Finite Group Databasebeta

← #23766161

Subgroups — #23766161

Order 10112.

596 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579132C211yesmaximal, characteristic
2#19098463C211yesmaximal, characteristic, complemented
3#19098463C211yesmaximal, characteristic, complemented
4#19098457C211yesmaximal, characteristic, complemented
5#19098451C211yesmaximal, characteristic, complemented
6#19098448C211yesmaximal, characteristic, complemented
7#19098446C211yesmaximal, characteristic, complemented
8#19098443C211yesmaximal, characteristic, complemented
9#19098442C211yesmaximal, characteristic, complemented
10#19098440C211yesmaximal, characteristic, complemented
11#19098425C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic79C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic79C211yesmaximal, characteristic, complemented
14#19098410C211yesmaximal, characteristic, complemented
15#386×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C23×Dic79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579132C418yescomplemented
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×C22⋊Dic79C2211yescharacteristic
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×C4×Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C22×D4×C79C2211yescharacteristic
46C23×C4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52C23×D79C2311yescharacteristic
53C2×C22⋊D79—41no—
54C2×C22⋊D79—41no—
55C2×C22⋊D79—41no—
56C2×C22⋊D79—41no—
57C2×C22⋊D79C2×C414yescomplemented
58C2×C22⋊D79C2×C414yescomplemented
59C22×Dic79—22no—
60C22×Dic79—41no—
61C22×Dic79—41no—
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C2×C4×D79—41no—
70C2×C4×D79—41no—
71C2×C4×D79C2×C414yescomplemented
72C4⋊Dic79C2×C414yescomplemented
73Dic79⋊C4—41no—
74Dic79⋊C4—41no—
75C22⋊Dic79—22no—
76C22⋊Dic79—41no—
77C22⋊Dic79—41no—
78C22⋊Dic79C2×C414yescomplemented
79C22⋊Dic79C2×C414yescomplemented
80(C2×D79)⋊C4—22no—
81(C2×D79)⋊C4—22no—
82(C2×D79)⋊C4—41no—
83(C2×D79)⋊C4—41no—
84C4×Dic79—41no—
85C4×Dic79—41no—
86C4×Dic79—41no—
87C4×Dic79—41no—
88C24×C79C2311yescharacteristic
89C24×C79C2311yescharacteristic
90C2×D4×C79—41no—
91C2×D4×C79—41no—
92C2×D4×C79C2×C414yes—
93C22×C4×C79—22no—
94C22×C4×C79—41no—
95C22×C4×C79—41no—
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C22⋊C4×C79—22no—
102C22⋊C4×C79—41no—
103C22⋊C4×C79—41no—
104C23×C79—21no—
105C23×C79—21no—
106C23×C79—21no—
107C23×C79—21no—
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79C22×C412yes—
117C23×C79C22×C412yes—
118C23×C79C2411yescharacteristic
119C22×D79—21no—
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—21no—
123C22×D79—21no—
124C22×D79—21no—
125C22×D79C22×C412yes—
126D4×C79—44no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—44no—
141C2×C4×C79C22×C412yes—
142C2×C4×C79#4112yes—
143C22⋊D79—44no—
144C22⋊D79—44no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—21no—
158C2×Dic79—21no—
159C2×Dic79—21no—
160C2×Dic79—21no—
161C2×Dic79—21no—
162C2×Dic79—44no—
163C2×Dic79C22×C412yes—
164C2×Dic79C22×C412yes—
165C2×Dic79C22×C412yes—
166C2×Dic79#4112yes—
167C4×D79—44no—
168C22×C79—22no—
169C22×C79—22no—
170C22×C79—22no—
171C22×C79—22no—
172C22×C79—22no—
173C22×C79—22no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79C23×C411yescharacteristic
183C22×C79C2×#4111yescharacteristic
184C22×C79C2×#4111yescharacteristic
185C22×C79H(5,𝔽2)11yescharacteristic
186C22×C79H(5,𝔽2)11yescharacteristic
187C22×C79H(5,𝔽2)11yescharacteristic
188C22×C79H(5,𝔽2)11yescharacteristic
189C2×D79—22no—
190C2×D79—22no—
191C2×D79—22no—
192C2×D79—41no—
193C2×D79—41no—
194C2×D79—41no—
195C2×D79—41no—
196C4×C79—22no—
197C4×C79—22no—
198C4×C79—41no—
199C4×C79—41no—
200C4×C79—41no—
201Dic79—22no—
202Dic79—22no—
203Dic79—22no—
204Dic79—22no—
205Dic79—41no—
206Dic79—41no—
207Dic79—41no—
208C2×C79—42no—
209C2×C79—42no—
210C2×C79C4×#4111yescharacteristic
211C2×C79#51811yescharacteristic
212C2×C79#51811yescharacteristic
213C2×C79#53811yescharacteristic
214C2×C79#53811yescharacteristic
215C2×C79#54011yescharacteristic
216C2×C79#54011yescharacteristic
217D79—42no—
218#2333—791nomaximal, Sylow
219C79#233311yescharacteristic, complemented, Sylow
220C2×#121—791no—
221#390—791no—
222#390—791no—
223#388—791no—
224#388—791no—
225#387—791no—
226#387—791no—
227#386—791no—
228#386—791no—
