1071no—
279C2×C4⋊C4—1071no—
280C2×C4⋊C4—1071no—
281C2×C4⋊C4—1071no—
282C2×C22⋊C4—1071no—
283C2×C22⋊C4—1071no—
284C2×C22⋊C4—1071no—
285C2×C22⋊C4—1071no—
286C2×C22⋊C4—1071no—
287C2×C22⋊C4—1071no—
288C2×C22⋊C4—1071no—
289C2×C22⋊C4—1071no—
290C2×C22⋊C4—1071no—
291C2×C22⋊C4—1071no—
292C2×C22⋊C4—1071no—
293C2×C22⋊C4—1071no—
294C2×C22⋊C4—1071no—
295C2×C22⋊C4—2144no—
296C2×C22⋊C4C2×D10711yescharacteristic
297C2×C22⋊C4C2×D10711yescharacteristic
298C2×C22⋊C4C2×D10711yescharacteristic
299C2×C42—1071no—
300#95—1071no—
301#95—1071no—
302#95—1071no—
303#95—1071no—
304#95—1071no—
305#95—1071no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24C22×D10711yescharacteristic
314C24C22×D10711yescharacteristic
315C24C22×D10711yescharacteristic
316C24C22×D10711yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4C22⋊D10714yes—
326C22×C4—1071no—
327C22×C4—1071no—
328C22×C4—1071no—
329C22×C4—1071no—
330C22×C4—1071no—
331C22×C4—1071no—
332C22×C4—1071no—
333C22×C4—1071no—
334C22×C4—4281no—
335C22×C4—4281no—
336C22×C4—4281no—
337C22×C4—2142no—
338C22×C4—2142no—
339C22×C4—2142no—
340C22×C4—2142no—
341C22×C4—2142no—
342C22×C4—2142no—
343C22×C4C22×D10711yescharacteristic
344C22×C4C22×D10711yescharacteristic
345C22×C4C22×D10711yescharacteristic
346C4⋊C4—4281no—
347C4⋊C4—4281no—
348C4⋊C4—2142no—
349C4⋊C4—2142no—
350C4⋊C4—2142no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—1074no—
355C22⋊C4—4281no—
356C22⋊C4—4281no—
357C22⋊C4—4281no—
358C22⋊C4—2142no—
359C22⋊C4—2142no—
360C22⋊C4—2142no—
361C22⋊C4—2142no—
362C22⋊C4—2142no—
363C22⋊C4—2142no—
364C22⋊C4—2142no—
365C22⋊C4—2142no—
366C22⋊C4—2142no—
367C42—2142no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
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—44no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23D4×D10712yes—
398C23C2×C22⋊D10712yes—
399C23C2×C22⋊D10712yes—
400C23#1313381712yes—
401C23#1313381712yes—
402C23#1313381712yes—
403C23C23×D10711yescharacteristic
404D4—28no—
405D4—44no—
406D4—44no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—1072no—
416C2×C4—1072no—
417C2×C4—4284no—
418C2×C4—4284no—
419C2×C4—4284no—
420C2×C4—2141no—
421C2×C4—2141no—
422C2×C4—2141no—
423C2×C4—2141no—
424C2×C4—2141no—
425C2×C4—2141no—
426C2×C4—2141no—
427C2×C4—2141no—
428C2×C4—2141no—
429C2×C4—2141no—
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×C4C2×C22⋊D10712yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—416no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22#1681209014yescomplemented
472C22C2×D4×D10711yescharacteristic
473C22C22×C22⋊D10711yescharacteristic
474C22C2×#1313381711yescharacteristic
475C22C2×#1313381711yescharacteristic
476C22C2×#1313381711yescharacteristic
477C22#1681215411yescharacteristic
478C22#1681215411yescharacteristic
479C4—22no—
480C4—41no—
481C4—41no—
482C4—4281no—
483C4—4281no—
484C4—4281no—
485C4—4281no—
486C4—4281no—
487C4—4281no—
488C4—2142no—
489C4—2142no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—42no—
494C2C2×#1681209011yescharacteristic
495C2#2029313311yescharacteristic
496C2#2029321211yescharacteristic
497C2D4×C22⋊D10711yescharacteristic
498C2#2029326411yescharacteristic
499C2#2029327111yescharacteristic
500C2#2029330811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting, prime radicalC2×#120×C107C2
hypercenterC2×#120D107
hypocenterC107#2418
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#16812090C2semidirect
2. C2×D4×Dic107C2semidirect
3. C22×C22⋊Dic107C2semidirect
4. #20292563C2semidirect
5. #20292552C2semidirect
6. #20292541C2semidirect
7. #20292541C2semidirect
8. #20292515C2semidirect
9. #20292515C2semidirect
10. #20292507C2semidirect
11. #20292507C2semidirect
12. #20292499C2semidirect
13. #20292485C2semidirect
14. #20292483C2semidirect
18. C23×Dic107C22semidirect
21. C2×C4⋊Dic107C22semidirect
22. C2×Dic107⋊C4C22semidirect
23. C2×Dic107⋊C4C22semidirect
24. C2×Dic107⋊C4C22semidirect
25. C2×Dic107⋊C4C22semidirect
37. C2×C22⋊Dic107C22semidirect
38. C2×C22⋊Dic107C22semidirect
39. C2×C22⋊Dic107C22semidirect
40. C2×C4×Dic107C22semidirect
41. C107⋊#95C22semidirect
42. C107⋊#95C22semidirect
43. C107⋊#95C22semidirect
44. C107⋊#95C22semidirect
45. C107⋊#95C22semidirect
46. C107⋊#95C22semidirect
89. C22⋊Dic107D4semidirect
220. C22×C107#123semidirect
251. C107#2418semidirect
471. C22#16812090semidirect

Maximal subgroups

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

subgroupindex
C2×#168120902
C2×D4×Dic1072
C22×C22⋊Dic1072
#202925632
#202925522
#202925412
#202925152
#202925072
#202924992
#202924852
#202924832
C2×#120×C1072
#2418107