Finite Group Databasebeta

← C2×#10594123 #11901414

Subgroups — C2×#10594123 #11901414

Order 1152.

2411 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64088C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×C3×#883C211yesmaximal, characteristic, complemented
4C2×Dic3×#67C211yesmaximal, characteristic, complemented
5C2×#63970C211yesmaximal, characteristic
6C2×#63969C211yesmaximal, characteristic, complemented
7C2×#63964C211yesmaximal, characteristic, complemented
8C2×#63905C211yesmaximal, characteristic, complemented
9C2×#63902C211yesmaximal, characteristic, complemented
10C2×#63899C211yesmaximal, characteristic, complemented
11C2×#63893C211yesmaximal, characteristic, complemented
12C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
13C2×#63872C211yesmaximal, characteristic, complemented
14C2×#63858C211yesmaximal, characteristic, complemented
15C2×#63847C211yesmaximal, characteristic, complemented
16#10594123C2116yesmaximal, direct product factor
17C2×#5660—31nomaximal
18C2×#5665—31nomaximal
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35#64088C2218yescomplemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C3×#886C2218yescomplemented
45C3×#883C2218yescomplemented
46Dic3×#67C2218yescomplemented
47#63970C2218yes—
48#63969C2218yescomplemented
49C2×#3724C2211yescharacteristic
50C2×#3724C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56#63964C2218yescomplemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63905C2218yescomplemented
62#63902C2218yescomplemented
63#63899C2218yescomplemented
64#63893C2218yescomplemented
65D3×C4⋊Dic3C2218yescomplemented
66#63872C2218yescomplemented
67#63858C2218yescomplemented
68#63847C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#123—31no—
71C2×#939—31no—
72C2×#938—31no—
73C2×#935—31no—
74C2×D4×Dic3—31no—
75C2×#929—31no—
76C2×C4×#67—31no—
77C22×C4⋊Dic3—31no—
78C2×#924—31no—
79#5665—316no—
80#5660—316no—
81C2×#898—31no—
82C2×#897—31no—
83C2×#896—31no—
84C2×D3×C4⋊C4—31no—
85C2×#890—31no—
86C2×#890—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#886D311yescharacteristic, complemented
90C2×#883—31no—
91C2×#883—31no—
92C2×#883D311yescharacteristic, complemented
93C2×#67⋊C4—31no—
94C2×#67⋊C4—31no—
95C2×#879—31no—
96C2×#879—31no—
97C2×#879—31no—
98C2×#879—61no—
99C2×#878—31no—
100C2×#878—31no—
101C2×#878—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C2×C3×#67—24no—
112C2×C3×#67—42no—
113C2×C3×#67C2314yes—
114C2×C3×#67C2314yes—
115C22×C3×Dic3—42no—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2314yes—
123C2×C3×C4×D3—24no—
124C2×C3×C4×D3C2314yes—
125C2×#627—42no—
126C2×#627C2314yes—
127C2×#625—24no—
128C2×#625C2314yes—
129C2×D3×Dic3—42no—
130C2×D3×Dic3—42no—
131C2×D3×Dic3—42no—
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2314yes—
134C2×D3×Dic3C2314yes—
135C32×C22⋊C4C2314yes—
136#3757C2314yes—
137#3757C2314yes—
138C4⋊(C3⋊Dic3)C2314yes—
139#3750C2314yes—
140#3750C2314yes—
141C4×C3⋊Dic3C2314yes—
142C3×#217C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×C4⋊Dic3C2314yes—
147C3×C4⋊Dic3C2314yes—
148C3×C4⋊Dic3C2314yes—
149C3×Dic3⋊C4C2314yes—
150#3724C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160Dic32C2314yes—
161C2×#539—91noSylow
162C22×C3×D4—31no—
163C22×C3×D4—31no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67C2×D311yescharacteristic
169C22×#67C2×D311yescharacteristic
170C23×Dic3—31no—
171C23×Dic3—31no—
172C23×Dic3—31no—
173C23×Dic3C2×D311yescharacteristic
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3C2×D311yescharacteristic
178C22×Dic6—31no—
179C22×Dic6—31no—
180C3×#123—38no—
