Finite Group Databasebeta

← C2×#10594935 #11901411

Subgroups — C2×#10594935 #11901411

Order 1152.

2449 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic, complemented
2C2×C3×#929C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×#63970C211yesmaximal, characteristic
5C2×#63969C211yesmaximal, characteristic, complemented
6C2×#63969C211yesmaximal, characteristic, complemented
7C2×#63956C211yesmaximal, characteristic, complemented
8#10594935C2116yesmaximal, direct product factor
9C2×#63896C211yesmaximal, characteristic, complemented
10C2×#63896C211yesmaximal, characteristic, complemented
11C2×#63891C211yesmaximal, characteristic, complemented
12C2×#63879C211yesmaximal, characteristic, complemented
13C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14C2×#63867C211yesmaximal, characteristic, complemented
15C2×#63859C211yesmaximal, characteristic, complemented
16C2×#63845C211yesmaximal, characteristic, complemented
17C2×#5660—31nomaximal
18C2×#5564—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31#64133C2218yescomplemented
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C3×#929C2218yescomplemented
37C3×C4×#67C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45#63970C2218yes—
46#63969C2218yescomplemented
47#63969C2218yescomplemented
48C2×#3724C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×#3724C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59#63956C2218yescomplemented
60C2×Dic32C2211yescharacteristic
61#63896C2218yescomplemented
62#63896C2218yescomplemented
63#63891C2218yescomplemented
64#63879C2218yescomplemented
65D3×Dic3⋊C4C2218yescomplemented
66#63867C2218yescomplemented
67#63859C2218yescomplemented
68#63845C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#938—31no—
73C2×#935—31no—
74C2×#935—31no—
75C2×#929D311yescharacteristic, complemented
76C2×C4×#67—31no—
77C2×C4×#67D311yescharacteristic, complemented
78C2×#924—31no—
79C2×#924—31no—
80C2×#924—61no—
81C22×Dic3⋊C4—31no—
82#5660—316no—
83#5564—316no—
84C2×#896—31no—
85C2×#896—31no—
86C2×D3×C4⋊C4—31no—
87C2×#890—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#886—31no—
91C2×#883—31no—
92C2×#883—31no—
93C2×#883—31no—
94C2×#67⋊C4—31no—
95C2×#879—31no—
96C2×#879—31no—
97C2×#879—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#876—31no—
101C2×#870—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4—42no—
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2314yes—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×#634—42no—
114C2×#634C2314yes—
115C2×C3×#67—24no—
116C2×C3×#67—42no—
117C2×C3×#67C2314yes—
118C2×C3×#67C2314yes—
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×C4×D3—42no—
126C2×C3×C4×D3C2314yes—
127C2×#625—24no—
128C2×#625C2314yes—
129C2×D3×Dic3—24no—
130C2×D3×Dic3—42no—
131C2×D3×Dic3—42no—
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2314yes—
134C2×D3×Dic3C2314yes—
135#3757C2314yes—
136#3757C2314yes—
137C4⋊(C3⋊Dic3)C2314yes—
138#3750C2314yes—
139#3750C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×C4×Dic3C2314yes—
149#3724C2314yes—
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—21no—
165C23×C3×C4—31no—
166C23×C3×C4C2×D311yescharacteristic
167C23×C3×C4C2×D311yescharacteristic
168C22×#67—31no—
169C22×#67—31no—
170C22×#67C2×D311yescharacteristic
171C22×#67C2×D311yescharacteristic
172C23×Dic3—31no—
173C23×Dic3—31no—
174C23×Dic3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3C2×D311yescharacteristic
179C22×Dic6—31no—
180C22×Dic6—31no—
181C22×Dic6—61no—
182C3×#123—38no—
183C3×C4×D4—38no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C42—31no—
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
203C2×#217C2×D311yescharacteristic
204#939—38no—
205#938—38no—
206#935—38no—
207#935—38no—
208#929C2×D318yescomplemented
209C4×#67—38no—
210C4×#67C2×D318yescomplemented
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3—61no—
225#924—38no—
226#924—38no—
227#924—68no—
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—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—38no—
244C2×Dic3⋊C4—61no—
245C2×Dic3⋊C4—61no—
246C2×Dic3⋊C4C2×D311yescharacteristic
247C2×Dic3⋊C4C2×D311yescharacteristic
248C2×Dic3⋊C4C2×D311yescharacteristic
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3C2×D311yescharacteristic
252#896—38no—
253#896—38no—
254D3×C4⋊C4—38no—
255#890—38no—
256#889—38no—
257#889—38no—
258#886—38no—
259#883—38no—
260#883—38no—
261#883—38no—
262#67⋊C4—38no—
263#879—38no—
264#879—38no—
265#879—38no—
266#878—38no—
267#878—38no—
268#876—38no—
269#870—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×C4—44no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3—22no—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C2×C3⋊Dic3C2412yes—
