Finite Group Databasebeta

← C2×#10594071 #11902677

Subgroups — C2×#10594071 #11902677

Order 1152.

3297 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#627C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64087C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C211yesmaximal, characteristic
5C2×C3×#878C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic3C211yesmaximal, characteristic
7C2×Dic3×#67C211yesmaximal, characteristic
8C2×#63964C211yesmaximal, characteristic, complemented
9C2×#63918C211yesmaximal, characteristic, complemented
10C2×#63899C211yesmaximal, characteristic, complemented
11C2×#63893C211yesmaximal, characteristic, complemented
12C2×#63851C211yesmaximal, characteristic, complemented
13C2×#63840C211yesmaximal, characteristic, complemented
14C2×#63839C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594071C2116yesmaximal, direct product factor
17C2×#5632—31nomaximal
18C2×D4×Dic6—31nomaximal
19C23×C3⋊Dic3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×#627—28no—
27C22×#627C2211yescharacteristic
28C22×#627C2211yescharacteristic
29C22×#627C2211yescharacteristic
30C22×#627C2211yescharacteristic
31C22×#627C2211yescharacteristic
32C22×#627C2218yescomplemented
33C22×D3×Dic3C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic
35C2×D3×Dic6—28no—
36C2×D3×Dic6C2218yescomplemented
37C2×C32×C22⋊C4C2211yescharacteristic
38C2×#3757C2211yescharacteristic
39C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
40C2×#3750C2211yescharacteristic
41C2×#3750C2211yescharacteristic
42#64087C2218yescomplemented
43C2×C3×#217C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×C4⋊Dic3C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×C4×Dic3C2211yescharacteristic
50C3×#67⋊C4C2218yes—
51C3×#878C2218yescomplemented
52#67⋊Dic3C2218yes—
53Dic3×#67C2218yes—
54C2×#3724C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2211yescharacteristic
57C2×Dic3⋊Dic3C2211yescharacteristic
58C2×Dic3⋊Dic3C2211yescharacteristic
59#63964C2218yescomplemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64#63918C2218yescomplemented
65#63899C2218yescomplemented
66#63893C2218yescomplemented
67#63851C2218yescomplemented
68#63840C2218yescomplemented
69#63839C2218yescomplemented
70#63837C2218yescomplemented
71C22×D3×Q8—31no—
72C23×Dic6—31no—
73C23×Dic6—31no—
74C23×Dic6—31no—
75C2×C3×C22⋊Q8—31no—
76C2×C3×C4×D4—31no—
77C2×#944—31no—
78C2×D4×Dic3—31no—
79C2×D4×Dic3—31no—
80C2×C4×#67—31no—
81C2×#924—31no—
82C2×#924—31no—
83#5632—316no—
84D4×Dic6—316no—
85C2×#897—31no—
86C2×#896—31no—
87C2×#896—31no—
88C2×#888—31no—
89C2×#888—31no—
90C2×#888—31no—
91C2×#888—31no—
92C2×#887—31no—
93C2×#67⋊C4—31no—
94C2×#67⋊C4D311yescharacteristic
95C2×#878—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—61no—
101C2×#878D311yescharacteristic, complemented
102C2×#869—31no—
103C2×C4×Dic6—31no—
104C24×C32C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3—24no—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2314yes—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C2×#634—24no—
115C2×#634C2314yes—
116C2×C3×#67Q818yescomplemented
117C2×C3×#67C2314yes—
118C22×C3×Dic3—24no—
