Finite Group Databasebeta

← C2×#10378 #238309

Subgroups — C2×#10378 #238309

Order 512.

1028 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2605C211yesmaximal, characteristic, complemented
2C2×#1980C211yesmaximal, characteristic
3C2×#1514C211yesmaximal, characteristic
4C2×#1505C211yesmaximal, characteristic
5#10378C218yesmaximal, direct product factor
6C2×#1300C211yesmaximal, characteristic, complemented
7C2×#1288C211yesmaximal, characteristic, complemented
8C2×#1285C211yesmaximal, characteristic, complemented
9C2×#532C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C22×#104—21no—
13C22×#104—21no—
14C2×C4×M16C2211yescharacteristic
15#2605—22no—
16#2605—22no—
17#2605—22no—
18#2605C2214yescomplemented
19C2×#400—21no—
20C2×#395—21no—
21C2×#391—21no—
22C2×#391—21no—
23C2×#387—21no—
24C2×#387—21no—
25C2×#383C2211yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×#376C2211yescharacteristic
28#1980—22no—
29#1980C2214yes—
30#1514—22no—
31#1514C2214yes—
32#1505—22no—
33#1505C2214yes—
34C2×#327—21no—
35C2×#327—21no—
36C2×#327—21no—
37C2×#327—21no—
38#1300C2214yescomplemented
39#1288C2214yescomplemented
40#1285C2214yescomplemented
41C22×#41—21no—
42C23×Q8—21no—
43C22×M16—21no—
44#532—21no—
45#532—21no—
46#532—21no—
47#532—21no—
48#532—21no—
49#532—21no—
50#532Q812yescomplemented
51#532C2312yes—
52C2×C4⋊Q8Q811yescharacteristic, complemented
53C2×#127Q811yescharacteristic, complemented
54C2×#124—21no—
55C2×#121—21no—
56C2×#121—21no—
57C2×C4×D4—21no—
58C2×C4×D4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C42—21no—
64C22×C42D411yescharacteristic
65C22×C42D411yescharacteristic
66C22×C42C2311yescharacteristic
67#432—21no—
68#432—21no—
69#432—21no—
70#432—21no—
71#432—21no—
72#432—21no—
73#432C2312yes—
74#432C2312yes—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×#104—24no—
78C2×#104—24no—
79C2×#104—44no—
80C2×#104—44no—
81C2×C22⋊C8—21no—
82C2×C22⋊C8—21no—
83C4×M16—21no—
84C4×M16—21no—
85C4×M16—21no—
86C4×M16C2312yes—
87C2×#97—21no—
88C2×#97—21no—
89C2×#97—21no—
90C2×C4×C8—21no—
91#400—24no—
92#400—24no—
93#395—24no—
94#395—24no—
95#391—24no—
96#391—24no—
97#391—24no—
98#391—24no—
99#387—24no—
100#387—24no—
101#387—24no—
102#387—24no—
103#383—21no—
104#383—21no—
105#383D412yes—
106#383C2312yes—
107C4×C4⋊C4—21no—
108C4×C4⋊C4—21no—
109C4×C4⋊C4D412yes—
110C4×C4⋊C4C2312yes—
111#376—21no—
112#376—21no—
113#376D412yes—
114#376C2312yes—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—21no—
121C2×#95—21no—
122C2×#95—21no—
123C2×#95D411yescharacteristic
124C2×#95D411yescharacteristic
125C2×#95D411yescharacteristic
126C2×#95D411yescharacteristic
127#327—24no—
128#327—24no—
129#327—24no—
130#327—24no—
131C2×#41—22no—
132C2×#41—22no—
133C2×#41—42no—
134C2×#41—42no—
135C2×#41—42no—
136C2×#41—42no—
137C2×#41—41no—
138C2×#41—41no—
139C22×Q8—24no—
140C22×Q8—21no—
141C22×Q8—44no—
142C22×Q8—44no—
143C22×Q8—82no—
144C22×D4—21no—
145C22×D4—21no—
146C22×D4—21no—
147C22×D4—41no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—41no—
155C23×C4C2×D411yescharacteristic
