Finite Group Databasebeta

← C2×#23762734 #34269439

Subgroups — C2×#23762734 #34269439

Order 20224.

894 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×#19098973C211yesmaximal, characteristic, complemented
2C2×#19098933C211yesmaximal, characteristic, complemented
3C2×#19098922C211yesmaximal, characteristic
4#23762734C218yesmaximal, direct product factor
5C2×#19098305C211yesmaximal, characteristic, complemented
6C2×#19098305C211yesmaximal, characteristic, complemented
7C2×#19098303C211yesmaximal, characteristic
8C2×#563×C79C211yesmaximal, characteristic
9C2×#14579161C2211yescharacteristic
10#19098973—22no—
11#19098973C2214yescomplemented
12#19098933—22no—
13#19098933C2214yescomplemented
14#19098922—22no—
15#19098922C2214yes—
16C2×#14579094—21no—
17C2×#14579092—21no—
18C2×#14579085—21no—
19C2×#14579084—21no—
20C2×#14579084—21no—
21C2×#14579082—21no—
22C2×#14579072C2211yescharacteristic
23C2×#14579072C2211yescharacteristic
24C2×#14579072C2211yescharacteristic
25#19098305C2214yescomplemented
26#19098305C2214yescomplemented
27#19098303C2214yes—
28#563×C79—22no—
29#563×C79—22no—
30#563×C79—22no—
31#563×C79C2214yes—
32C2×C4⋊Q8×C79—21no—
33C2×#126×C79—21no—
34C2×#126×C79—21no—
35C2×#125×C79C2211yescharacteristic
36C2×#125×C79C2211yescharacteristic
37C2×#124×C79C2211yescharacteristic
38C2×#123×C79—21no—
39C2×C22⋊Q8×C79—21no—
40C2×C22⋊Q8×C79—21no—
41C22×Dic158—21no—
42C22×C79⋊C8—21no—
43C22×C79⋊C8—21no—
44C22×C79⋊C8—21no—
45#14579161—21no—
46#14579161—21no—
47#14579161—21no—
48#14579161C2312yes—
49C2×C4⋊Dic79—21no—
50C2×C4⋊Dic79—21no—
51#14579094—24no—
52#14579092—24no—
53#14579085—24no—
54#14579084—24no—
55#14579084—24no—
56#14579082—24no—
57#14579072—21no—
58#14579072—21no—
59#14579072—21no—
60#14579072C2312yes—
61#14579072C2312yes—
62#14579072C2312yes—
63C22×Q8×C79—21no—
64C22×Q8×C79D411yescharacteristic
65C22×D4×C79D411yescharacteristic
66C23×C4×C79—21no—
67C4⋊Q8×C79—24no—
68C4⋊Q8×C79—24no—
69#126×C79—24no—
70#126×C79—24no—
71#126×C79—24no—
72#126×C79—24no—
73#125×C79—21no—
74#125×C79—21no—
75#125×C79—21no—
76#125×C79—21no—
77#125×C79D412yes—
78#125×C79D412yes—
79#125×C79C2312yes—
80#125×C79C2312yes—
81#124×C79—21no—
82#124×C79—21no—
83#124×C79D412yes—
84#124×C79C2312yes—
85#123×C79—24no—
86#123×C79—24no—
87C22⋊Q8×C79—24no—
88C22⋊Q8×C79—24no—
89C22⋊Q8×C79—24no—
90C22⋊Q8×C79—24no—
91C2×C4⋊C4×C79—21no—
92C2×C4⋊C4×C79—21no—
93C2×C4⋊C4×C79—21no—
94C2×C4⋊C4×C79—21no—
95C2×C4⋊C4×C79—21no—
96C2×C4⋊C4×C79—21no—
97C2×C4⋊C4×C79D411yescharacteristic
98C2×C4⋊C4×C79D411yescharacteristic
99C2×C4⋊C4×C79D411yescharacteristic
100C2×C4⋊C4×C79D411yescharacteristic
101C2×C22⋊C4×C79—21no—
102C2×C22⋊C4×C79—21no—
103C2×C22⋊C4×C79—21no—
104C2×C22⋊C4×C79—21no—
105C2×C22⋊C4×C79—21no—
106C2×C42×C79—21no—
107C2×C42×C79C2311yescharacteristic
108C2×Dic158—22no—
109C2×Dic158—44no—
110C2×Dic158—41no—
111C22×Dic79—41no—
112C2×C79⋊C8—24no—
113C2×C79⋊C8—22no—
114C2×C79⋊C8—22no—
115C2×C79⋊C8—22no—
116C2×C79⋊C8—42no—
117C2×C79⋊C8—42no—
118C4⋊Dic79—22no—
119C4⋊Dic79—22no—
120C4⋊Dic79—41no—
121C4⋊Dic79—41no—
122C24×C79—21no—
123C2×Q8×C79—24no—
124C2×Q8×C79—21no—
125C2×Q8×C79—42no—
126C2×Q8×C79—82no—
127C2×Q8×C79C2×D412yes—
128C2×D4×C79—21no—
129C2×D4×C79—42no—
130C2×D4×C79C2×D412yes—
131C22×C4×C79—21no—
132C22×C4×C79—21no—
133C22×C4×C79—21no—
134C22×C4×C79—21no—
135C22×C4×C79—21no—
136C22×C4×C79—24no—