119C22×C3×Dic3—24no—
120C22×C3×Dic3C2314yes—
121C22×C3×Dic3C2314yes—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—24no—
130C2×C3×C4×D3C2314yes—
131C2×C3×Dic6—24no—
132C2×C3×Dic6C2314yes—
133C2×#627—24no—
134C2×#627—24no—
135C2×#627—24no—
136C2×#627—24no—
137C2×#627—232no—
138C2×#627D418yescomplemented
139C2×#627C2314yes—
140C2×#627C2314yes—
141C2×#627C2314yes—
142C2×#627C2314yes—
143C2×#627C2314yes—
144C2×D3×Dic3—24no—
145C2×D3×Dic3—24no—
146C2×D3×Dic3C2314yes—
147C2×D3×Dic3C2314yes—
148D3×Dic6—232no—
149C32×C22⋊C4C2314yes—
150#3757C2314yes—
151C4⋊(C3⋊Dic3)C2314yes—
152#3750C2314yes—
153#3750C2314yes—
154C3×#217C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×C4⋊Dic3C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×C4×Dic3C2314yes—
161#3724C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164Dic3⋊Dic3C2314yes—
165Dic3⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168Dic32C2314yes—
169Dic32C2314yes—
170C2×D4×Q8—91noSylow
171C22×C3×Q8—31no—
172C22×C3×D4—31no—
173C23×C3×C4—31no—
174C23×C3×C4—31no—
175C23×C3×C4—31no—
176C22×#67C2×D311yescharacteristic
177C23×Dic3—31no—
178C23×Dic3—31no—
179C23×Dic3—31no—
180C23×Dic3—31no—
181C23×Dic3—61no—
182C23×Dic3C2×D311yescharacteristic
183C23×Dic3C2×D311yescharacteristic
184C2×D3×Q8—38no—
185C2×D3×Q8—68no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3C2×D311yescharacteristic
189C22×Dic6—31no—
190C22×Dic6—31no—
191C22×Dic6—31no—
192C22×Dic6—31no—
193C22×Dic6—38no—
194C22×Dic6—31no—
195C22×Dic6—31no—
196C22×Dic6—31no—
197C22×Dic6—31no—
198C22×Dic6—31no—
199C22×Dic6—31no—
200C22×Dic6—31no—
201C22×Dic6—38no—
202C22×Dic6—31no—
203C22×Dic6—38no—
204C22×Dic6—61no—
205C22×Dic6—68no—
206C22×Dic6—68no—
207C22×Dic6—68no—
208C22×Dic6C2×D311yescharacteristic
209C3×C22⋊Q8—38no—
210C3×C4×D4—38no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C4⋊C4—31no—
214C2×C3×C4⋊C4—31no—
215C2×C3×C22⋊C4—21no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C22⋊C4C2×D311yescharacteristic
219C2×C3×C22⋊C4C2×D311yescharacteristic
220C2×C3×C42—31no—
221C2×#217—31no—
222C2×#217—31no—
223C2×#217—31no—
224C2×#217—31no—
225C2×#217—61no—
226C2×#217C2×D311yescharacteristic
227#944—38no—
228D4×Dic3—38no—
229D4×Dic3—38no—
230C4×#67—38no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4C2×D311yescharacteristic
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3—31no—
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3—61no—
241C2×C4⋊Dic3C2×D311yescharacteristic
242#924—38no—
243#924—38no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—61no—
255C2×Dic3⋊C4—61no—
256C2×Dic3⋊C4C2×D311yescharacteristic
257C2×Dic3⋊C4C2×D311yescharacteristic
258C2×Dic3⋊C4C2×D311yescharacteristic
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3—31no—
262C2×C4×Dic3—31no—
263C2×C4×Dic3C2×D311yescharacteristic
264#897—38no—
265#896—38no—
266#896—38no—
267#888—38no—
268#888—38no—
269#888—38no—
270#888—38no—
271#887—38no—
272#67⋊C4—38no—
273#67⋊C4C2×D318yes—
274#878—38no—
275#878—38no—
276#878—38no—
277#878—38no—
278#878—38no—
279#878—68no—
280#878C2×D318yescomplemented
281#869—38no—
282C4×Dic6—38no—
283C23×C32—22no—
284C23×C32—22no—
285C23×C32C2×Q814yescomplemented
