Finite Group Databasebeta

← C2×#9270 #198595

Subgroups — C2×#9270 #198595

Order 512.

1100 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×#3230C211yesmaximal, characteristic
2C2×#2962C211yesmaximal, characteristic
3C2×#1997C211yesmaximal, characteristic
4C2×#1550C211yesmaximal, characteristic
5C22×#332C211yesmaximal, characteristic
6#9270C218yesmaximal, direct product factor
7C2×#1301C211yesmaximal, characteristic
8C2×#1283C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4⋊Q8C2211yescharacteristic
11#3230—22no—
12#3230—22no—
13#3230C414yes—
14#3230C2214yes—
15C2×#500—21no—
16C2×#487—21no—
17C2×#484C414yes—
18C2×#477—22no—
19#2962—22no—
20#2962—22no—
21#2962—22no—
22#2962C2214yes—
23C2×#446—21no—
24C2×#446—22no—
25C2×C8×Q8—21no—
26C2×#431C2211yescharacteristic
27C2×#424—21no—
28C2×#423C2211yescharacteristic
29C22×C4⋊C8C2211yescharacteristic
30C22×C4⋊C8C2211yescharacteristic
31C2×#405—21no—
32C2×C4×M16C2211yescharacteristic
33#1997—22no—
34#1997C2214yes—
35C2×#343—21no—
36C2×#343—21no—
37#1550—22no—
38#1550C2214yes—
39C2×#333—21no—
40C2×#332—21no—
41C2×#332—21no—
42C2×#332—22no—
43C2×#332—21no—
44C2×#332C2214yes—
45#1301C2214yes—
46#1283C2214yes—
47C23×Q8—21no—
48C22×M16—21no—
49C22×M16D411yescharacteristic
50C22×M16D411yescharacteristic
51C23×C8—21no—
52C23×C8—21no—
53#533—21no—
54#533—21no—
55#533—21no—
56#533—21no—
57#533C2×C412yes—
58#533D412yes—
59#533D412yes—
60#533C2312yes—
61C2×C4⋊Q8—21no—
62C2×C4⋊Q8—21no—
63C2×C4⋊Q8—21no—
64C2×C4⋊Q8—21no—
65C2×C4⋊Q8—21no—
66C2×C4⋊Q8—21no—
67C2×C4⋊Q8—21no—
68C2×C4⋊Q8—21no—
69C2×C4⋊Q8—21no—
70C2×C4⋊Q8—21no—
71C2×C4⋊Q8C2×C412yes—
72C2×C4⋊Q8D411yescharacteristic
73C2×C4⋊Q8D411yescharacteristic
74C2×C4⋊Q8C2312yes—
75C2×#125—21no—
76C2×C22⋊Q8—21no—
77C2×C22⋊Q8C2×C412yes—
78C2×C4×Q8—21no—
79C2×C4×Q8D412yes—
80C2×#117—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4C2×C412yes—
83C22×C42C2311yescharacteristic
84#500—24no—
85#500—24no—
86#487—24no—
87#487—24no—
88#484—28no—
89#484C2×C4116yes—
90#477—28no—
91#477—28no—
92#446—28no—
93#446—24no—
94#446—28no—
95#446—24no—
96C8×Q8—24no—
97C8×Q8—24no—
98#431—21no—
99#431—21no—
100#431C2×C412yes—
101#431C2312yes—
102C2×#107—24no—
103#424—24no—
104#424—24no—
105#423—21no—
106#423—21no—
107#423—21no—
108#423C2312yes—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8—21no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8—21no—
118C2×C4⋊C8—21no—
119C2×C4⋊C8—21no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8D411yescharacteristic
123C2×C4⋊C8D411yescharacteristic
124C2×C4⋊C8D412yes—
125C2×C4⋊C8C2312yes—
126C2×C4⋊C8C2312yes—
127C2×#103—24no—
128C2×C22⋊C8C2×C412yes—
129#405—24no—
130#405—24no—
131C4×M16—21no—
132C4×M16—21no—
133C4×M16D412yes—
134C4×M16C2312yes—
135C2×#97—22no—
136C2×#97—21no—
137C2×C4×C8—22no—
138C2×C4×C8—21no—
139C2×C4×C8—21no—
140#343—24no—
141#343—24no—
142#333—24no—
143#332—24no—
144#332—24no—
145#332—24no—
146C22×Q8—22no—
147C22×Q8—21no—
148C22×Q8—22no—
149C22×Q8—41no—
150C22×Q8—41no—
151C22×Q8—41no—
152C22×Q8—41no—
153C22×Q8—82no—
154C22×Q8—82no—
155C22×Q8C22⋊C412yes—
156C23×C4—22no—
157C23×C4C22×C411yescharacteristic
158C23×C4C2×D411yescharacteristic
159C23×C4#4111yescharacteristic
160C2×M16—21no—
161C2×M16—22no—
162C2×M16—21no—
163C2×M16—22no—
164C2×M16—22no—
165C2×M16—22no—