137C22×C4×C79—82no—
138C22×C4×C79C2×D411yescharacteristic
139C22×C4×C79C2×D411yescharacteristic
140C22×C4×C79C2×D411yescharacteristic
141C4⋊C4×C79—24no—
142C4⋊C4×C79—24no—
143C4⋊C4×C79—22no—
144C4⋊C4×C79—22no—
145C4⋊C4×C79—22no—
146C4⋊C4×C79—22no—
147C4⋊C4×C79—21no—
148C4⋊C4×C79—21no—
149C4⋊C4×C79—21no—
150C4⋊C4×C79—21no—
151C4⋊C4×C79—22no—
152C4⋊C4×C79—22no—
153C4⋊C4×C79—22no—
154C4⋊C4×C79—22no—
155C4⋊C4×C79C2×D412yes—
156C4⋊C4×C79C2×D412yes—
157C4⋊C4×C79C2×D412yes—
158C4⋊C4×C79C2×D412yes—
159C22⋊C4×C79—24no—
160C22⋊C4×C79—24no—
161C22⋊C4×C79—24no—
162C22⋊C4×C79—22no—
163C22⋊C4×C79—22no—
164C22⋊C4×C79—22no—
165C22⋊C4×C79—22no—
166C42×C79—24no—
167C42×C79C2×D411yescharacteristic
168C42×C79C2×D411yescharacteristic
169C42×C79C2×D411yescharacteristic
170C42×C79C2411yescharacteristic
171C23×C79—22no—
172C23×C79—42no—
173C23×C79—42no—
174C23×C79—42no—
175C23×C79#12011yescharacteristic
176Q8×C79—42no—
177Q8×C79—81no—
178Q8×C79—84no—
179D4×C79—42no—
180D4×C79—81no—
181C2×C4×C79—22no—
182C2×C4×C79—22no—
183C2×C4×C79—22no—
184C2×C4×C79—22no—
185C2×C4×C79—22no—
186C2×C4×C79—22no—
187C2×C4×C79—22no—
188C2×C4×C79—22no—
189C2×C4×C79—42no—
190C2×C4×C79—42no—
191C2×C4×C79—42no—
192C2×C4×C79—42no—
193C2×C4×C79—42no—
194C2×C4×C79—84no—
195C2×C4×C79#12011yescharacteristic
196C2×C4×C79#12011yescharacteristic
197C2×C4×C79#12011yescharacteristic
198C2×C4×C79C22×D411yescharacteristic
199C2×C4×C79C22×D411yescharacteristic
200C2×C4×C79C22×D411yescharacteristic
201C2×Dic79—42no—
202C2×Dic79—82no—
203Dic158—44no—
204Dic158—82no—
205C79⋊C8—24no—
206C79⋊C8—42no—
207C79⋊C8—42no—
208C22×C79—42no—
209C22×C79—42no—
210C22×C79—42no—
211C22×C79—84no—
212C22×C79#45412yes—
213C22×C79#45512yes—
214C22×C79#45612yes—
215C22×C79C2×#12011yescharacteristic
216C4×C79—21no—
217C4×C79—21no—
218C4×C79—21no—
219C4×C79—21no—
220C4×C79—21no—
221C4×C79—21no—
222C4×C79—42no—
223C4×C79—42no—
224C4×C79—42no—
225C4×C79—42no—
226C4×C79—42no—
227Dic79—82no—
228C2×#1664—791nomaximal, Sylow
229C2×C79—82no—
230C2×C79#166414yescomplemented
231C2×C79C2×#45511yescharacteristic
232C2×C79C2×#45411yescharacteristic
233C2×C79C2×#45611yescharacteristic
234C2×#563D7911yescharacteristic
235C2×#501—791no—
236C2×#491—791no—
237C2×#489—791no—
238#1664—798no—
239C2×#330—791no—
240C2×#330—791no—
241C2×#329—791no—
242C79C2×#166411yescharacteristic, complemented, Sylow
243#563—22no—
244#563—22no—
245#563—22no—
246#563C2×D7914yes—
247C2×C4⋊Q8—21no—
248C2×C4⋊Q8—791no—
249C2×#126—21no—
250C2×#126—21no—
251C2×#125C2×D7911yescharacteristic
252C2×#125C2×D7911yescharacteristic
253C2×#124C2×D7911yescharacteristic
254C2×#123—21no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8—21no—
257#501—794no—
258#501—1582no—
259#491—794no—
260#491—1582no—
261#489—794no—
262#489—1582no—
263C2×#107—1581no—
264C2×#106—1581no—
265C2×#103—1581no—
266C2×#103—1581no—
267C2×#103—1581no—
268C2×#102—1581no—
269C2×#97—791no—
270C2×#97—791no—
271C2×#97—791no—
272#330—794no—
273#330—794no—
274#329—794no—
275C22×Q8—21no—
276C22×Q8—1581no—
277C22×Q8C22⋊D7911yescharacteristic
278C22×D4C22⋊D7911yescharacteristic
279C23×C4—21no—
280C22×C8—1581no—
281C22×C8—1581no—
282C22×C8—1581no—
283C4⋊Q8—24no—
284C4⋊Q8—24no—
285C4⋊Q8—792no—
286C4⋊Q8—1581no—
287C4⋊Q8—1581no—
288C4⋊Q8—1581no—
289#126—24no—
290#126—24no—
291#126—24no—
292#126—24no—
293#125—21no—
294#125—21no—