181C3×#123—38no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C22⋊C4—21no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4C2×D311yescharacteristic
192C2×C3×C22⋊C4C2×D311yescharacteristic
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—61no—
201C2×#217—61no—
202C2×#217C2×D311yescharacteristic
203#939—38no—
204#938—38no—
205#935—38no—
206D4×Dic3—38no—
207#929—38no—
208C4×#67—38no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—38no—
223C2×C4⋊Dic3—61no—
224C2×C4⋊Dic3C2×D311yescharacteristic
225C2×C4⋊Dic3C2×D311yescharacteristic
226C2×C4⋊Dic3C2×D311yescharacteristic
227#924—38no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—31no—
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—61no—
242C2×Dic3⋊C4—61no—
243C2×Dic3⋊C4C2×D311yescharacteristic
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—61no—
249#898—38no—
250#897—38no—
251#896—38no—
252D3×C4⋊C4—38no—
253#890—38no—
254#890—38no—
255#889—38no—
256#889—38no—
257#886C2×D318yescomplemented
258#883—38no—
259#883—38no—
260#883C2×D318yescomplemented
261#67⋊C4—38no—
262#67⋊C4—38no—
263#879—38no—
264#879—38no—
265#879—38no—
266#879—68no—
267#878—38no—
268#878—38no—
269#878—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2412yes—
274C23×C32C2411yescharacteristic
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3#4114yes—
281C22×C3×D3C2412yes—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4C2412yes—
286C2×C32×C4C2412yes—
287C2×C3⋊Dic3—22no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3C2412yes—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C3×#67—28no—
296C3×#67—44no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—44no—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C3×C4×D3—28no—
311#627—44no—
312#625—28no—
313D3×Dic3—44no—
314D3×Dic3—44no—
315D3×Dic3—44no—
316#539—916no—
317C2×#126—91no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#125—91no—
321C2×#123—31no—
322C2×#123—31no—
323C2×#123—91no—
324C2×#123—91no—
325C2×C22⋊Q8—91no—
326C2×C22⋊Q8—91no—
327C2×C22⋊Q8—91no—
328C2×#121—91no—
329C2×C4×D4—91no—
330C2×C4×D4—91no—
331C22×C4⋊C4—91no—
332C24×C3—21no—
333C24×C3—31no—
334C24×C3—31no—
335C24×C3C22×D311yescharacteristic
336C24×C3C22×D311yescharacteristic
337C23×D3C22×D311yescharacteristic
338C23×D3C22×D311yescharacteristic
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C2×C3×D4—64no—
342C2×C3×D4—122no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—64no—
354C22×C3×C4—122no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—24no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—42no—
363C2×#67—64no—
364C2×#67—64no—
365C2×#67C22×D314yes—
366C2×#67C22×D314yes—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—34no—
376C22×Dic3—34no—
377C22×Dic3—34no—
378C22×Dic3—42no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—122no—
384C22×Dic3—122no—
385C22×Dic3—122no—
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D314yes—
393C2×C4×D3—24no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—34no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C2×C4×D3—122no—
400C2×C4×D3C22×D314yes—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—122no—
404C2×Dic6—122no—
405C3×C4⋊C4—34no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—34no—
409C3×C22⋊C4—24no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4C22×D314yes—
415C3×C22⋊C4C22×D314yes—
416#217—34no—
417#217—34no—
418#217—34no—
419#217—34no—
420#217—34no—
421#217—34no—
422#217—34no—
423#217—64no—
424#217—64no—
425#217C22×D314yes—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4C22×D314yes—
430(C2×D3)⋊C4C22×D314yes—
431(C2×D3)⋊C4C22×D314yes—
432C4⋊Dic3—34no—
