Finite Group Databasebeta

← C2×#10594839 #11900641

Subgroups — C2×#10594839 #11900641

Order 1152.

2677 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63978C211yesmaximal, characteristic
5C2×#63966C211yesmaximal, characteristic, complemented
6C2×#63964C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8C2×C4×#627C211yesmaximal, characteristic, complemented
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×#63874C211yesmaximal, characteristic, complemented
11C2×#63868C211yesmaximal, characteristic, complemented
12C2×#63867C211yesmaximal, characteristic, complemented
13C2×#63859C211yesmaximal, characteristic, complemented
14C2×#63855C211yesmaximal, characteristic, complemented
15#10594839C2116yesmaximal, direct product factor
16C2×#63852C211yesmaximal, characteristic, complemented
17C2×#5538—31nomaximal
18C2×#5479—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C4×#638C2218yescomplemented
30C2×#3752C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C3×C4×#67C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2218yescomplemented
43#63978C2218yes—
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47#63966C2218yescomplemented
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53#63964C2218yescomplemented
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57#63961C2218yescomplemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C4×#627C2218yescomplemented
62C4×#626C2218yescomplemented
63#63874C2218yescomplemented
64#63868C2218yescomplemented
65#63867C2218yescomplemented
66#63859C2218yescomplemented
67#63855C2218yescomplemented
68#63852C2218yescomplemented
69C2×C3×C4×D4—31no—
70C22×C3×C42—31no—
71C2×#939—31no—
72C2×#935—31no—
73C2×#930—31no—
74C2×#929—31no—
75C2×#929—31no—
76C2×C4×#67—31no—
77C2×C4×#67—31no—
78C2×C4×#67—31no—
79C2×C4×#67—61no—
80C2×C4×#67D311yescharacteristic, complemented
81C2×#926—31no—
82C2×#924—31no—
83C22×C4×Dic3D311yescharacteristic, complemented
84#5538—316no—
85C2×#898—31no—
86C2×#889—31no—
87C2×#886—31no—
88C2×#885—31no—
89C2×#879—31no—
90C2×#878—31no—
91#5479—316no—
92C2×#876—31no—
93C2×#876—31no—
94C2×#875—31no—
95C2×C4×D12—31no—
96C2×#872—31no—
97C2×#872—31no—
98C2×#872—31no—
99C2×#870—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4—24no—
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2314yes—
108C22×C32×C4C2311yescharacteristic
109C2×#638—24no—
110C2×#638C2314yes—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C2×C4×C3⋊D3—24no—
115C2×C4×C3⋊D3C2314yes—
116C2×C3×#67—24no—
117C2×C3×#67C2314yes—
118C22×C3×Dic3—24no—
119C22×C3×Dic3—24no—
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2314yes—
126C22×C3×Dic3C2314yes—
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—24no—
130C2×C3×C4×D3C2314yes—
131C2×#627—24no—
132C2×#627C2314yes—
133C2×#626—24no—
134C2×#626C2314yes—
135#3757C2314yes—
136#3752C2314yes—
137#3750C2314yes—
138C4×C3⋊Dic3C2314yes—
139C3×#217C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×C4×Dic3C2314yes—
143C3×C4×Dic3C2314yes—
144C3×C4×Dic3C2314yes—
145C3×C4×Dic3C2314yes—
146C3×C4×Dic3C2314yes—
147#3724C2314yes—
148#3724C2314yes—
149#3724C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161C2×#529—91noSylow
162C22×C3×D4—31no—
163C23×C3×C4—21no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C23×C3×C4C2×D311yescharacteristic
168C23×C3×C4C2×D311yescharacteristic
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—61no—
173C22×#67C2×D311yescharacteristic
174C23×Dic3C2×D311yescharacteristic
175C23×Dic3C2×D311yescharacteristic
176C22×D12—31no—
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×C4×D3—61no—
180C22×C4×D3C2×D311yescharacteristic
181C22×Dic6—31no—
182C22×Dic6—31no—
183C3×C4×D4—38no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C42—31no—
188C2×C3×C42—31no—
189C2×C3×C42—31no—
190C2×C3×C42—31no—
191C2×C3×C42—31no—
192C2×C3×C42—38no—
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—61no—
199C2×#217C2×D311yescharacteristic
200#939—38no—
201#935—38no—
202#930—38no—