286C23×C32C2412yes—
287C23×C32C2411yescharacteristic
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3C2×Q814yescomplemented
291C22×C3×D3C2412yes—
292C2×C32×C4—22no—
293C2×C32×C4—22no—
294C2×C32×C4C2412yes—
295C2×C32×C4C2412yes—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—28no—
300C2×C3⋊Dic3C2×D414yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
304C2×C3⋊Dic3C2412yes—
305#634—28no—
306C3×#67C2×Q8116yescomplemented
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—28no—
312C2×C3×Dic3—28no—
313C2×C3×Dic3C2×D414yes—
314C2×C3×Dic3C2×D414yes—
315C2×C3×Dic3C2×Q814yescomplemented
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C3×C4×D3—28no—
324C3×Dic6—28no—
325#627—28no—
326#627—28no—
327#627—28no—
328#627—28no—
329#627C2×D4116yescomplemented
330D3×Dic3—28no—
331D3×Dic3—28no—
332C23×Q8—91no—
333C23×Q8—91no—
334D4×Q8—916no—
335C2×C4⋊Q8—91no—
336C2×C4⋊Q8—91no—
337C2×C4⋊Q8—91no—
338C2×C22⋊Q8—31no—
339C2×C22⋊Q8—91no—
340C2×C22⋊Q8—91no—
341C2×C22⋊Q8—91no—
342C2×C22⋊Q8—91no—
343C2×C22⋊Q8—91no—
344C2×C4×Q8—91no—
345C2×C4×D4—31no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C24×C3—21no—
349C24×C3—31no—
350C24×C3C22×D311yescharacteristic
351C24×C3C22×D311yescharacteristic
352C23×D3C22×D311yescharacteristic
353C2×C3×Q8—34no—
354C2×C3×Q8—64no—
355C2×C3×D4—38no—
356C2×C3×D4—34no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—34no—
367C22×C3×C4—34no—
368C22×C3×C4—34no—
369C22×C3×C4—64no—
370C22×C3×C4—64no—
371C22×C3×C4—64no—
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C2×#67Dic618yescomplemented
377C2×#67C22×D314yes—
378C22×Dic3—24no—
379C22×Dic3—24no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—34no—
383C22×Dic3—34no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—34no—
391C22×Dic3—34no—
392C22×Dic3—61no—
393C22×Dic3—64no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—64no—
398C22×Dic3—64no—
399C22×Dic3—64no—
400C22×Dic3—64no—
401C22×Dic3—124no—
402C22×Dic3C22×D314yes—
403C22×Dic3C22×D314yes—
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411D3×Q8—632no—
412C2×C4×D3—24no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—64no—
416C2×C4×D3—64no—
417C2×C4×D3C22×D314yes—
418C2×Dic6—24no—
419C2×Dic6—38no—
420C2×Dic6—38no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—34no—
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—34no—
429C2×Dic6—34no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—34no—
433C2×Dic6—64no—
434C2×Dic6—632no—
435C2×Dic6—632no—
436C2×Dic6—632no—
437C2×Dic6—64no—
438C2×Dic6—64no—
439C2×Dic6—64no—
440C2×Dic6—64no—
441C2×Dic6—64no—
442C2×Dic6—64no—
443C2×Dic6—64no—
444C2×Dic6—64no—
445C2×Dic6—64no—
446C2×Dic6—64no—
447C2×Dic6—124no—
448C2×Dic6C22×D314yes—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—34no—
453C3×C22⋊C4—24no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4C22×D314yes—
457C3×C22⋊C4C22×D314yes—
458C3×C42—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—64no—
464#217C22×D314yes—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4C22×D314yes—
468C4⋊Dic3—34no—
469C4⋊Dic3—34no—
470C4⋊Dic3—34no—
471C4⋊Dic3—34no—
472C4⋊Dic3—34no—
473C4⋊Dic3—34no—
