Finite Group Databasebeta

← #23770139

Subgroups — #23770139

Order 10112.

548 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×#14579147C211yesmaximal, characteristic, complemented
2C2×#14579143C211yesmaximal, characteristic, complemented
3#19098499C211yesmaximal, characteristic, complemented
4#19098491C211yesmaximal, characteristic, complemented
5#19098478C211yesmaximal, characteristic, complemented
6#19098477C211yesmaximal, characteristic, complemented
7#19098475C211yesmaximal, characteristic, complemented
8#19098471C211yesmaximal, characteristic
9#19098469C211yesmaximal, characteristic, complemented
10#19098458C211yesmaximal, characteristic, complemented
11#19098457C211yesmaximal, characteristic, complemented
12#19098454C211yesmaximal, characteristic, complemented
13#19098439C211yesmaximal, characteristic, complemented
14#19098434C211yesmaximal, characteristic, complemented
15#390×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C22×C22⋊D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579147—24no—
21#14579143—24no—
22C2×C4⋊Dic79C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
30C2×C22⋊Dic79C2211yescharacteristic
31C2×C22⋊Dic79C2211yescharacteristic
32C2×C22⋊Dic79C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×(C2×D79)⋊C4C2211yescharacteristic
37C2×C4×Dic79C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C22×D4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C22⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52C2×C42×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C2×Dic158—22no—
55C2×Dic158—22no—
56C2×Dic158—41no—
57C2×C22⋊D79—22no—
58C2×C22⋊D79—22no—
59C2×C22⋊D79—22no—
60C2×C22⋊D79—41no—
61C2×C22⋊D79—41no—
62C2×C22⋊D79—41no—
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C2×C4×D79—22no—
71C2×C4×D79—41no—
72C2×C4×D79—41no—
73C4⋊Dic79—22no—
74Dic79⋊C4—22no—
75Dic79⋊C4—22no—
76Dic79⋊C4—41no—
77Dic79⋊C4—41no—
78C22⋊Dic79—22no—
79C22⋊Dic79—22no—
80C22⋊Dic79—22no—
81C22⋊Dic79—41no—
82C22⋊Dic79—41no—
83C22⋊Dic79—41no—
84(C2×D79)⋊C4—22no—
85(C2×D79)⋊C4—22no—
86(C2×D79)⋊C4—41no—
87(C2×D79)⋊C4D414yescomplemented
88C4×Dic79—22no—
89C24×C79C2311yescharacteristic
90C24×C79C2311yescharacteristic
91C2×D4×C79—22no—
92C2×D4×C79—41no—
93C2×D4×C79—41no—
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C4⋊C4×C79—41no—
100C22⋊C4×C79—22no—
101C22⋊C4×C79—22no—
102C22⋊C4×C79—41no—
103C22⋊C4×C79—41no—
104C42×C79—41no—
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×C79C2411yescharacteristic
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—21no—
123C22×D79—21no—
124C22×D79—21no—
125C22×D79—21no—
126C22×D79C2×D412yes—
127D4×C79—44no—
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—21no—
141C2×C4×C79C2×D412yes—
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—21no—
163C2×Dic79—21no—
164C2×Dic79C2×D412yes—
165C2×Dic79#4112yes—
166C4×D79—44no—
167Dic158—44no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79—41no—
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×C79C22×D411yescharacteristic
183C22×C79C2×#4111yescharacteristic
184C22×C79C2×#4111yescharacteristic
185C22×C79H(5,𝔽2)11yescharacteristic
186C22×C79H(5,𝔽2)11yescharacteristic
187C22×C79H(5,𝔽2)11yescharacteristic
188C22×C792−1+411yescharacteristic
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—41no—
204Dic79—41no—
205Dic79—41no—
206Dic79—41no—
207Dic79—41no—
208C2×C79—81no—
209C2×C79—81no—
210C2×C79#53511yescharacteristic
211C2×C79#53811yescharacteristic
212C2×C79#54211yescharacteristic
213C2×C79#54611yescharacteristic
214C2×C79#54711yescharacteristic
215C2×C79#55911yescharacteristic
216C2×C79#56211yescharacteristic
217D79—42no—
218#2710—791nomaximal, Sylow
219C79#271011yescharacteristic, complemented, Sylow
220C2×#124—791no—
221C2×#123—791no—
