Finite Group Databasebeta

← C2×#23773937 #35157900

Subgroups — C2×#23773937 #35157900

Order 20224.

1854 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099193C212yesmaximal
2#23773937C2116yesmaximal, direct product factor
3C2×#19098973C212yesmaximal, complemented
4C2×#19098970C212yesmaximal, complemented
5C2×#19098968C211yesmaximal, characteristic, complemented
6C2×#19098967C211yesmaximal, characteristic, complemented
7C2×#19098964C211yesmaximal, characteristic, complemented
8C2×#19098602C212yesmaximal
9C2×#19098600C211yesmaximal, characteristic
10C2×#107×D79C211yesmaximal, characteristic
11C2×#19098517C211yesmaximal, characteristic
12C2×#499×C79C211yesmaximal, characteristic, complemented
13C22×#11929607C2211yescharacteristic
14C22×C8×D79C2211yescharacteristic
15#19099193—28no—
16#19099193C22116yes—
17C2×#14579161C2212yes—
18C2×#14579160—22no—
19C2×#14579160C2212yes—
20C2×#14579152C2212yes—
21C2×#14579151—22no—
22C2×#14579141—22no—
23C2×#14579139—22no—
24C2×#14579119C2212yes—
25C2×#14579118C2211yescharacteristic
26C2×C4⋊C4×D79C2212yes—
27#19098973C22116yescomplemented
28#19098970C22116yescomplemented
29#19098968C2218yescomplemented
30#19098967C2218yescomplemented
31#19098964C2218yescomplemented
32#19098602C22116yes—
33#19098600C2218yes—
34C2×#14579095C2211yescharacteristic
35C2×#14579095C2211yescharacteristic
36C2×#14579095C2212yes—
37C2×#14579094C2212yes—
38C2×#14579094C2212yes—
39#107×D79C2218yes—
40C2×#14579092C2212yes—
41C2×#14579092C2212yes—
42#19098517C2218yes—
43C2×#14579072C2211yescharacteristic
44C2×#14579071C2211yescharacteristic
45C2×C8×Dic79C2211yescharacteristic
46C2×#125×C79C2212yes—
47#499×C79C2218yescomplemented
48C2×#107×C79C2211yescharacteristic
49C2×#107×C79C2211yescharacteristic
50C2×#106×C79C2212yes—
51C2×C4×C8×C79C2211yescharacteristic
52C22×Dic158—22no—
53C22×Dic158—22no—
54C22×C4×D79—22no—
55C22×C4×D79C2311yescharacteristic
56C2×#11929607Q818yescomplemented
57C2×#11929607C2314yes—
58C22×C79⋊C8C2311yescharacteristic
59C22×C79⋊C8C2311yescharacteristic
60C2×C8×D79Q818yescomplemented
61C2×C8×D79C2314yes—
62#14579161—24no—
63#14579161C2318yes—
64#14579160—216no—
65#14579160—24no—
66#14579160C2318yes—
67#14579152—24no—
68#14579152C2318yes—
69#14579151—216no—
70#14579141—216no—
71#14579139—216no—
72#14579119—24no—
73#14579119C2318yes—
74#14579118D414yes—
75#14579118C2314yes—
76C2×C4⋊Dic79—22no—
77C2×C4⋊Dic79—22no—
78C2×C4⋊Dic79C2312yes—
79C2×C4⋊Dic79C2312yes—
80C2×Dic79⋊C4—22no—
81C2×Dic79⋊C4—22no—
82C2×Dic79⋊C4—22no—
83C2×Dic79⋊C4D411yescharacteristic
84C2×Dic79⋊C4D411yescharacteristic
85C4⋊C4×D79—24no—
86C4⋊C4×D79C2318yes—
87C2×(C2×D79)⋊C4—22no—
88C2×(C2×D79)⋊C4D411yescharacteristic
89C2×(C2×D79)⋊C4D411yescharacteristic
90C2×C4×Dic79—22no—
91C2×C4×Dic79C2311yescharacteristic
92#14579095C2314yes—
93#14579095C2314yes—
94#14579095C2318yes—
95#14579094C2318yes—
96#14579094C2318yes—