203#929—38no—
204#929—38no—
205C4×#67—38no—
206C4×#67—38no—
207C4×#67—38no—
208C4×#67—68no—
209C4×#67C2×D318yescomplemented
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—61no—
222C2×(C2×D3)⋊C4C2×D311yescharacteristic
223#926—38no—
224C2×C4⋊Dic3—31no—
225C2×C4⋊Dic3—31no—
226C2×C4⋊Dic3—31no—
227C2×C4⋊Dic3—31no—
228C2×C4⋊Dic3—31no—
229#924—38no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—61no—
244C2×Dic3⋊C4C2×D311yescharacteristic
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3—61no—
248C2×C4×Dic3C2×D311yescharacteristic
249C2×C4×Dic3C2×D311yescharacteristic
250C2×C4×Dic3C2×D311yescharacteristic
251C2×C4×Dic3C2×D311yescharacteristic
252C2×C4×Dic3C2×D311yescharacteristic
253C2×C4×Dic3C2×D318yescomplemented
254#898—38no—
255#889—38no—
256#886—38no—
257#885—38no—
258#879—38no—
259#878—38no—
260#876—38no—
261#876—38no—
262#875—38no—
263C4×D12—38no—
264#872—38no—
265#872—38no—
266#872—38no—
267#870—38no—
268C4×Dic6—38no—
269C4×Dic6—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32#4114yes—
273C23×C32C2412yes—
274C23×C32C2411yescharacteristic
275C22×C3⋊D3—22no—
276C22×C3⋊D3—22no—
277C22×C3⋊D3—22no—
278C22×C3⋊D3C2412yes—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—28no—
285C2×C32×C4#4114yes—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288#638—28no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3—22no—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C4×C3⋊D3—28no—
296C3×#67—28no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—28no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—28no—
305C2×C3×Dic3#4114yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C3×C4×D3—28no—
314#627—28no—
315#626—28no—
316#529—916no—
317C2×#126—91no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#124—91no—
321C2×#123—91no—
322C2×#123—91no—
323C2×C22⋊Q8—91no—
324C2×#121—91no—
325C2×C4×Q8—91no—
326C2×C4×D4—31no—
327C2×C4×D4—91no—
328C2×C4×D4—91no—
329C2×#117—91no—
330C2×#117—91no—
331C22×C42—31no—
332C24×C3—21no—
333C24×C3—31no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C23×D3—31no—
337C23×D3—31no—
338C23×D3—61no—
339C23×D3C22×D311yescharacteristic
340C2×C3×D4—34no—
341C2×C3×D4—64no—
342C22×C3×C4—24no—
343C22×C3×C4—24no—
344C22×C3×C4—21no—
345C22×C3×C4—24no—
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—34no—
355C22×C3×C4—34no—
356C22×C3×C4—34no—
357C22×C3×C4—44no—
358C22×C3×C4—64no—
359C22×C3×C4—64no—
360C22×C3×C4—64no—
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D314yes—
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D314yes—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C2×#67—24no—
368C2×#67—34no—
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—64no—
372C2×#67—68no—
373C2×#67—64no—
374C2×#67—64no—
375C2×#67—64no—
376C2×#67C22×D314yes—
377C22×Dic3—24no—
378C22×Dic3—24no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3C22×D314yes—
389C22×Dic3C22×D314yes—
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C2×D12—34no—
398C2×D12—64no—
399C2×C4×D3—24no—
400C2×C4×D3—34no—
401C2×C4×D3—34no—
402C2×C4×D3—64no—
403C2×C4×D3—64no—
404C2×C4×D3—64no—
405C2×C4×D3—124no—
406C2×C4×D3C22×D314yes—
407C2×Dic6—34no—
408C2×Dic6—34no—
409C2×Dic6—64no—
410C2×Dic6—64no—
411C3×C4⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C42—34no—
415C3×C42—34no—
416C3×C42—34no—
417C3×C42—34no—
418C3×C42—34no—
419#217—34no—
420#217—34no—
421#217—34no—
422#217—34no—
423#217—34no—
424#217—64no—
425#217C22×D314yes—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—64no—
438(C2×D3)⋊C4C22×D314yes—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—64no—
458Dic3⋊C4C22×D314yes—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—64no—
462C4×Dic3C22×D314yes—
463C4×Dic3C22×D314yes—
464C4×Dic3C22×D314yes—
465C4×Dic3C22×D314yes—
466C4×Dic3C22×D314yes—
467C22×C32—28no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32C2×#4114yes—
471C22×C32C2×#4112yes—
472C22×C32C2×#4112yes—
473C22×C32C2×#4112yes—
474C22×C32C2511yescharacteristic