433C4⋊Dic3—34no—
434C4⋊Dic3—34no—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—34no—
439C4⋊Dic3—64no—
440C4⋊Dic3C22×D314yes—
441C4⋊Dic3C22×D314yes—
442C4⋊Dic3C22×D314yes—
443Dic3⋊C4—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—64no—
457Dic3⋊C4—64no—
458Dic3⋊C4C22×D314yes—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—64no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—44no—
468C22×C32C2×#4112yes—
469C22×C32H(5,𝔽2)12yes—
470C22×C322−1+412yes—
471C22×C32C2511yescharacteristic
472C2×C3×D3—28no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—44no—
479C2×C3×D3C2×#4114yes—
480C32×C4—22no—
481C32×C4—22no—
482C3⋊Dic3—22no—
483C3⋊Dic3—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C22×Q8—91no—
493C22×D4—31no—
494C22×D4—31no—
495C22×D4—91no—
496C23×C4—31no—
497C23×C4—31no—
498C23×C4—91no—
499C23×C4—91no—
500C23×C4—91no—
501#126—98no—
502#126—98no—
503#125—98no—
504#125—98no—
505#123—38no—
506#123—38no—
507#123—98no—
508#123—98no—
509C22⋊Q8—98no—
510C22⋊Q8—98no—
511C22⋊Q8—98no—
512#121—98no—
513C4×D4—98no—
514C4×D4—98no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—98no—
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×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4D3211yescharacteristic
540C2×C42—91no—
541C2×C42—91no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—21no—
550C23×C3—34no—
551C23×C3—32no—
552C23×C3—32no—
553C23×C3—42no—
554C23×C3—42no—
555C23×C3—42no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—62no—
561C23×C3C23×D312yes—
562C23×C3C23×D312yes—
563C23×C3C23×D311yescharacteristic
564C23×C3C23×D311yescharacteristic
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3#23714yes—
571C22×D3C23×D312yes—
572C22×D3C23×D312yes—
573C3×D4—68no—
574C3×D4—124no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—68no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—62no—
593C2×C3×C4—62no—
594C2×C3×C4—62no—
595C2×C3×C4—62no—
596C2×C3×C4—124no—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601#67—28no—
602#67—44no—
603#67—68no—
604#67—68no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—44no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—62no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—122no—
633C2×Dic3—122no—
634C2×Dic3—122no—
635C2×Dic3—122no—
636C2×Dic3—124no—
637C2×Dic3—124no—
638C2×Dic3—124no—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C4×D3—28no—
646C4×D3—124no—
647C4×D3—124no—
648C4×D3—124no—
649Dic6—124no—
650Dic6—124no—
651C2×C32—42no—
652C2×C32#53914yescomplemented
653C2×C32C22×#4111yescharacteristic
654C2×C32C2×H(5,𝔽2)11yescharacteristic
655C2×C32C2×2−1+411yescharacteristic
656C3×D3—24no—
657C3×D3—42no—
658C24—31no—
659C24—31no—
660C24C2×D3211yescharacteristic
661C2×Q8—94no—
662C2×Q8—362no—
663C2×D4—34no—
664C2×D4—34no—
665C2×D4—64no—
666C2×D4—94no—
667C2×D4—122no—
668C2×D4—184no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—34no—
676C22×C4—34no—
677C22×C4—64no—
678C22×C4—94no—
679C22×C4—94no—
680C22×C4—94no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—122no—
686C22×C4—362no—
687C22×C4—362no—
688C22×C4—362no—
689C22×C4C2×D3211yescharacteristic
690C22×C4C2×D3211yescharacteristic
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—94no—
696C4⋊C4—94no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—94no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4C2×D3214yes—
715C42—94no—
716C42—94no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—21no—
727C22×C3—34no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—44no—
732C22×C3—44no—
733C22×C3—68no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—84no—