97#14579092C2318yes—
98#14579092C2318yes—
99#14579072C2314yes—
100#14579071C2314yes—
101C8×Dic79C2314yes—
102C22×C8×C79C2311yescharacteristic
103C22×C8×C79C2311yescharacteristic
104#125×C79—24no—
105#125×C79C2318yes—
106C2×C4⋊C4×C79—22no—
107C2×C4⋊C4×C79—22no—
108C2×C4⋊C4×C79C2312yes—
109C2×C4⋊C4×C79C2312yes—
110C2×C42×C79C2311yescharacteristic
111#107×C79C2314yes—
112#107×C79C2314yes—
113#106×C79C2318yes—
114C4×C8×C79C2314yes—
115C23×D79C2×D411yescharacteristic
116C2×Dic158—28no—
117C2×Dic158—28no—
118C2×Dic158—84no—
119C2×Dic158—84no—
120C22×Dic79—22no—
121C22×Dic79—22no—
122C22×Dic79C2×D411yescharacteristic
123C22×Dic79C2×D411yescharacteristic
124C22×Dic79C2×D411yescharacteristic
125C2×C4×D79—28no—
126C2×C4×D79—84no—
127C2×C4×D79C2×D412yes—
128C2×C4×D79C2×Q814yes—
129C2×C4×D79C2×Q814yes—
130C2×C4×D79C2412yes—
131#11929607C2×Q8116yescomplemented
132C2×C79⋊C8C2×Q814yes—
133C2×C79⋊C8C2×Q814yes—
134C2×C79⋊C8C2412yes—
135C2×C79⋊C8C2412yes—
136C8×D79C2×Q8116yescomplemented
137C4⋊Dic79—28no—
138C4⋊Dic79—22no—
139C4⋊Dic79—28no—
140C4⋊Dic79—22no—
141C4⋊Dic79C2414yes—
142C4⋊Dic79C2414yes—
143Dic79⋊C4—28no—
144Dic79⋊C4—28no—
145Dic79⋊C4—28no—
146Dic79⋊C4C2×D414yes—
147Dic79⋊C4C2×D414yes—
148(C2×D79)⋊C4—28no—
149(C2×D79)⋊C4C2×D414yes—
150(C2×D79)⋊C4C2×D414yes—
151C4×Dic79—28no—
152C4×Dic79C2×D412yes—
153C4×Dic79C2412yes—
154C22×C4×C79—22no—
155C22×C4×C79—22no—
156C22×C4×C79C2×D411yescharacteristic
157C22×C4×C79C2×D411yescharacteristic
158C22×C4×C79C2411yescharacteristic
159C2×C8×C79C2×Q814yes—
160C2×C8×C79C2×Q814yes—
161C2×C8×C79C2412yes—
162C2×C8×C79C2412yes—
163C4⋊C4×C79—28no—
164C4⋊C4×C79—28no—
165C4⋊C4×C79—22no—
166C4⋊C4×C79—22no—
167C4⋊C4×C79C2414yes—
168C4⋊C4×C79C2414yes—
169C42×C79C2×D412yes—
170C42×C79C2412yes—
171C23×C79C22×D411yescharacteristic
172C22×D79—22no—
173C22×D79—22no—
174C22×D79C4⋊Q814yes—
175C22×D79C22×D412yes—
176C2×C4×C79—22no—
177C2×C4×C79—22no—
178C2×C4×C79—24no—
179C2×C4×C79—24no—
180C2×C4×C79—44no—
181C2×C4×C79—44no—
182C2×C4×C79C22×D412yes—
183C2×C4×C79C22×D412yes—
184C2×C4×C79C22×D411yescharacteristic
185C2×C4×C79C22×Q812yes—
186C2×C4×C79C22×Q812yes—
187C2×C4×C79C2511yescharacteristic
188C2×Dic79—22no—
189C2×Dic79—22no—
190C2×Dic79—24no—
191C2×Dic79—24no—
192C2×Dic79—44no—
193C2×Dic79—44no—
194C2×Dic79C4⋊Q814yes—
195C2×Dic79C22×D412yes—
196C2×Dic79C22×D412yes—
197C2×Dic79C22×D412yes—
198C4×D79—88no—
199C4×D79C4⋊Q818yes—
200C4×D79C22×Q814yes—
201C4×D79C22×Q814yes—
202Dic158—88no—
203Dic158—88no—
204C8×C79C22×Q814yes—
205C8×C79C22×Q814yes—
206C79⋊C8C22×Q814yes—
207C79⋊C8C22×Q814yes—
208C22×C79C2×C4⋊Q812yes—
209C22×C79#57612yes—
210C22×C79#57812yes—
211C22×C79C23×D411yescharacteristic
212C2×D79—28no—
213C2×D79—22no—
214C2×D79—22no—
215C2×D79C2×C4⋊Q814yes—
216C4×C79—22no—
217C4×C79—22no—
218C4×C79—44no—
219C4×C79—44no—
220C4×C79C2×C4⋊Q812yes—
221C4×C79C23×Q811yescharacteristic
222C4×C79C23×Q811yescharacteristic