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—22no—
478C2×C3⋊D3—44no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—44no—
483C32×C4—22no—
484C32×C4C2×#4114yes—
485C3⋊Dic3—22no—
486C3⋊Dic3—22no—
487C3⋊Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3C2×#4114yes—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—91no—
499C23×C4—31no—
500C23×C4—31no—
501C23×C4—31no—
502C23×C4—91no—
503C23×C4D3211yescharacteristic
504#126—98no—
505#126—98no—
506#125—98no—
507#124—98no—
508#123—98no—
509#123—98no—
510C22⋊Q8—98no—
511#121—98no—
512C4×Q8—98no—
513C4×D4—38no—
514C4×D4—98no—
515C4×D4—98no—
516#117—98no—
517#117—98no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C42—31no—
539C2×C42—31no—
540C2×C42—38no—
541C2×C42—31no—
542C2×C42—31no—
543C2×C42—31no—
544C2×C42—91no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—21no—
550C23×C3—22no—
551C23×C3—24no—
552C23×C3—32no—
553C23×C3—42no—
554C23×C3—42no—
555C23×C3—62no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3#23514yes—
559C23×C3#23514yes—
560C23×C3C23×D312yes—
561C23×C3C23×D312yes—
562C23×C3C23×D311yescharacteristic
563C23×C3C23×D311yescharacteristic
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—32no—
568C22×D3—32no—
569C22×D3—62no—
570C22×D3—64no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—62no—
574C22×D3—62no—
575C22×D3—62no—
576C22×D3—62no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3C23×D312yes—
580C3×D4—68no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—28no—
584C2×C3×C4—28no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—24no—
588C2×C3×C4—34no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—48no—
597C2×C3×C4—42no—
598C2×C3×C4—68no—
599C2×C3×C4—62no—
600C2×C3×C4—68no—
601C2×C3×C4—62no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—62no—
605C2×C3×C4—62no—
606C2×C3×C4—68no—
607C2×C3×C4#23514yes—
608C2×C3×C4#23714yes—
609C2×C3×C4C23×D312yes—
610C2×C3×C4C23×D312yes—
611C2×C3×C4C23×D312yes—
612C2×C3×C4C23×D312yes—
613#67—28no—
614#67—616no—
615#67—68no—
616#67—68no—
617#67—68no—
618C2×Dic3—28no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—28no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—32no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—64no—
636C2×Dic3—62no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—62no—
640C2×Dic3—62no—
641C2×Dic3—62no—
642C2×Dic3—122no—
643C2×Dic3—122no—
644C2×Dic3#23514yes—
645C2×Dic3C23×D312yes—
646C2×Dic3C23×D312yes—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D312yes—
649C2×Dic3C23×D312yes—
650C2×Dic3C23×D312yes—
651C2×Dic3C23×D312yes—
652D12—68no—
653C4×D3—28no—
654C4×D3—68no—
655C4×D3—68no—
656C4×D3—128no—
657Dic6—68no—
658Dic6—68no—
659C2×C32—24no—
660C2×C32#52914yescomplemented
661C2×C32C22×#4111yescharacteristic
662C2×C32C22×#4111yescharacteristic
663C2×C32C22×#4111yescharacteristic
664C3⋊D3—42no—
665C3×D3—42no—
666C24—31no—
667C24—91no—
668C24C2×D3211yescharacteristic
669C2×Q8—94no—
670C2×Q8—184no—
671C2×D4—34no—
672C2×D4—64no—
673C2×D4—94no—
674C2×D4—94no—
675C2×D4—184no—
676C2×D4—184no—
677C22×C4—24no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—34no—
683C22×C4—34no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—34no—
688C22×C4—64no—
689C22×C4—64no—
690C22×C4—64no—
691C22×C4—91no—
692C22×C4—91no—
693C22×C4—91no—
694C22×C4—94no—
695C22×C4—184no—
696C22×C4C2×D3211yescharacteristic
697C22×C4C2×D3214yes—
698C22×C4C2×D3211yescharacteristic
699C4⋊C4—34no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C22⋊C4—34no—
710C22⋊C4—34no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C42—34no—
720C42—34no—
721C42—34no—
722C42—34no—
723C42—34no—
724C42—94no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—28no—
730C22×C3—28no—
731C22×C3—22no—
732C22×C3—24no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—42no—
737C22×C3—48no—
738C22×C3—42no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—124no—
743C22×C3C2×#23514yes—
744C22×C3C2×#23514yes—
745C22×C3C2×#23512yes—
746C22×C3C2×#23512yes—