740C22×C3—124no—
741C22×C3C2×#23712yes—
742C22×C3#100412yes—
743C22×C3D3×#4112yes—
744C22×C3#100912yes—
745C22×C3#101012yes—
746C22×C3#101012yes—
747C22×C3C24×D311yescharacteristic
748C22×C3C24×D311yescharacteristic
749C2×D3—28no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—44no—
756C2×D3C2×#23714yes—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—62no—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—62no—
783Dic3—122no—
784Dic3—122no—
785Dic3—122no—
786Dic3—122no—
787C32C2×#53911yescharacteristic, complemented, Sylow
788C23—22no—
789C23—22no—
790C23—22no—
791C23—34no—
792C23—32no—
793C23—32no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23C22×D3212yes—
800C23C22×D3211yescharacteristic
801Q8—364no—
802D4—68no—
803D4—124no—
804D4—188no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—68no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—92no—
821C2×C4—92no—
822C2×C4—92no—
823C2×C4—92no—
824C2×C4—124no—
825C2×C4—182no—
826C2×C4—182no—
827C2×C4—182no—
828C2×C4—182no—
829C2×C4—364no—
830C2×C4—364no—
831C2×C4—364no—
832C2×C4C22×D3212yes—
833C2×C4C22×D3212yes—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—24no—
838C2×C3—42no—
839C2×C3—42no—
840C2×C3—64no—
841C2×C3—82no—
842C2×C3—122no—
843C2×C3#566014yescomplemented
844C2×C3#566514yescomplemented
845C2×C3C22×#23711yescharacteristic
846C2×C3C2×#100411yescharacteristic
847C2×C3C2×D3×#4111yescharacteristic
848C2×C3C2×#100911yescharacteristic
849C2×C3C2×#101011yescharacteristic
850C2×C3C2×#101011yescharacteristic
851D3—24no—
852D3—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—34no—
857C22—44no—
858C22—62no—
859C22—62no—
860C22—68no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—124no—
865C22#6430712yes—
866C22#6430912yes—
867C22D3×#23712yes—
868C22C23×D3211yescharacteristic
869C4—22no—
870C4—22no—
871C4—62no—
872C4—62no—
873C4—62no—
874C4—62no—
875C4—62no—
876C4—62no—
877C4—182no—
878C4—182no—
879C4—182no—
880C4—182no—
881C3—21no—
882C3C2×#566511yescharacteristic, complemented
883C3C2×#566011yescharacteristic, complemented
884C2—42no—
885C2—64no—
886C2—122no—
887C2#1059412314yesdirect product factor
888C2C2×#6430711yescharacteristic
889C2C2×#6430911yescharacteristic
890C2C2×D3×#23711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63970C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64088C2semidirect
2. C2×C3×#886C2semidirect
3. C2×C3×#883C2semidirect
4. C2×Dic3×#67C2semidirect
6. C2×#63969C2semidirect
7. C2×#63964C2semidirect
8. C2×#63905C2semidirect
9. C2×#63902C2semidirect
10. C2×#63899C2semidirect
11. C2×#63893C2semidirect
12. C2×D3×C4⋊Dic3C2semidirect
13. C2×#63872C2semidirect
14. C2×#63858C2semidirect
15. C2×#63847C2semidirect
16. #10594123C2direct (N × H)
35. #64088C22semidirect
44. C3×#886C22semidirect
45. C3×#883C22semidirect
46. Dic3×#67C22semidirect
48. #63969C22semidirect
56. #63964C22semidirect
61. #63905C22semidirect
62. #63902C22semidirect
63. #63899C22semidirect
64. #63893C22semidirect
65. D3×C4⋊Dic3C22semidirect
66. #63872C22semidirect
67. #63858C22semidirect
68. #63847C22semidirect
89. C2×#886D3semidirect
92. C2×#883D3semidirect
257. #886C2×D3semidirect
260. #883C2×D3semidirect
652. C2×C32#539semidirect
787. C32C2×#539semidirect
843. C2×C3#5660semidirect
844. C2×C3#5665semidirect
882. C3C2×#5665semidirect
883. C3C2×#5660semidirect
887. C2#10594123direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640882
C2×C3×#8862
C2×C3×#8832
C2×Dic3×#672
C2×#639702
C2×#639692
C2×#639642
C2×#639052
C2×#639022
C2×#638992
C2×#638932
C2×D3×C4⋊Dic32
C2×#638722
C2×#638582
C2×#638472
#105941232
C2×#56603
C2×#56653