295#125—21no—
296#125—21no—
297#125C22⋊D7912yes—
298#125C22⋊D7912yes—
299#125C22×D7912yes—
300#125C22×D7912yes—
301#124—21no—
302#124—21no—
303#124C22⋊D7912yes—
304#124C22×D7912yes—
305#123—24no—
306#123—24no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—24no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—1581no—
318C2×C4⋊C4—1581no—
319C2×C4⋊C4C22⋊D7911yescharacteristic
320C2×C4⋊C4C22⋊D7911yescharacteristic
321C2×C4⋊C4C22⋊D7911yescharacteristic
322C2×C4⋊C4C22⋊D7911yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C42—21no—
329C2×C42C22×D7911yescharacteristic
330#107—1584no—
331#106—1584no—
332#103—1584no—
333#103—1584no—
334#103—1584no—
335#102—1584no—
336#97—792no—
337#97—792no—
338#97—792no—
339#97—1581no—
340#97—1581no—
341#97—1581no—
342C24—21no—
343C2×Q8—24no—
344C2×Q8—21no—
345C2×Q8—42no—
346C2×Q8—82no—
347C2×Q8—3164no—
348C2×Q8—3161no—
349C2×Q8—1582no—
350C2×Q8C2×C22⋊D7912yes—
351C2×D4—21no—
352C2×D4—42no—
353C2×D4C2×C22⋊D7912yes—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—24no—
360C22×C4—82no—
361C22×C4—3161no—
362C22×C4C2×C22⋊D7911yescharacteristic
363C22×C4C2×C22⋊D7911yescharacteristic
364C22×C4C2×C22⋊D7911yescharacteristic
365C2×C8—3162no—
366C2×C8—3162no—
367C2×C8—1582no—
368C2×C8—1582no—
369C2×C8—1584no—
370C2×C8—1582no—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—3161no—
386C4⋊C4—3161no—
387C4⋊C4—1582no—
388C4⋊C4—1582no—
389C4⋊C4C2×C22⋊D7912yes—
390C4⋊C4C2×C22⋊D7912yes—
391C4⋊C4C2×C22⋊D7912yes—
392C4⋊C4C2×C22⋊D7912yes—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C42—24no—
401C42C2×C22⋊D7911yescharacteristic
402C42C2×C22⋊D7911yescharacteristic
403C42C2×C22⋊D7911yescharacteristic
404C42C23×D7911yescharacteristic
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23#1457913011yescharacteristic
410Q8—42no—
411Q8—81no—
412Q8—84no—
413Q8—3164no—
414Q8—6322no—
415D4—42no—
416D4—81no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—84no—
431C2×C4—3162no—
432C2×C4—6322no—
433C2×C4#1457913011yescharacteristic
434C2×C4#1457913011yescharacteristic
435C2×C4#1457913011yescharacteristic
436C2×C4C22×C22⋊D7911yescharacteristic
437C2×C4C22×C22⋊D7911yescharacteristic
438C2×C4C22×C22⋊D7911yescharacteristic
439C8—3162no—
440C8—3162no—
441C8—1584no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—84no—
446C22#1909873612yes—
447C22#1909874112yes—
448C22#1909874612yes—
449C22C2×#1457913011yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—42no—
461C4—6322no—
462C2—82no—
463C2#2376273414yesdirect product factor
464C2C2×#1909874111yescharacteristic
465C2C2×#1909873611yescharacteristic
466C2C2×#1909874611yescharacteristic
subgroupG/H
centerC23#14579130
commutator, cosocleC42×C79C24
FrattiniC42C23×D79
FittingC2×#563×C79C2
socleC23×C79#120
prime radicalC22×D4×C79D4
hypercenterC2×#563D79
hypocenterC79C2×#1664
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. C2×#19098973C2semidirect
2. C2×#19098933C2semidirect
4. #23762734C2direct (N × H)
5. C2×#19098305C2semidirect
6. C2×#19098305C2semidirect
11. #19098973C22semidirect
13. #19098933C22semidirect
25. #19098305C22semidirect
26. #19098305C22semidirect
230. C2×C79#1664semidirect
242. C79C2×#1664semidirect
463. C2#23762734direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190989732
C2×#190989332
C2×#190989222
#237627342
C2×#190983052
C2×#190983032
C2×#563×C792
C2×#166479