Finite Group Databasebeta

← #23769802

Subgroups — #23769802

Order 10112.

562 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579148C211yesmaximal, characteristic, complemented
2#19098491C211yesmaximal, characteristic, complemented
3#19098483C211yesmaximal, characteristic, complemented
4#19098477C211yesmaximal, characteristic, complemented
5#19098477C211yesmaximal, characteristic, complemented
6#19098477C211yesmaximal, characteristic, complemented
7#19098475C211yesmaximal, characteristic, complemented
8#19098451C211yesmaximal, characteristic, complemented
9#19098444C211yesmaximal, characteristic, complemented
10#19098443C211yesmaximal, characteristic, complemented
11#19098443C211yesmaximal, characteristic, complemented
12#19098436C211yesmaximal, characteristic, complemented
13#19098426C211yesmaximal, characteristic, complemented
14#19098421C211yesmaximal, characteristic, complemented
15C2×#121×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C23×Dic79C2211yescharacteristic
18#14579148—24no—
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×C22⋊Dic79C2211yescharacteristic
24C2×C22⋊Dic79C2211yescharacteristic
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
30C2×C22⋊Dic79C2211yescharacteristic
31C2×C22⋊Dic79C2211yescharacteristic
32C2×C22⋊Dic79C2211yescharacteristic
33C2×C22⋊Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C22×D4×C79C2211yescharacteristic
46C22×D4×C79C2211yescharacteristic
47C22×D4×C79C2211yescharacteristic
48C23×C4×C79C2211yescharacteristic
49#121×C79—24no—
50C2×C4⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52C2×C22⋊C4×C79C2211yescharacteristic
53C2×Dic158—22no—
54C2×Dic158—41no—
55C2×Dic158—41no—
56C22×Dic79—22no—
57C22×Dic79—41no—
58C22×Dic79—41no—
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67Dic79⋊C4—22no—
68Dic79⋊C4—41no—
69Dic79⋊C4—41no—
70Dic79⋊C4—41no—
71C22⋊Dic79—22no—
72C22⋊Dic79—22no—
73C22⋊Dic79—22no—
74C22⋊Dic79—22no—
75C22⋊Dic79—22no—
76C22⋊Dic79—22no—
77C22⋊Dic79—41no—
78C22⋊Dic79—41no—
79C22⋊Dic79—41no—
80C22⋊Dic79—41no—
81C22⋊Dic79—41no—
82C4×Dic79—22no—
83C24×C79C2311yescharacteristic
84C24×C79C2311yescharacteristic
85C24×C79C2311yescharacteristic
86C2×D4×C79—22no—
87C2×D4×C79—22no—
88C2×D4×C79—22no—
89C2×D4×C79—41no—
90C2×D4×C79—41no—
91C2×D4×C79—41no—
92C2×D4×C79—41no—
93C2×D4×C79—41no—
94C2×D4×C79D414yes—
95C22×C4×C79—22no—
96C22×C4×C79—22no—
97C22×C4×C79—41no—
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102C4⋊C4×C79—22no—
103C22⋊C4×C79—22no—
104C22⋊C4×C79—22no—
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×C79—21no—
117C23×C79—21no—
118C23×C79—21no—
119C23×C79—21no—
120C23×C79—21no—
121C23×C79—21no—
122C23×C79—21no—
123C23×C79—21no—
124C23×C79C2×D412yes—
125C23×C79C2×D412yes—
126C23×C79C2411yescharacteristic
127D4×C79—44no—
128D4×C79—44no—
129D4×C79—44no—
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×C79C2×D412yes—
142C2×C4×C79#4112yes—
143C2×Dic79—21no—
144C2×Dic79—21no—
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—21no—
163C2×Dic79—21no—
164C2×Dic79—21no—
165C2×Dic79—21no—
166C2×Dic79—44no—
167C2×Dic79#4112yes—
168Dic158—44no—
169C22×C79—22no—
170C22×C79—22no—
171C22×C79—22no—
172C22×C79—22no—
173C22×C79—22no—
174C22×C79—22no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79—41no—
183C22×C79—41no—
184C22×C79—41no—
185C22×C79—41no—
186C22×C79—41no—
187C22×C79—41no—
188C22×C79—41no—
189C22×C79—41no—
190C22×C79C22×D411yescharacteristic
191C22×C79C2×#4111yescharacteristic
192C22×C79C2×#4111yescharacteristic
193C22×C79H(5,𝔽2)11yescharacteristic
194C22×C79H(5,𝔽2)11yescharacteristic
195C22×C79H(5,𝔽2)11yescharacteristic
196C22×C792−1+411yescharacteristic
197C4×C79—22no—
198C4×C79—22no—
199C4×C79—41no—
200C4×C79—41no—
201Dic79—22no—
202Dic79—41no—
203Dic79—41no—
204Dic79—41no—
205Dic79—41no—
206Dic79—41no—
207Dic79—41no—
208Dic79—41no—
209C2×C79—42no—
210C2×C79—42no—
211C2×C79—81no—
212C2×C79#53411yescharacteristic
213C2×C79#53811yescharacteristic