166C2×M16—41no—
167C2×M16—42no—
168C2×M16—42no—
169C2×M16Q1614yes—
170C2×M16C2×D412yes—
171C2×M16C2×D412yes—
172C22×C8—21no—
173C22×C8—22no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—22no—
177C22×C8—21no—
178C22×C8—22no—
179C22×C8—22no—
180C22×C8—42no—
181C22×C8—42no—
182C22×C8—41no—
183C22×C8—41no—
184C22×C8—41no—
185C22×C8—82no—
186C4⋊Q8—22no—
187C4⋊Q8—22no—
188C4⋊Q8—22no—
189C4⋊Q8—22no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—22no—
195C4⋊Q8—22no—
196C4⋊Q8—22no—
197C4⋊Q8—22no—
198C4⋊Q8—41no—
199C4⋊Q8—41no—
200C4⋊Q8—41no—
201C4⋊Q8—41no—
202C4⋊Q8—41no—
203C4⋊Q8—41no—
204C4⋊Q8—41no—
205C4⋊Q8—41no—
206C4⋊Q8C22⋊C412yes—
207C4⋊Q8C22⋊C412yes—
208C4⋊Q8C2×D412yes—
209C4⋊Q8C2×D412yes—
210#125—22no—
211#125—22no—
212#125—22no—
213#125—22no—
214C22⋊Q8—22no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C22⋊Q8—22no—
218C22⋊Q8—22no—
219C22⋊Q8—22no—
220C22⋊Q8C22⋊C414yes—
221C22⋊Q8C22×C414yes—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8C22⋊C414yes—
229C4×Q8C2×D414yes—
230#117—22no—
231#117—22no—
232#117—22no—
233#117—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—41no—
247C2×C4⋊C4—41no—
248C2×C4⋊C4—41no—
249C2×C4⋊C4—41no—
250C2×C4⋊C4C22⋊C412yes—
251C2×C4⋊C4C22×C414yes—
252C2×C22⋊C4—22no—
253C2×C42—22no—
254C2×C42C22×C411yescharacteristic
255C2×C42C2×D411yescharacteristic
256C2×C42C2×D411yescharacteristic
257C2×C42C2×D411yescharacteristic
258C2×C42C2×D411yescharacteristic
259C2×C42C2×D411yescharacteristic
260C2×C42C2×D411yescharacteristic
261C2×C42C2×D411yescharacteristic
262C2×C42#4111yescharacteristic
263C2×C42#4111yescharacteristic
264C2×C42#4111yescharacteristic
265C2×C42C2411yescharacteristic
266#107—216no—
267C4⋊C8—28no—
268C4⋊C8—28no—
269C4⋊C8—22no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—22no—
273C4⋊C8—22no—
274C4⋊C8—22no—
275C4⋊C8—22no—
276C4⋊C8—22no—
277C4⋊C8—22no—
278C4⋊C8—22no—
279C4⋊C8—41no—
280C4⋊C8—41no—
281C4⋊C8—41no—
282C4⋊C8—41no—
283C4⋊C8C2×D412yes—
284C4⋊C8C2×D412yes—
285#103—216no—
286C22⋊C8—22no—
287C22⋊C8C22×C414yes—
288#97—28no—
289#97—22no—
290#97—22no—
291C4×C8—28no—
292C4×C8—22no—
293C4×C8—22no—
294C4×C8—22no—
295C4×C8—22no—
296C24C4×D411yescharacteristic
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8—44no—
301C2×Q8—42no—
302C2×Q8—42no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8—42no—
306C2×Q8—42no—
307C2×Q8—84no—
308C2×Q8—82no—
309C2×Q8—82no—
310C2×Q8—84no—
311C2×Q8—84no—
312C2×Q8—82no—
313C2×Q8—82no—
314C2×Q8—82no—
315C2×Q8—82no—
316C2×Q8C2×C22⋊C414yes—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—84no—
326C22×C4C2×C22⋊C411yescharacteristic
327C22×C4C2×C22⋊C411yescharacteristic
328C22×C4C4×D411yescharacteristic
329C22×C4C4×D411yescharacteristic
330C22×C4C4×D411yescharacteristic
331C22×C4C4×D411yescharacteristic
332C22×C4C4×D411yescharacteristic
333C22×C4#12011yescharacteristic
334C22×C4#12011yescharacteristic
335C22×C4#12111yescharacteristic
336C22×C4#12111yescharacteristic
337C22×C4#12111yescharacteristic
338C22×C4#12111yescharacteristic
339C22×C4#12311yescharacteristic
340C22×C4#12311yescharacteristic
341C22×C4C2×Q1612yes—
342C22×C4#13512yes—
343C22×C4#13712yes—
344C22×C4#13712yes—
345C22×C4C23×C411yescharacteristic
346C22×C4C22×D411yescharacteristic
347C22×C4C2×#4111yescharacteristic
348M16—22no—