222#399—791no—
223#397—791no—
224#394—791no—
225#394—791no—
226#393—791no—
227#392—791no—
228#391—791no—
229#390D7911yescharacteristic, complemented
230#389—791no—
231#388—791no—
232#388—791no—
233#386—791no—
234#385—791no—
235C22×Q8—791no—
236C22×D4—791no—
237C22×D4—791no—
238C22×D4C2×D7911yescharacteristic
239C23×C4—791no—
240#124—1584no—
241#123—1584no—
242C2×C4⋊C4—791no—
243C2×C4⋊C4—791no—
244C2×C4⋊C4—791no—
245C2×C4⋊C4—791no—
246C2×C4⋊C4—791no—
247C2×C4⋊C4C2×D7911yescharacteristic
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⋊C4—791no—
255C2×C22⋊C4—791no—
256C2×C22⋊C4—791no—
257C2×C22⋊C4—791no—
258C2×C22⋊C4C2×D7911yescharacteristic
259C2×C22⋊C4C2×D7911yescharacteristic
260C2×C22⋊C4C2×D7911yescharacteristic
261C2×C22⋊C4C2×D7911yescharacteristic
262C2×C42—791no—
263C2×C42C2×D7911yescharacteristic
264#95—791no—
265#95—791no—
266#95—791no—
267#95—791no—
268#95—791no—
269#95—791no—
270#95—791no—
271#95—791no—
272C24—791no—
273C24C22×D7911yescharacteristic
274C24C22×D7911yescharacteristic
275C2×Q8—3161no—
276C2×Q8—1582no—
277C2×Q8—1582no—
278C2×D4—22no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—3161no—
282C2×D4—3161no—
283C2×D4—3161no—
284C2×D4—1582no—
285C2×D4—1582no—
286C2×D4—1582no—
287C22×C4—3161no—
288C22×C4—3161no—
289C22×C4—791no—
290C22×C4—791no—
291C22×C4—791no—
292C22×C4—791no—
293C22×C4—791no—
294C22×C4—791no—
295C22×C4—791no—
296C22×C4—1582no—
297C22×C4C22×D7911yescharacteristic
298C22×C4C22×D7911yescharacteristic
299C22×C4C22×D7911yescharacteristic
300C22×C4C22×D7911yescharacteristic
301C22×C4C22×D7911yescharacteristic
302C4⋊C4—41no—
303C4⋊C4—3161no—
304C4⋊C4—3161no—
305C4⋊C4—1582no—
306C4⋊C4—1582no—
307C4⋊C4—1582no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—3161no—
313C22⋊C4—3161no—
314C22⋊C4—3161no—
315C22⋊C4—3161no—
316C22⋊C4—794no—
317C22⋊C4—1582no—
318C22⋊C4—1582no—
319C22⋊C4—1582no—
320C22⋊C4—1582no—
321C22⋊C4—1582no—
322C42—41no—
323C42—1582no—
324C23—21no—
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—792no—
339C23—1581no—
340C23—1581no—
341C23—1581no—
342C23—1581no—
343C23—1581no—
344C23—1581no—
345C23C23×D7911yescharacteristic
346Q8—3164no—
347D4—44no—
348D4—3164no—
349D4—3164no—
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—21no—
362C2×C4—21no—
363C2×C4—3164no—
364C2×C4—792no—
365C2×C4—792no—
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×C4D4×D7912yes—
386C2×C4#1192962412yes—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
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—
408C22C2×D4×D7911yescharacteristic
409C22#41×D7911yescharacteristic
410C22C2×#1192962411yescharacteristic
411C22#1457920611yescharacteristic
412C22#1457920611yescharacteristic
413C22#1457920611yescharacteristic
414C22#1457920811yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—3161no—
421C4—3161no—
422C4—3161no—
423C4—3161no—
424C4—3161no—
425C4—1582no—
426C4—1582no—
427C2—81no—
428C2—81no—
429C2—3162no—
430C2#1909912611yescharacteristic
431C2#1909915111yescharacteristic
432C2#1909917711yescharacteristic
433C2#1909920211yescharacteristic
434C2#1909921811yescharacteristic
435C2#1909929611yescharacteristic
436C2#1909930811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#390×C79C2
prime radical#19098471C2
hypercenter#390D79
hypocenterC79#2710
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14579147C2semidirect
2. C2×#14579143C2semidirect
3. #19098499C2semidirect
4. #19098491C2semidirect
5. #19098478C2semidirect
6. #19098477C2semidirect
7. #19098475C2semidirect
9. #19098469C2semidirect
10. #19098458C2semidirect
11. #19098457C2semidirect
12. #19098454C2semidirect
13. #19098439C2semidirect
14. #19098434C2semidirect
15. #390×C79C2semidirect
87. (C2×D79)⋊C4D4semidirect
219. C79#2710semidirect
229. #390D79semidirect