474C4⋊Dic3—64no—
475C4⋊Dic3C22×D314yes—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—34no—
480Dic3⋊C4—34no—
481Dic3⋊C4—34no—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—64no—
487Dic3⋊C4—64no—
488Dic3⋊C4C22×D314yes—
489Dic3⋊C4C22×D314yes—
490Dic3⋊C4C22×D314yes—
491C4×Dic3—34no—
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3—34no—
495C4×Dic3C22×D314yes—
496C22×C32—28no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32C22×D412yes—
500C22×C32C22×Q812yes—
501C22×C32C22×Q814yescomplemented
502C22×C322−1+412yes—
503C22×C32C2511yescharacteristic
504C2×C3×D3—28no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3C22×Q814yescomplemented
508C32×C4—22no—
509C32×C4—22no—
510C3⋊Dic3—22no—
511C3⋊Dic3—22no—
512C3⋊Dic3—22no—
513C3⋊Dic3C22×D414yes—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—22no—
517C3×Dic3—22no—
518C3×Dic3C22×D414yes—
519C3×Dic3C22×D414yes—
520C3×Dic3C22×Q814yescomplemented
521C22×Q8—31no—
522C22×Q8—91no—
523C22×Q8—91no—
524C22×Q8—91no—
525C22×Q8—91no—
526C22×Q8—91no—
527C22×Q8—98no—
528C22×Q8—98no—
529C22×Q8—91no—
530C22×Q8—188no—
531C22×Q8—188no—
532C22×D4—31no—
533C23×C4—31no—
534C23×C4—31no—
535C23×C4—31no—
536C23×C4—91no—
537C23×C4—91no—
538C23×C4—91no—
539C4⋊Q8—98no—
540C4⋊Q8—98no—
541C4⋊Q8—98no—
542C22⋊Q8—38no—
543C22⋊Q8—98no—
544C22⋊Q8—98no—
545C22⋊Q8—98no—
546C22⋊Q8—98no—
547C22⋊Q8—98no—
548C4×Q8—98no—
549C4×D4—38no—
550C4×D4—98no—
551C4×D4—98no—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—31no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—31no—
556C2×C4⋊C4—91no—
557C2×C4⋊C4—91no—
558C2×C4⋊C4—91no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—91no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4D3211yescharacteristic
570C2×C42—31no—
571C2×C42—91no—
572C2×C42—91no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—21no—
579C23×C3—24no—
580C23×C3—34no—
581C23×C3—32no—
582C23×C3—42no—
583C23×C3—42no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3C2×Dic614yescomplemented
587C23×C3D3×Q814yescomplemented
588C23×C3C23×D312yes—
589C23×C3C23×D312yes—
590C23×C3C23×D311yescharacteristic
591C23×C3C23×D311yescharacteristic
592C22×D3—22no—
593C22×D3—22no—
594C22×D3C2×Dic614yescomplemented
595C22×D3C23×D312yes—
596C3×Q8—68no—
597C3×D4—316no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—34no—
605C2×C3×C4—34no—
606C2×C3×C4—34no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—42no—
615C2×C3×C4—42no—
616C2×C3×C4—68no—
617C2×C3×C4—68no—
618C2×C3×C4—68no—
619C2×C3×C4—62no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4C23×D312yes—
624C2×C3×C4C23×D312yes—
625C2×C3×C4C23×D312yes—
626C2×C3×C4C23×D312yes—
627#67C2×Dic6116yescomplemented
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—28no—
633C2×Dic3—28no—
634C2×Dic3—34no—
635C2×Dic3—34no—
636C2×Dic3—32no—
637C2×Dic3—32no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—64no—
645C2×Dic3—62no—
646C2×Dic3—62no—
647C2×Dic3—62no—
648C2×Dic3—62no—
649C2×Dic3—68no—
650C2×Dic3—68no—
651C2×Dic3—68no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—68no—
659C2×Dic3—128no—
660C2×Dic3—122no—
661C2×Dic3—122no—
662C2×Dic3—122no—
