Finite Group Databasebeta

← C2×#10595260 #11910265

Subgroups — C2×#10595260 #11910265

Order 1152.

2475 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×#63969C211yesmaximal, characteristic, complemented
8C2×#63964C211yesmaximal, characteristic, complemented
9C2×#63961C211yesmaximal, characteristic, complemented
10C2×#63959C211yesmaximal, characteristic, complemented
11C2×#63959C211yesmaximal, characteristic, complemented
12#10595260C2116yesmaximal, direct product factor
13C2×#63905C211yesmaximal, characteristic, complemented
14C2×#63899C211yesmaximal, characteristic, complemented
15C2×#63851C211yesmaximal, characteristic, complemented
16C2×#63847C211yesmaximal, characteristic, complemented
17C2×#5621—31nomaximal
18C2×#5621—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×#627C2211yescharacteristic
28C22×#627C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34#64144C2218yescomplemented
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C3×#939C2218yescomplemented
41C3×#938C2218yescomplemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×C4⋊Dic3C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45#63982C2218yescomplemented
46#63980C2218yescomplemented
47#63970C2218yescomplemented
48#63969C2218yescomplemented
49C2×#3724C2211yescharacteristic
50C2×#3724C2211yescharacteristic
51C2×#3724C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55#63964C2218yescomplemented
56#63961C2218yescomplemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62#63959C2218yescomplemented
63#63959C2218yescomplemented
64C2×Dic32C2211yescharacteristic
65#63905C2218yescomplemented
66#63899C2218yescomplemented
67#63851C2218yescomplemented
68#63847C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×#121—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#939D311yescharacteristic, complemented
75C2×#938—31no—
76C2×#938D311yescharacteristic, complemented
77C2×#936—31no—
78C2×#936—31no—
79C2×#935—31no—
80C2×#935—31no—
81C2×#935—31no—
82C2×#935—31no—
83C2×#935—61no—
84C2×#929—31no—
85C2×#929—31no—
86C2×#924—31no—
87C2×#924—31no—
88#5621—316no—
89#5621—316no—
90C2×#896—31no—
91C2×#896—31no—
92C2×#889—31no—
93C2×#889—31no—
94C2×#885—31no—
95C2×#885—31no—
96C2×#883—31no—
97C2×#883—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—31no—
101C2×#878—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C2×C32×D4—42no—
107C2×C32×D4C2314yes—
108C22×C32×C4C2311yescharacteristic
109C22×C3⋊Dic3—42no—
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2314yes—
115C2×C3×#67—42no—
116C2×C3×#67—42no—
117C2×C3×#67—42no—
118C2×C3×#67—42no—
119C2×C3×#67C2314yes—
120C2×C3×#67C2314yes—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C22×C3×Dic3—42no—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2314yes—
131C2×C3×C4×D3—42no—
132C2×C3×C4×D3C2314yes—
133C2×#627—42no—
134C2×#627—42no—
135C2×#627C2314yes—
136C2×#627C2314yes—
137C2×#625—42no—
138C2×#625C2314yes—
139C2×D3×Dic3—42no—
140C2×D3×Dic3C2314yes—
141#3757C2314yes—
142#3757C2314yes—
143#3757C2314yes—
144#3750C2314yes—
145#3750C2314yes—
146C3×#217C2314yes—
147C3×#217C2314yes—
148C3×#217C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×C4⋊Dic3C2314yes—
151C3×Dic3⋊C4C2314yes—
152#3724C2314yes—
153#3724C2314yes—
154#3724C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164C2×#562—91noSylow
165C22×C3×D4—21no—
166C22×C3×D4—31no—
167C22×C3×D4—31no—
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C22×C3×D4C2×D311yescharacteristic
171C22×C3×D4C2×D311yescharacteristic
172C23×C3×C4—31no—
173C23×C3×C4—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67C2×D311yescharacteristic
177C22×#67C2×D311yescharacteristic
178C22×#67C2×D311yescharacteristic
179C22×#67C2×D311yescharacteristic
180C23×Dic3—31no—
181C23×Dic3—31no—
182C23×Dic3—31no—
183C23×Dic3—61no—
184C23×Dic3C2×D311yescharacteristic
185C22×C4×D3—31no—
186C22×C4×D3C2×D311yescharacteristic
187C22×Dic6—31no—
188C22×Dic6—31no—
189C22×Dic6—31no—
190C22×Dic6—31no—
191C3×#121—38no—
192C3×#121—38no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—61no—
211C2×#217—61no—
212C2×#217—61no—
213C2×#217C2×D311yescharacteristic
214C2×#217C2×D311yescharacteristic
215C2×#217C2×D311yescharacteristic
216#939—38no—
217#939—38no—
218#939—38no—
219#939C2×D318yescomplemented
220#938—38no—
221#938C2×D318yescomplemented
222#936—38no—
223#936—38no—
224#935—38no—
225#935—38no—
226#935—38no—
227#935—38no—
228#935—68no—
229#929—38no—
230#929—38no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4C2×D311yescharacteristic