229#386—791no—
230#386D7911yescharacteristic, complemented
231#381—791no—
232C4×C22⋊C4—791no—
233C4×C22⋊C4—791no—
234C4×C22⋊C4—791no—
235C22×D4—791no—
236C22×D4—791no—
237C22×D4C2×D7911yescharacteristic
238C23×C4—791no—
239C23×C4—791no—
240C23×C4C2×D7911yescharacteristic
241#121—798no—
242C2×C4⋊C4—791no—
243C2×C4⋊C4—791no—
244C2×C4⋊C4—791no—
245C2×C22⋊C4—791no—
246C2×C22⋊C4—791no—
247C2×C22⋊C4—791no—
248C2×C22⋊C4—791no—
249C2×C22⋊C4—791no—
250C2×C22⋊C4—791no—
251C2×C22⋊C4—791no—
252C2×C22⋊C4—791no—
253C2×C22⋊C4—791no—
254C2×C22⋊C4C2×D7911yescharacteristic
255C2×C22⋊C4C2×D7911yescharacteristic
256C2×C22⋊C4C2×D7911yescharacteristic
257C2×C42—791no—
258C2×C42—791no—
259C2×C42—791no—
260C2×C42—791no—
261#95—791no—
262#95—791no—
263#95—791no—
264#95—791no—
265#95—791no—
266#95—791no—
267#95—791no—
268#95—791no—
269#95C2×D7911yescharacteristic
270#95C2×D7911yescharacteristic
271C24—791no—
272C24C22×D7911yescharacteristic
273C24C22×D7911yescharacteristic
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—3161no—
277C2×D4—3161no—
278C2×D4—3161no—
279C2×D4—3161no—
280C2×D4—794no—
281C2×D4—794no—
282C2×D4C4×D7914yes—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—3161no—
287C22×C4—3161no—
288C22×C4—3161no—
289C22×C4—3161no—
290C22×C4—794no—
291C22×C4—791no—
292C22×C4—791no—
293C22×C4—791no—
294C22×C4—791no—
295C22×C4—791no—
296C22×C4—791no—
297C22×C4—791no—
298C22×C4—1582no—
299C22×C4C22×D7911yescharacteristic
300C22×C4C22×D7911yescharacteristic
301C22×C4C22×D7911yescharacteristic
302C22×C4C22×D7911yescharacteristic
303C22×C4C22×D7911yescharacteristic
304C4⋊C4—3161no—
305C4⋊C4—3161no—
306C4⋊C4—794no—
307C22⋊C4—22no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—3161no—
311C22⋊C4—3161no—
312C22⋊C4—3161no—
313C22⋊C4—3161no—
314C22⋊C4—794no—
315C22⋊C4—794no—
316C22⋊C4—1582no—
317C22⋊C4—1582no—
318C22⋊C4—1582no—
319C42—3161no—
320C42—3161no—
321C42—3161no—
322C42—3161no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—792no—
336C23—1581no—
337C23—1581no—
338C23—1581no—
339C23—1581no—
340C23—1581no—
341C23—1581no—
342C23C2×C4×D7912yes—
343C23C2×C4×D7912yes—
344C23C23×D7911yescharacteristic
345D4—44no—
346D4—3164no—
347D4—3164no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—3164no—
363C2×C4—3164no—
364C2×C4—792no—
365C2×C4—792no—
366C2×C4—792no—
367C2×C4—792no—
368C2×C4—1581no—
369C2×C4—1581no—
370C2×C4—1581no—
371C2×C4—1581no—
372C2×C4—1581no—
373C2×C4—1581no—
374C2×C4—1581no—
375C2×C4—1581no—
376C2×C4—1581no—
377C2×C4—1581no—
378C2×C4—1581no—
379C2×C4—1581no—
380C2×C4—1581no—
381C2×C4—1581no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4C2×C4×D7912yes—
386C2×C4#1192962312yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—3161no—
402C22—3161no—
403C22—3161no—
404C22—3161no—
405C22—1582no—
406C22—1582no—
407C22—1582no—
408C22C22×C4×D7911yescharacteristic
409C22#41×D7911yescharacteristic
410C22C2×#1192962311yescharacteristic
411C22#1457920611yescharacteristic
412C22#1457920611yescharacteristic
413C22#1457920611yescharacteristic
414C22#1457920711yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—3161no—
421C4—3161no—
422C4—3161no—
423C4—1582no—
424C4—1582no—
425C4—1582no—
426C4—1582no—
427C2—42no—
428C2—42no—
429C2—3162no—
430C2C4×#1192962311yescharacteristic
431C2#1909903511yescharacteristic
432C2#1909903611yescharacteristic
433C2#1909914811yescharacteristic
434C2#1909914911yescharacteristic
435C2#1909916311yescharacteristic
436C2#1909916611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#386×C79C2
socle, cosocleC23×C79C24
prime radicalC2×#14579132C2
hypercenter#386D79
hypocenterC79#2333
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. #19098463C2semidirect
3. #19098463C2semidirect
4. #19098457C2semidirect
5. #19098451C2semidirect
6. #19098448C2semidirect
7. #19098446C2semidirect
8. #19098443C2semidirect
9. #19098442C2semidirect
10. #19098440C2semidirect
11. #19098425C2semidirect
12. C22⋊C4×Dic79C2semidirect
13. C4×C22⋊Dic79C2semidirect
14. #19098410C2semidirect
15. #386×C79C2semidirect
20. #14579132C4semidirect
57. C2×C22⋊D79C2×C4semidirect
58. C2×C22⋊D79C2×C4semidirect
71. C2×C4×D79C2×C4semidirect
72. C4⋊Dic79C2×C4semidirect
78. C22⋊Dic79C2×C4semidirect
79. C22⋊Dic79C2×C4semidirect
219. C79#2333semidirect
230. #386D79semidirect