214C2×C79#54211yescharacteristic
215C2×C79#54611yescharacteristic
216C2×C79#54711yescharacteristic
217C2×C79#55511yescharacteristic
218C2×C79#56211yescharacteristic
219#2686—791nomaximal, Sylow
220C79#268611yescharacteristic, complemented, Sylow
221C2×#124—791no—
222C2×#121D7911yescharacteristic
223#397—791no—
224#395—791no—
225#394—791no—
226#394—791no—
227#394—791no—
228#393—791no—
229#388—791no—
230#387—791no—
231#386—791no—
232#386—791no—
233#385—791no—
234#381—791no—
235#380—791no—
236C22×Q8—791no—
237C22×D4C2×D7911yescharacteristic
238C22×D4C2×D7911yescharacteristic
239C22×D4C2×D7911yescharacteristic
240C23×C4—791no—
241C23×C4C2×D7911yescharacteristic
242#124—1584no—
243#121—24no—
244C2×C4⋊C4—791no—
245C2×C4⋊C4—791no—
246C2×C4⋊C4—791no—
247C2×C4⋊C4—791no—
248C2×C4⋊C4C2×D7911yescharacteristic
249C2×C22⋊C4—791no—
250C2×C22⋊C4—791no—
251C2×C22⋊C4—791no—
252C2×C22⋊C4—791no—
253C2×C22⋊C4—791no—
254C2×C22⋊C4—791no—
255C2×C22⋊C4—791no—
256C2×C22⋊C4—791no—
257C2×C22⋊C4—791no—
258C2×C22⋊C4—791no—
259C2×C22⋊C4—791no—
260C2×C22⋊C4C2×D7911yescharacteristic
261C2×C22⋊C4C2×D7911yescharacteristic
262C2×C42—791no—
263#95—791no—
264#95—791no—
265#95—791no—
266#95—791no—
267#95—791no—
268#95—791no—
269#95—791no—
270#95—791no—
271#95—791no—
272#95—791no—
273C24C22×D7911yescharacteristic
274C24C22×D7911yescharacteristic
275C24C22×D7911yescharacteristic
276C2×Q8—3161no—
277C2×Q8—3161no—
278C2×Q8—1582no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4C22⋊D7914yes—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—3161no—
292C22×C4—3161no—
293C22×C4—791no—
294C22×C4—791no—
295C22×C4—791no—
296C22×C4—791no—
297C22×C4—791no—
298C22×C4—791no—
299C22×C4—791no—
300C22×C4—791no—
301C22×C4—1582no—
302C22×C4C22×D7911yescharacteristic
303C22×C4C22×D7911yescharacteristic
304C22×C4C22×D7911yescharacteristic
305C22×C4C22×D7911yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—3161no—
308C4⋊C4—3161no—
309C4⋊C4—3161no—
310C4⋊C4—1582no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—3161no—
314C22⋊C4—3161no—
315C22⋊C4—3161no—
316C22⋊C4—3161no—
317C22⋊C4—3161no—
318C22⋊C4—1582no—
319C22⋊C4—1582no—
320C22⋊C4—1582no—
321C22⋊C4—1582no—
322C22⋊C4—1582no—
323C22⋊C4—1582no—
324C42—1582no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23C2×C22⋊D7912yes—
345C23C2×C22⋊D7912yes—
346C23C23×D7911yescharacteristic
347Q8—3164no—
348D4—44no—
349D4—44no—
350D4—44no—
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—792no—
364C2×C4—1581no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4—1581no—
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×C4—1581no—
386C2×C4—1581no—
387C2×C4C2×C22⋊D7912yes—
388C2×C4#1192962312yes—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22C22×C22⋊D7911yescharacteristic
411C22#41×D7911yescharacteristic
412C22C2×#1192962311yescharacteristic
413C22#1457920611yescharacteristic
414C22#1457920611yescharacteristic
415C22#1457920611yescharacteristic
416C22#1457920811yescharacteristic
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—3161no—
422C4—3161no—
423C4—3161no—
424C4—3161no—
425C4—3161no—
426C4—3161no—
427C4—3161no—
428C4—1582no—
429C2—42no—
430C2—42no—
431C2—81no—
432C2#1909912211yescharacteristic
433C2#1909914511yescharacteristic
434C2#1909918011yescharacteristic
435C2#1909920711yescharacteristic
436C2#1909921211yescharacteristic
437C2#1909927711yescharacteristic
438C2#1909930811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting, prime radicalC2×#121×C79C2
hypercenterC2×#121D79
hypocenterC79#2686
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14579148C2semidirect
2. #19098491C2semidirect
3. #19098483C2semidirect
4. #19098477C2semidirect
5. #19098477C2semidirect
6. #19098477C2semidirect
7. #19098475C2semidirect
8. #19098451C2semidirect
9. #19098444C2semidirect
10. #19098443C2semidirect
11. #19098443C2semidirect
12. #19098436C2semidirect
13. #19098426C2semidirect
14. #19098421C2semidirect
220. C79#2686semidirect