663C2×Dic3C2×Dic614yescomplemented
664C2×Dic3D3×D414yes—
665C2×Dic3D3×D414yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C4×D3—28no—
674C4×D3—68no—
675C4×D3—68no—
676Dic6—28no—
677Dic6—316no—
678Dic6—316no—
679Dic6—68no—
680Dic6—68no—
681Dic6—68no—
682Dic6—68no—
683Dic6—68no—
684Dic6—68no—
685Dic6—68no—
686Dic6—68no—
687Dic6—68no—
688Dic6—68no—
689Dic6—128no—
690C2×C32—24no—
691C2×C32D4×Q814yescomplemented
692C2×C32C23×D411yescharacteristic
693C2×C32C23×Q811yescharacteristic
694C2×C32C2×2−1+411yescharacteristic
695C3×D3—24no—
696C24—31no—
697C24C2×D3211yescharacteristic
698C2×Q8—34no—
699C2×Q8—64no—
700C2×Q8—94no—
701C2×Q8—98no—
702C2×Q8—94no—
703C2×Q8—94no—
704C2×Q8—94no—
705C2×Q8—94no—
706C2×Q8—94no—
707C2×Q8—184no—
708C2×Q8—184no—
709C2×Q8—184no—
710C2×Q8—184no—
711C2×Q8—184no—
712C2×Q8—1832no—
713C2×Q8—1832no—
714C2×D4—34no—
715C2×D4—38no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—34no—
720C22×C4—34no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—34no—
726C22×C4—64no—
727C22×C4—64no—
728C22×C4—64no—
729C22×C4—94no—
730C22×C4—94no—
731C22×C4—91no—
732C22×C4—94no—
733C22×C4—91no—
734C22×C4—91no—
735C22×C4—91no—
736C22×C4—184no—
737C22×C4—184no—
738C22×C4—184no—
739C22×C4C2×D3211yescharacteristic
740C22×C4C2×D3211yescharacteristic
741C4⋊C4—34no—
742C4⋊C4—34no—
743C4⋊C4—34no—
744C4⋊C4—34no—
745C4⋊C4—94no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C22⋊C4—34no—
754C22⋊C4—34no—
755C22⋊C4—94no—
756C22⋊C4—94no—
757C22⋊C4—94no—
758C22⋊C4C2×D3214yes—
759C42—34no—
760C42—94no—
761C42—94no—
762C22×C3—28no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—28no—
768C22×C3—22no—
769C22×C3—24no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—21no—
773C22×C3—34no—
774C22×C3—42no—
775C22×C3—48no—
776C22×C3—42no—
777C22×C3—68no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3C22×Dic612yes—
781C22×C3C22×Dic614yescomplemented
782C22×C3C2×D3×D412yes—
783C22×C3C2×D3×D412yes—
784C22×C3C2×D3×Q812yes—
785C22×C3C2×D3×Q814yescomplemented
786C22×C3#101012yes—
787C22×C3#101012yes—
788C22×C3C24×D311yescharacteristic
789C22×C3C24×D311yescharacteristic
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—28no—
793C2×D3C22×Dic614yescomplemented
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—34no—
799C3×C4—34no—
800C3×C4—34no—
801C3×C4—42no—
802C3×C4—42no—
803C3×C4—62no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—62no—
807Dic3—22no—
808Dic3—22no—
809Dic3—22no—
810Dic3—22no—
811Dic3—34no—
812Dic3—34no—
813Dic3—64no—
814Dic3—62no—
815Dic3—62no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—122no—
821Dic3—122no—
822Dic3—122no—
823Dic3C22×Dic614yescomplemented
824Dic3C2×D3×D414yes—
825Dic3C2×D3×D414yes—
826C32C2×D4×Q811yescharacteristic, complemented, Sylow
827C23—22no—
828C23—22no—
829C23—34no—
830C23—32no—
831C23—62no—
832C23—62no—
833C23D3×Dic614yescomplemented
834C23C22×D3212yes—
835C23C22×D3211yescharacteristic
836Q8—68no—
837Q8—916no—
838Q8—188no—
839Q8—188no—
840Q8—188no—
841Q8—188no—
842Q8—188no—
843D4—316no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—34no—
847C2×C4—34no—
848C2×C4—34no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—68no—