349M16—24no—
350M16—22no—
351M16—22no—
352M16—42no—
353M16—42no—
354M16—42no—
355M16—82no—
356M16C2×Q1614yes—
357C2×C8—22no—
358C2×C8—24no—
359C2×C8—24no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—44no—
364C2×C8—42no—
365C2×C8—42no—
366C2×C8—42no—
367C2×C8—42no—
368C2×C8—44no—
369C2×C8—42no—
370C2×C8—42no—
371C2×C8—42no—
372C2×C8—82no—
373C2×C8—82no—
374C2×C8—82no—
375C2×C8—82no—
376C4⋊C4—24no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4C2×C22⋊C414yes—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C42—24no—
399C42—24no—
400C42C2×C22⋊C411yescharacteristic
401C42C2×C22⋊C411yescharacteristic
402C42C4×D411yescharacteristic
403C42C4×D411yescharacteristic
404C42#12011yescharacteristic
405C42#12011yescharacteristic
406C42#12111yescharacteristic
407C42#12111yescharacteristic
408C42#12111yescharacteristic
409C42#12111yescharacteristic
410C42#12311yescharacteristic
411C42#12311yescharacteristic
412C42C22×D411yescharacteristic
413C42C22×D411yescharacteristic
414C42C22×D411yescharacteristic
415C42C2×#4111yescharacteristic
416C23—22no—
417C23—22no—
418C23#38611yescharacteristic
419C23#38611yescharacteristic
420C23C4×Q1612yes—
421C23#44112yes—
422C23C2×C4×D411yescharacteristic
423Q8—44no—
424Q8—44no—
425Q8—42no—
426Q8—42no—
427Q8—82no—
428Q8—84no—
429Q8—84no—
430Q8—84no—
431Q8—82no—
432Q8—82no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—84no—
452C2×C4—84no—
453C2×C4—84no—
454C2×C4#38611yescharacteristic
455C2×C4#38611yescharacteristic
456C2×C4#38611yescharacteristic
457C2×C4#38611yescharacteristic
458C2×C4#38611yescharacteristic
459C2×C4#38611yescharacteristic
460C2×C4C4×Q1612yes—
461C2×C4#44112yes—
462C2×C4#45112yes—
463C2×C4#45112yes—
464C2×C4#45212yes—
465C2×C4#45212yes—
466C2×C4#46212yes—
467C2×C4#46212yes—
468C2×C4#46412yes—
469C2×C4#46412yes—
470C2×C4#47112yes—
471C2×C4#47212yes—
472C2×C4C22×C22⋊C411yescharacteristic
473C2×C4C2×C4×D411yescharacteristic
474C2×C4C2×#12011yescharacteristic
475C2×C4C2×#12111yescharacteristic
476C2×C4C2×#12111yescharacteristic
477C2×C4C2×#12311yescharacteristic
478C2×C4C22×Q1611yescharacteristic
479C2×C4C2×#13511yescharacteristic
480C2×C4C2×#13711yescharacteristic
481C2×C4C2×#13711yescharacteristic
482C8—24no—
483C8—44no—
484C8—42no—
485C8—42no—
486C8—42no—
487C8—82no—
488C8—82no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—24no—
494C22—24no—
495C22#187812yes—
496C22#187812yes—
497C22#190712yes—
498C22#191512yes—
499C22C2×#38611yescharacteristic
500C22C2×C4×Q1611yescharacteristic
501C22C2×#44111yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—44no—
509C4—44no—
510C4—84no—
511C4#187812yes—
512C4#187812yes—
513C4#190712yes—
514C4C2×#45111yescharacteristic
515C4C2×#45211yescharacteristic
516C4C2×#46211yescharacteristic
517C4C2×#46411yescharacteristic
518C4C2×#47111yescharacteristic
519C4C2×#47211yescharacteristic
520C2—22no—
521C2—21no—
522C2—21no—
523C2#927014yesdirect product factor
524C2C2×#187811yescharacteristic
525C2C2×#190711yescharacteristic
526C2C2×#191511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ 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
6. #9270C2direct (N × H)
523. C2#9270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32302
C2×#29622
C2×#19972
C2×#15502
C22×#3322
#92702
C2×#13012
C2×#12832