223Dic79—22no—
224Dic79—22no—
225Dic79—44no—
226Dic79—44no—
227Dic79C2×C4⋊Q814yes—
228C2×#3164—791nomaximal, Sylow
229C2×C79#316414yescomplemented
230C2×C79C22×C4⋊Q811yescharacteristic
231C2×C79C2×#57611yescharacteristic
232C2×C79C2×#57811yescharacteristic
233D79—24no—
234C2×#544—792no—
235#3164—7916no—
236C2×#501—792no—
237C2×#501—792no—
238C2×#500—791no—
239C2×#500—791no—
240C2×#499—791no—
241C2×#499D7911yescharacteristic, complemented
242C2×#428—792no—
243C2×#427—791no—
244C22×#107—791no—
245C2×#405—791no—
246C79C2×#316411yescharacteristic, complemented, Sylow
247C22×M16—791no—
248C23×C8—791no—
249#544—7916no—
250#544—1588no—
251C2×C4⋊Q8—792no—
252C2×C4⋊Q8—792no—
253C2×C4⋊Q8—1582no—
254C2×#125—792no—
255C2×#125—1582no—
256C2×#125C2×D7912yes—
257C2×C22⋊Q8—1582no—
258C2×C22⋊Q8—1582no—
259C2×#117—791no—
260C2×#117—792no—
261C22×C4⋊C4—792no—
262#501—7916no—
263#501—7916no—
264#500—798no—
265#500—798no—
266#499—798no—
267#499C2×D7918yescomplemented
268#428—7916no—
269#427—798no—
270C2×#107—791no—
271C2×#107—791no—
272C2×#107—792no—
273C2×#107—792no—
274C2×#107—792no—
275C2×#107—798no—
276C2×#107C2×D7911yescharacteristic
277C2×#107C2×D7911yescharacteristic
278C2×#106—792no—
279C2×#106—792no—
280C2×#106C2×D7912yes—
281#405—798no—
282C2×#97—791no—
283C2×#97—791no—
284C2×C4×C8—791no—
285C2×C4×C8C2×D7911yescharacteristic
286C22×Q8—1582no—
287C22×Q8—1582no—
288C23×C4—791no—
289C23×C4—1582no—
290C2×M16—798no—
291C2×M16—794no—
292C22×C8—791no—
293C22×C8—791no—
294C22×C8—798no—
295C22×C8—794no—
296C22×C8C22×D7911yescharacteristic
297C22×C8C22×D7911yescharacteristic
298C4⋊Q8—798no—
299C4⋊Q8—798no—
300C4⋊Q8—1584no—
301C4⋊Q8—15816no—
302C4⋊Q8—1584no—
303#125—24no—
304#125—798no—
305#125—1584no—
306#125—15816no—
307#125C22×D7918yes—
308C22⋊Q8—15816no—
309C22⋊Q8—15816no—
310#117—794no—
311#117—794no—
312#117—798no—
313#117—1584no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—791no—
317C2×C4⋊C4—791no—
318C2×C4⋊C4—792no—
319C2×C4⋊C4—792no—
320C2×C4⋊C4—798no—
321C2×C4⋊C4—1584no—
322C2×C4⋊C4—1582no—
323C2×C4⋊C4—1582no—
324C2×C4⋊C4—1582no—
325C2×C4⋊C4—1582no—
326C2×C4⋊C4—1582no—
327C2×C4⋊C4C22×D7912yes—
328C2×C4⋊C4C22×D7912yes—
329C2×C22⋊C4—791no—
330C2×C22⋊C4—791no—
331C2×C22⋊C4—1582no—
332C2×C42—791no—
333C2×C42—1582no—
334C2×C42C22×D7911yescharacteristic
335#107—794no—
336#107—794no—
337#107—798no—
338#107—798no—
339#107—798no—
340#107C22×D7914yes—
341#107C22×D7914yes—
342#106—798no—
343#106—798no—
344#106C22×D7918yes—
345#97—794no—
346#97—794no—
347C4×C8—794no—
348C4×C8C22×D7914yes—
349C24—791no—
350C2×Q8—6324no—
351C2×Q8—6324no—
352C2×Q8—1588no—
353C2×Q8—1588no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—791no—
357C22×C4—794no—
358C22×C4—794no—
359C22×C4—792no—
360C22×C4—792no—
361C22×C4—791no—
362C22×C4—791no—
363C22×C4—6324no—
364C22×C4—1588no—
365C22×C4—1582no—
366C22×C4—1582no—
367C22×C4D4×D7911yescharacteristic