156C23×C4C2×D411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C2×M16—24no—
159C2×M16—22no—
160C2×M16—42no—
161C2×M16—41no—
162C22×C8—41no—
163C22×C8—41no—
164C22×C8—41no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8C2×Q812yescomplemented
169#127—21no—
170#127—21no—
171#127—21no—
172#127C2×Q812yescomplemented
173#124—22no—
174#124—22no—
175#124—41no—
176#124—41no—
177#121—22no—
178#121—22no—
179#121—22no—
180#121—22no—
181#121—41no—
182#121—41no—
183#121—41no—
184#121—41no—
185C4×D4—22no—
186C4×D4—22no—
187C4×D4—22no—
188C4×D4—22no—
189C4×D4—41no—
190C4×D4—41no—
191C4×D4—41no—
192C4×D4—41no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4—44no—
202C2×C4⋊C4—44no—
203C2×C4⋊C4—82no—
204C2×C22⋊C4—41no—
205C2×C22⋊C4—41no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42—44no—
211C2×C42—42no—
212C2×C42—42no—
213C2×C42C2×D412yes—
214C2×C42C2×D412yes—
215C2×C42C2×D411yescharacteristic
216C2×C42C2×D411yescharacteristic
217C2×C42C2×D411yescharacteristic
218C2×C42C2×Q811yescharacteristic
219C2×C42C2×Q811yescharacteristic
220C2×C42#4111yescharacteristic
221C2×C42#4111yescharacteristic
222C2×C42#4111yescharacteristic
223C2×C42#4111yescharacteristic
224C2×C42#4111yescharacteristic
225C2×C42#4111yescharacteristic
226C2×C42C2411yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—41no—
230C4⋊C8—41no—
231#104—48no—
232#104—48no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—41no—
236C22⋊C8—41no—
237#97—22no—
238#97—22no—
239#97—22no—
240#97—41no—
241#97—41no—
242#97—41no—
243C4×C8—22no—
244C4×C8—41no—
245#95—24no—
246#95—24no—
247#95—24no—
248#95—24no—
249#95—22no—
250#95—22no—
251#95—22no—
252#95—22no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95C2×D412yes—
262#95C2×D412yes—
263#95C2×D412yes—
264#95C2×D412yes—
265C24—41no—
266C24#12011yescharacteristic
267#41—42no—
268#41—42no—
269#41—42no—
270#41—42no—
271#41—44no—
272#41—44no—
273#41—82no—
274#41—82no—
275#41—82no—
276#41—82no—
277C2×Q8—22no—
278C2×Q8—48no—
279C2×Q8—48no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—41no—
283C2×Q8—84no—
284C2×Q8—816no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—82no—
296C2×D4—82no—
297C2×D4—82no—
298C2×D4—82no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—82no—
331C22×C4—82no—
332C22×C4#12011yescharacteristic
333C22×C4#12011yescharacteristic
334C22×C4#12011yescharacteristic
335C22×C4C22⋊Q811yescharacteristic
336C22×C4C22⋊Q811yescharacteristic
337C22×C4C22⋊Q811yescharacteristic
338C22×C4C22⋊Q811yescharacteristic
339C22×C4C22⋊Q811yescharacteristic
340C22×C4C22⋊Q811yescharacteristic
341C22×C4#12411yescharacteristic
342C22×C4#12411yescharacteristic
343C22×C4#12411yescharacteristic
344C22×C4#12411yescharacteristic
345C22×C4#12411yescharacteristic
346C22×C4#12411yescharacteristic
347C22×C4C22×D411yescharacteristic
348C22×C4C22×D411yescharacteristic
349C22×C4C22×D411yescharacteristic
350M16—24no—
351M16—42no—
352M16—44no—
353C2×C8—44no—
354C2×C8—42no—
355C2×C8—42no—
356C2×C8—42no—
357C2×C8—82no—
358C2×C8—82no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—48no—