296#634—44no—
297C3×#67—28no—
298C3×#67—44no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C3×C4×D3—44no—
312#625—28no—
313D3×Dic3—28no—
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—91no—
323C2×#123—91no—
324C2×#123—91no—
325C2×C22⋊Q8—91no—
326C2×C22⋊Q8—91no—
327C2×C22⋊Q8—91no—
328C2×#121—91no—
329C2×C4×D4—31no—
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—24no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—34no—
353C22×C3×C4—42no—
354C22×C3×C4—42no—
355C22×C3×C4—44no—
356C22×C3×C4—122no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D314yes—
362C22×C3×C4C22×D314yes—
363C2×#67—24no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—42no—
367C2×#67—64no—
368C2×#67—64no—
369C2×#67C22×D314yes—
370C2×#67C22×D314yes—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—34no—
380C22×Dic3—34no—
381C22×Dic3—34no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—64no—
387C22×Dic3—122no—
388C22×Dic3—122no—
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C2×C4×D3—34no—
396C2×C4×D3—34no—
397C2×C4×D3—34no—
398C2×C4×D3—42no—
399C2×C4×D3—64no—
400C2×C4×D3—122no—
401C2×C4×D3—122no—
402C2×C4×D3C22×D314yes—
403C2×Dic6—34no—
404C2×Dic6—34no—
405C2×Dic6—64no—
406C2×Dic6—122no—
407C2×Dic6—122no—
408C2×Dic6—124no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C42—34no—
418#217—34no—
419#217—34no—
420#217—34no—
421#217—34no—
422#217—34no—
423#217—34no—
424#217—34no—
425#217—64no—
426#217—64no—
427#217C22×D314yes—
428#217C22×D314yes—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4C22×D314yes—
433(C2×D3)⋊C4C22×D314yes—
434(C2×D3)⋊C4C22×D314yes—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—64no—
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—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—64no—
459Dic3⋊C4—64no—
460Dic3⋊C4C22×D314yes—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3C22×D314yes—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—44no—
470C22×C32C2×#4112yes—
471C22×C32H(5,𝔽2)12yes—
472C22×C322−1+412yes—
473C22×C32C2511yescharacteristic
474C2×C3×D3—28no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—44no—
481C2×C3×D3C2×#4114yes—
482C32×C4—22no—
483C32×C4—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—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C22×Q8—91no—
495C22×D4—31no—
496C22×D4—31no—
497C22×D4—91no—
498C23×C4—31no—
499C23×C4—91no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4D3211yescharacteristic
503#126—98no—
504#126—98no—
505#125—98no—
506#125—98no—
507#123—38no—
508#123—98no—
509#123—98no—
510#123—98no—
511C22⋊Q8—98no—
512C22⋊Q8—98no—
513C22⋊Q8—98no—
514#121—98no—
515C4×D4—38no—
516C4×D4—98no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—98no—
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×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C42—31no—
543C2×C42—91no—
544C23×C3—24no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—21no—
553C23×C3—34no—
554C23×C3—32no—
555C23×C3—32no—
556C23×C3—42no—
557C23×C3—42no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—62no—
561C23×C3—62no—
562C23×C3—62no—
563C23×C3C23×D312yes—
564C23×C3C23×D312yes—
565C23×C3C23×D311yescharacteristic
566C23×C3C23×D311yescharacteristic
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3#23514yes—
573C22×D3C23×D312yes—
574C22×D3C23×D312yes—
575C3×D4—68no—
576C3×D4—124no—
577C2×C3×C4—24no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—42no—
591C2×C3×C4—44no—
592C2×C3×C4—44no—
593C2×C3×C4—48no—
594C2×C3×C4—62no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—62no—
598C2×C3×C4—62no—
599C2×C3×C4—62no—
600C2×C3×C4—124no—
601C2×C3×C4C23×D312yes—
602C2×C3×C4C23×D312yes—
603C2×C3×C4C23×D312yes—
604C2×C3×C4C23×D312yes—
605#67—28no—
606#67—44no—
607#67—68no—
608#67—68no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—68no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—122no—
637C2×Dic3—122no—
638C2×Dic3—122no—
639C2×Dic3—122no—
640C2×Dic3—124no—
641C2×Dic3—124no—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C2×Dic3C23×D312yes—
646C2×Dic3C23×D312yes—
647C2×Dic3C23×D312yes—
648C4×D3—44no—
649C4×D3—68no—
650C4×D3—124no—
651C4×D3—124no—
652Dic6—124no—
653Dic6—124no—
654Dic6—128no—
655C2×C32—42no—
656C2×C32#53914yescomplemented
657C2×C32C22×#4111yescharacteristic
658C2×C32C2×H(5,𝔽2)11yescharacteristic
659C2×C32C2×2−1+411yescharacteristic
660C3×D3—24no—
661C3×D3—42no—
662C24—31no—
663C24—31no—
664C24C2×D3211yescharacteristic
665C2×Q8—94no—
666C2×Q8—362no—
667C2×D4—34no—
668C2×D4—34no—
669C2×D4—64no—
670C2×D4—94no—
671C2×D4—122no—