368C22×C4D4×D7911yescharacteristic
369C22×C4C23×D7911yescharacteristic
370M16—7916no—
371C2×C8—794no—
372C2×C8—794no—
373C2×C8—792no—
374C2×C8—792no—
375C2×C8—7916no—
376C2×C8Q8×D7914yes—
377C2×C8Q8×D7914yes—
378C2×C8C23×D7912yes—
379C2×C8C23×D7912yes—
380C4⋊C4—28no—
381C4⋊C4—28no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—794no—
385C4⋊C4—794no—
386C4⋊C4—794no—
387C4⋊C4—794no—
388C4⋊C4—1588no—
389C4⋊C4—1588no—
390C4⋊C4—1588no—
391C4⋊C4—1588no—
392C4⋊C4—1582no—
393C4⋊C4—1582no—
394C4⋊C4—1588no—
395C4⋊C4C23×D7914yes—
396C4⋊C4C23×D7914yes—
397C22⋊C4—794no—
398C22⋊C4—794no—
399C22⋊C4—1588no—
400C42—792no—
401C42—792no—
402C42—1588no—
403C42D4×D7912yes—
404C42C23×D7912yes—
405C23—794no—
406C23—792no—
407C23—1582no—
408C23—1582no—
409C23C2×D4×D7911yescharacteristic
410Q8—6328no—
411Q8—6328no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—3164no—
419C2×C4—3164no—
420C2×C4—794no—
421C2×C4—792no—
422C2×C4—798no—
423C2×C4—794no—
424C2×C4—794no—
425C2×C4—792no—
426C2×C4—792no—
427C2×C4—6328no—
428C2×C4—1584no—
429C2×C4—1584no—
430C2×C4—1582no—
431C2×C4—1582no—
432C2×C4C2×D4×D7912yes—
433C2×C4C2×D4×D7912yes—
434C2×C4C2×D4×D7911yescharacteristic
435C2×C4C2×Q8×D7912yes—
436C2×C4C2×Q8×D7912yes—
437C2×C4C24×D7911yescharacteristic
438C8—794no—
439C8—794no—
440C8C2×Q8×D7914yes—
441C8C2×Q8×D7914yes—
442C22—794no—
443C22—1582no—
444C22—1582no—
445C22—1588no—
446C22C4⋊Q8×D7912yes—
447C22#1909936512yes—
448C22#1909937712yes—
449C22C22×D4×D7911yescharacteristic
450C4—22no—
451C4—22no—
452C4—44no—
453C4—44no—
454C4—3164no—
455C4—3164no—
456C4—794no—
457C4—1582no—
458C4—1582no—
459C4C4⋊Q8×D7912yes—
460C4C22×Q8×D7911yescharacteristic
461C4C22×Q8×D7911yescharacteristic
462C2—1584no—
463C2#2377393714yesdirect product factor
464C2C2×C4⋊Q8×D7911yescharacteristic
465C2C2×#1909936511yescharacteristic
466C2C2×#1909937711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#499×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×#499D79
hypocenterC79C2×#3164
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
2. #23773937C2direct (N × H)
3. C2×#19098973C2semidirect
4. C2×#19098970C2semidirect
5. C2×#19098968C2semidirect
6. C2×#19098967C2semidirect
7. C2×#19098964C2semidirect
12. C2×#499×C79C2semidirect
27. #19098973C22semidirect
28. #19098970C22semidirect
29. #19098968C22semidirect
30. #19098967C22semidirect
31. #19098964C22semidirect
47. #499×C79C22semidirect
56. C2×#11929607Q8semidirect
60. C2×C8×D79Q8semidirect
131. #11929607C2×Q8semidirect
136. C8×D79C2×Q8semidirect
229. C2×C79#3164semidirect
241. C2×#499D79semidirect
246. C79C2×#3164semidirect
267. #499C2×D79semidirect
463. C2#23773937direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991932
#237739372
C2×#190989732
C2×#190989702
C2×#190989682
C2×#190989672
C2×#190989642
C2×#190986022
C2×#190986002
C2×#107×D792
C2×#190985172
C2×#499×C792
C2×#316479