747C22×C3C2×#23512yes—
748C22×C3C2×#23512yes—
749C22×C3C2×#23712yes—
750C22×C3D3×#4112yes—
751C22×C3C24×D311yescharacteristic
752C22×C3C24×D311yescharacteristic
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—44no—
757C2×D3—64no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—122no—
765C2×D3—122no—
766C2×D3—128no—
767C2×D3—124no—
768C2×D3—124no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—24no—
772C3×C4—34no—
773C3×C4—42no—
774C3×C4—62no—
775C3×C4—62no—
776C3×C4—62no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—62no—
780C3×C4C2×#23514yes—
781C3×C4C2×#23714yes—
782Dic3—22no—
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3—22no—
787Dic3—22no—
788Dic3—64no—
789Dic3—62no—
790Dic3—62no—
791Dic3—62no—
792Dic3—62no—
793Dic3—62no—
794Dic3—62no—
795Dic3—122no—
796Dic3—122no—
797Dic3C2×#23514yes—
798C32C2×#52911yescharacteristic, complemented, Sylow
799C23—22no—
800C23—22no—
801C23—32no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—92no—
806C23—182no—
807C23—182no—
808C23—182no—
809C23#379814yes—
810C23C22×D3212yes—
811C23C22×D3211yescharacteristic
812Q8—188no—
813D4—68no—
814D4—188no—
815D4—188no—
816C2×C4—22no—
817C2×C4—28no—
818C2×C4—34no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—68no—
827C2×C4—68no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—68no—
835C2×C4—92no—
836C2×C4—92no—
837C2×C4—92no—
838C2×C4—182no—
839C2×C4—182no—
840C2×C4—182no—
841C2×C4—188no—
842C2×C4#380414yes—
843C2×C4C22×D3212yes—
844C2×C4C22×D3212yes—
845C2×C3—24no—
846C2×C3—24no—
847C2×C3—24no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—44no—
852C2×C3—122no—
853C2×C3#547914yescomplemented
854C2×C3#553814yescomplemented
855C2×C3C22×#23511yescharacteristic
856C2×C3C22×#23511yescharacteristic
857C2×C3C22×#23511yescharacteristic
858C2×C3C22×#23511yescharacteristic
859C2×C3C22×#23711yescharacteristic
860C2×C3C2×D3×#4111yescharacteristic
861D3—42no—
862D3—124no—
863D3—122no—
864D3—122no—
865C22—28no—
866C22—22no—
867C22—22no—
868C22—62no—
869C22—62no—
870C22—62no—
871C22—124no—
872C22—182no—
873C22—182no—
874C22—182no—
875C22—364no—
876C22C2×#379814yes—
877C22C2×#379812yes—
878C22D3×#23512yes—
879C22C2×#380412yes—
880C22C23×D3211yescharacteristic
881C4—22no—
882C4—34no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—182no—
890C4—182no—
891C4—182no—
892C4C2×#380414yes—
893C3—21no—
894C3C2×#547911yescharacteristic, complemented
895C3C2×#553811yescharacteristic, complemented
896C2—24no—
897C2—122no—
898C2—362no—
899C2#1059483914yesdirect product factor
900C2C22×#379811yescharacteristic
901C2C2×D3×#23511yescharacteristic
902C2C22×#380411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×#63978C2
hypercenterC23×C4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C22×C3×C4×Dic3C2semidirect
5. C2×#63966C2semidirect
6. C2×#63964C2semidirect
7. C2×#63961C2semidirect
8. C2×C4×#627C2semidirect
9. C2×C4×#626C2semidirect
10. C2×#63874C2semidirect
11. C2×#63868C2semidirect
12. C2×#63867C2semidirect
13. C2×#63859C2semidirect
14. C2×#63855C2semidirect
15. #10594839C2direct (N × H)
16. C2×#63852C2semidirect
29. C4×#638C22semidirect
34. C3×C4×#67C22semidirect
42. C2×C3×C4×Dic3C22semidirect
47. #63966C22semidirect
53. #63964C22semidirect
57. #63961C22semidirect
61. C4×#627C22semidirect
62. C4×#626C22semidirect
63. #63874C22semidirect
64. #63868C22semidirect
65. #63867C22semidirect
66. #63859C22semidirect
67. #63855C22semidirect
68. #63852C22semidirect
80. C2×C4×#67D3semidirect
83. C22×C4×Dic3D3semidirect
209. C4×#67C2×D3semidirect
253. C2×C4×Dic3C2×D3semidirect
660. C2×C32#529semidirect
798. C32C2×#529semidirect
853. C2×C3#5479semidirect
854. C2×C3#5538semidirect
894. C3C2×#5479semidirect
895. C3C2×#5538semidirect
899. C2#10594839direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×C4×#672
C22×C3×C4×Dic32
C2×#639782
C2×#639662
C2×#639642
C2×#639612
C2×C4×#6272
C2×C4×#6262
C2×#638742
C2×#638682
C2×#638672
C2×#638592
C2×#638552
#105948392
C2×#638522
C2×#55383
C2×#54793