672C2×D4—184no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—34no—
680C22×C4—42no—
681C22×C4—94no—
682C22×C4—94no—
683C22×C4—94no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—91no—
687C22×C4—91no—
688C22×C4—122no—
689C22×C4—184no—
690C22×C4—362no—
691C22×C4—362no—
692C22×C4C2×D3211yescharacteristic
693C22×C4C2×D3211yescharacteristic
694C22×C4C2×D3214yes—
695C4⋊C4—34no—
696C4⋊C4—34no—
697C4⋊C4—34no—
698C4⋊C4—94no—
699C4⋊C4—94no—
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—34no—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C42—34no—
720C42—94no—
721C22×C3—24no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—34no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—48no—
736C22×C3—44no—
737C22×C3—44no—
738C22×C3—68no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—124no—
745C22×C3C2×#23512yes—
746C22×C3#100412yes—
747C22×C3#100412yes—
748C22×C3D3×#4112yes—
749C22×C3#101012yes—
750C22×C3#101012yes—
751C22×C3C24×D311yescharacteristic
752C22×C3C24×D311yescharacteristic
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—28no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—44no—
760C2×D3C2×#23514yes—
761C3×C4—24no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—42no—
767C3×C4—62no—
768C3×C4—62no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—62no—
773Dic3—22no—
774Dic3—22no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—22no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—62no—
783Dic3—62no—
784Dic3—62no—
785Dic3—62no—
786Dic3—62no—
787Dic3—122no—
788Dic3—122no—
789Dic3—122no—
790Dic3—122no—
791C32C2×#53911yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—34no—
796C23—32no—
797C23—32no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23C22×D3212yes—
804C23C22×D3211yescharacteristic
805Q8—364no—
806D4—68no—
807D4—124no—
808D4—188no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—44no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—92no—
825C2×C4—92no—
826C2×C4—92no—
827C2×C4—92no—
828C2×C4—124no—
829C2×C4—188no—
830C2×C4—182no—
831C2×C4—182no—
832C2×C4—182no—
833C2×C4—182no—
834C2×C4—364no—
835C2×C4—364no—
836C2×C4C22×D3212yes—
837C2×C4C22×D3212yes—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—24no—
842C2×C3—44no—
843C2×C3—42no—
844C2×C3—42no—
845C2×C3—64no—
846C2×C3—122no—
847C2×C3#556414yescomplemented
848C2×C3#566014yescomplemented
849C2×C3C22×#23511yescharacteristic
850C2×C3C2×#100411yescharacteristic
851C2×C3C2×#100411yescharacteristic
852C2×C3C2×D3×#4111yescharacteristic
853C2×C3C2×#101011yescharacteristic
854C2×C3C2×#101011yescharacteristic
855D3—24no—
856D3—42no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—34no—
861C22—44no—
862C22—62no—
863C22—62no—
864C22—68no—
865C22—62no—
866C22—62no—
867C22—62no—
868C22—124no—
869C22#6429812yes—
870C22D3×#23512yes—
871C22#6433012yes—
872C22C23×D3211yescharacteristic
873C4—22no—
874C4—22no—
875C4—62no—
876C4—62no—
877C4—62no—
878C4—62no—
879C4—62no—
880C4—62no—
881C4—182no—
882C4—182no—
883C4—182no—
884C4—182no—
885C3—21no—
886C3C2×#556411yescharacteristic, complemented
887C3C2×#566011yescharacteristic, complemented
888C2—42no—
889C2—64no—
890C2—122no—
891C2#1059493514yesdirect product factor
892C2C2×#6429811yescharacteristic
893C2C2×D3×#23511yescharacteristic
894C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×#63970C2
hypercenterC23×C4D32
hypocenterC32C2×#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64133C2semidirect
2. C2×C3×#929C2semidirect
3. C2×C3×C4×#67C2semidirect
5. C2×#63969C2semidirect
6. C2×#63969C2semidirect
7. C2×#63956C2semidirect
8. #10594935C2direct (N × H)
9. C2×#63896C2semidirect
10. C2×#63896C2semidirect
11. C2×#63891C2semidirect
12. C2×#63879C2semidirect
13. C2×D3×Dic3⋊C4C2semidirect
14. C2×#63867C2semidirect
15. C2×#63859C2semidirect
16. C2×#63845C2semidirect
31. #64133C22semidirect
36. C3×#929C22semidirect
37. C3×C4×#67C22semidirect
46. #63969C22semidirect
47. #63969C22semidirect
59. #63956C22semidirect
61. #63896C22semidirect
62. #63896C22semidirect
63. #63891C22semidirect
64. #63879C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. #63867C22semidirect
67. #63859C22semidirect
68. #63845C22semidirect
75. C2×#929D3semidirect
77. C2×C4×#67D3semidirect
208. #929C2×D3semidirect
210. C4×#67C2×D3semidirect
656. C2×C32#539semidirect
791. C32C2×#539semidirect
847. C2×C3#5564semidirect
848. C2×C3#5660semidirect
886. C3C2×#5564semidirect
887. C3C2×#5660semidirect
891. C2#10594935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9292
C2×C3×C4×#672
C2×#639702
C2×#639692
C2×#639562
#105949352
C2×#638962
C2×#638912
C2×#638792
C2×D3×Dic3⋊C42
C2×#638672
C2×#638592
C2×#638452
C2×#56603
C2×#55643