857C2×C4—68no—
858C2×C4—68no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—94no—
864C2×C4—92no—
865C2×C4—92no—
866C2×C4—92no—
867C2×C4—92no—
868C2×C4—188no—
869C2×C4—188no—
870C2×C4—188no—
871C2×C4—182no—
872C2×C4—182no—
873C2×C4—182no—
874C2×C4C22×D3212yes—
875C2×C4C22×D3212yes—
876C2×C3—24no—
877C2×C3—24no—
878C2×C3—24no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—44no—
883C2×C3—64no—
884C2×C3D4×Dic614yescomplemented
885C2×C3#563214yescomplemented
886C2×C3C23×Dic611yescharacteristic
887C2×C3C22×D3×D411yescharacteristic
888C2×C3C22×D3×D411yescharacteristic
889C2×C3C22×D3×Q811yescharacteristic
890C2×C3C2×#101011yescharacteristic
891C2×C3C2×#101011yescharacteristic
892D3—24no—
893C22—28no—
894C22—22no—
895C22—22no—
896C22—34no—
897C22—68no—
898C22—62no—
899C22—62no—
900C22C2×D3×Dic612yes—
901C22C2×D3×Dic614yescomplemented
902C22#6430912yes—
903C22D32×D412yes—
904C22C23×D3211yescharacteristic
905C4—22no—
906C4—22no—
907C4—34no—
908C4—34no—
909C4—34no—
910C4—62no—
911C4—62no—
912C4—62no—
913C4—62no—
914C4—94no—
915C4—182no—
916C4—182no—
917C4—182no—
918C3—21no—
919C3C2×D4×Dic611yescharacteristic, complemented
920C3C2×#563211yescharacteristic, complemented
921C2—24no—
922C2—64no—
923C2#1059407114yesdirect product factor
924C2C22×D3×Dic611yescharacteristic
925C2C2×#6430911yescharacteristic
926C2C2×D32×D411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#627C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×#64087C2semidirect
5. C2×C3×#878C2semidirect
8. C2×#63964C2semidirect
9. C2×#63918C2semidirect
10. C2×#63899C2semidirect
11. C2×#63893C2semidirect
12. C2×#63851C2semidirect
13. C2×#63840C2semidirect
14. C2×#63839C2semidirect
15. C2×#63837C2semidirect
16. #10594071C2direct (N × H)
32. C22×#627C22semidirect
36. C2×D3×Dic6C22semidirect
42. #64087C22semidirect
51. C3×#878C22semidirect
59. #63964C22semidirect
64. #63918C22semidirect
65. #63899C22semidirect
66. #63893C22semidirect
67. #63851C22semidirect
68. #63840C22semidirect
69. #63839C22semidirect
70. #63837C22semidirect
101. C2×#878D3semidirect
116. C2×C3×#67Q8semidirect
138. C2×#627D4semidirect
280. #878C2×D3semidirect
285. C23×C32C2×Q8semidirect
290. C22×C3×D3C2×Q8semidirect
306. C3×#67C2×Q8semidirect
315. C2×C3×Dic3C2×Q8semidirect
329. #627C2×D4semidirect
376. C2×#67Dic6semidirect
501. C22×C32C22×Q8semidirect
507. C2×C3×D3C22×Q8semidirect
520. C3×Dic3C22×Q8semidirect
586. C23×C3C2×Dic6semidirect
587. C23×C3D3×Q8semidirect
594. C22×D3C2×Dic6semidirect
627. #67C2×Dic6semidirect
663. C2×Dic3C2×Dic6semidirect
691. C2×C32D4×Q8semidirect
781. C22×C3C22×Dic6semidirect
785. C22×C3C2×D3×Q8semidirect
793. C2×D3C22×Dic6semidirect
823. Dic3C22×Dic6semidirect
826. C32C2×D4×Q8semidirect
833. C23D3×Dic6semidirect
884. C2×C3D4×Dic6semidirect
885. C2×C3#5632semidirect
901. C22C2×D3×Dic6semidirect
919. C3C2×D4×Dic6semidirect
920. C3C2×#5632semidirect
923. C2#10594071direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×D3×Dic62
C2×#640872
C2×C3×#67⋊C42
C2×C3×#8782
C2×#67⋊Dic32
C2×Dic3×#672
C2×#639642
C2×#639182
C2×#638992
C2×#638932
C2×#638512
C2×#638402
C2×#638392
C2×#638372
#105940712
C2×#56323
C2×D4×Dic63