362C4⋊C4—44no—
363C4⋊C4—44no—
364C4⋊C4—48no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—84no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C22⋊C4—42no—
372C42—42no—
373C42—42no—
374C42—44no—
375C42—44no—
376C42—81no—
377C42—81no—
378C42C22⋊Q811yescharacteristic
379C42C22⋊Q811yescharacteristic
380C42C22⋊Q811yescharacteristic
381C42C22⋊Q811yescharacteristic
382C42C22⋊Q811yescharacteristic
383C42C22⋊Q811yescharacteristic
384C42#12411yescharacteristic
385C42#12411yescharacteristic
386C42#12411yescharacteristic
387C42#12411yescharacteristic
388C42#12411yescharacteristic
389C42#12411yescharacteristic
390C42C22×Q811yescharacteristic
391C42C2×#4111yescharacteristic
392C42C2×#4111yescharacteristic
393C42C2×#4111yescharacteristic
394C23—22no—
395C23—22no—
396C23—42no—
397C23—82no—
398C23—82no—
399C23—82no—
400C23#39311yescharacteristic
401C23#39311yescharacteristic
402C23#45312yes—
403C23#45412yes—
404C23C2×#12011yescharacteristic
405Q8—42no—
406Q8—42no—
407Q8—82no—
408Q8—816no—
409D4—42no—
410D4—42no—
411D4—82no—
412D4—82no—
413D4—82no—
414D4—82no—
415D4—82no—
416D4—82no—
417D4—82no—
418D4—84no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—48no—
444C2×C4—48no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—84no—
463C2×C4—84no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—84no—
467C2×C4—82no—
468C2×C4#39311yescharacteristic
469C2×C4#39311yescharacteristic
470C2×C4#39311yescharacteristic
471C2×C4#39311yescharacteristic
472C2×C4#39311yescharacteristic
473C2×C4#39311yescharacteristic
474C2×C4C2×C22⋊Q811yescharacteristic
475C2×C4C2×C22⋊Q811yescharacteristic
476C2×C4C2×C22⋊Q811yescharacteristic
477C2×C4C2×#12411yescharacteristic
478C2×C4C2×#12411yescharacteristic
479C2×C4C2×#12411yescharacteristic
480C8—44no—
481C8—82no—
482C8—82no—
483C22—24no—
484C22—24no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—82no—
490C22—82no—
491C22—82no—
492C22—164no—
493C22#202712yes—
494C22#202712yes—
495C22#203112yes—
496C22#203112yes—
497C22C2×#39311yescharacteristic
498C22C2×#45311yescharacteristic
499C22C2×#45411yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—44no—
513C4—44no—
514C4—82no—
515C4—82no—
516C4—82no—
517C4—82no—
518C4—82no—
519C2—21no—
520C2—21no—
521C2—22no—
522C2—162no—
523C2#1037814yesdirect product factor
524C2C2×#202711yescharacteristic
525C2C2×#203111yescharacteristic
526C2C2×#203111yescharacteristic
subgroupG/H
center, socleC23#393
commutator, Frattini, cosocleC2×C42C24
prime radicalC2×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2605C2semidirect
5. #10378C2direct (N × H)
6. C2×#1300C2semidirect
7. C2×#1288C2semidirect
8. C2×#1285C2semidirect
18. #2605C22semidirect
38. #1300C22semidirect
39. #1288C22semidirect
40. #1285C22semidirect
50. #532Q8semidirect
52. C2×C4⋊Q8Q8semidirect
53. C2×#127Q8semidirect
168. C4⋊Q8C2×Q8semidirect
172. #127C2×Q8semidirect
523. C2#10378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26052
C2×#19802
C2×#15142
C2×#15052
#103782
C2×#13002
C2×#12882
C2×#12852