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3—31no—
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3C2×D311yescharacteristic
241#924—38no—
242#924—38no—
243C2×Dic3⋊C4—31no—
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—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—61no—
257C2×Dic3⋊C4—61no—
258C2×Dic3⋊C4C2×D311yescharacteristic
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261#896—38no—
262#896—38no—
263#889—38no—
264#889—38no—
265#885—38no—
266#885—38no—
267#883—38no—
268#883—38no—
269#878—38no—
270#878—38no—
271#878—38no—
272#878—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32C2412yes—
280C23×C32C2412yes—
281C23×C32C2411yescharacteristic
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C32×D4—44no—
291C2×C32×C4—22no—
292C2×C32×C4C2412yes—
293C2×C3⋊Dic3—22no—
294C2×C3⋊Dic3—22no—
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—44no—
298C2×C3⋊Dic3C2412yes—
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C3×#67—44no—
303C3×#67—44no—
304C3×#67—44no—
305C3×#67—44no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—44no—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C3×C4×D3—44no—
320#627—44no—
321#627—44no—
322#625—44no—
323D3×Dic3—44no—
324#562—916no—
325C2×#125—91no—
326C2×#124—91no—
327C2×#124—91no—
328C2×#123—91no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×C22⋊Q8—91no—
335C2×C22⋊Q8—91no—
336C2×#121—31no—
337C2×#121—31no—
338C2×#121—91no—
339C2×#121—91no—
340C24×C3—21no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3—31no—
344C24×C3C22×D311yescharacteristic
345C24×C3C22×D311yescharacteristic
346C24×C3C22×D311yescharacteristic
347C24×C3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C2×C3×D4—24no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—34no—
354C2×C3×D4—34no—
355C2×C3×D4—42no—
356C2×C3×D4—42no—
357C2×C3×D4—44no—
358C2×C3×D4—122no—
359C2×C3×D4—122no—
360C2×C3×D4—122no—
361C2×C3×D4—122no—
362C2×C3×D4C22×D314yes—
363C2×C3×D4C22×D314yes—
364C22×C3×C4—21no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—34no—
372C22×C3×C4—34no—
373C22×C3×C4—122no—
374C22×C3×C4—122no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—42no—
380C2×#67—42no—
381C2×#67—42no—
382C2×#67—42no—
383C2×#67—122no—
384C2×#67—122no—
385C2×#67C22×D314yes—
386C2×#67C22×D314yes—
387C2×#67C22×D314yes—
388C2×#67C22×D314yes—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—34no—
398C22×Dic3—34no—
399C22×Dic3—34no—
400C22×Dic3—42no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—61no—
405C22×Dic3—64no—
406C22×Dic3—122no—
407C22×Dic3—122no—
408C22×Dic3—122no—
409C22×Dic3—124no—
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D314yes—
417C2×C4×D3—34no—
418C2×C4×D3—42no—
419C2×C4×D3—122no—
420C2×C4×D3C22×D314yes—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—122no—
426C2×Dic6—122no—
427C2×Dic6—122no—
428C2×Dic6—122no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435#217—34no—
436#217—34no—
437#217—34no—
438#217—34no—
439#217—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—34no—
445#217—34no—
446#217—64no—
447#217—64no—
448#217—64no—
449#217C22×D314yes—
450#217C22×D314yes—
451#217C22×D314yes—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4C22×D314yes—
458C4⋊Dic3—34no—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3C22×D314yes—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—64no—
476Dic3⋊C4—64no—
477Dic3⋊C4C22×D314yes—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—44no—
487C22×C32—44no—
488C22×C32H(5,𝔽2)12yes—
489C22×C32H(5,𝔽2)12yes—
490C22×C322−1+412yes—
491C22×C32C2511yescharacteristic
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—44no—
499C2×C3×D3—44no—
500C32×C4—22no—
501C3⋊Dic3—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C22×Q8—91no—
512C22×Q8—91no—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—31no—
516C22×D4—31no—
517C22×D4—91no—
518C22×D4D3211yescharacteristic
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—91no—
522C23×C4—91no—
523#125—98no—
524#124—98no—
525#124—98no—
526#123—98no—
527#123—98no—
528#123—98no—
529#123—98no—
530C22⋊Q8—98no—
531C22⋊Q8—98no—
532C22⋊Q8—98no—
533C22⋊Q8—98no—
534#121—38no—
535#121—38no—
536#121—98no—
537#121—98no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4—91no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C42—91no—
561C23×C3—24no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—21no—
577C23×C3—32no—
578C23×C3—32no—
579C23×C3—42no—
580C23×C3—42no—
581C23×C3—42no—
582C23×C3—42no—
583C23×C3—42no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3C23×D312yes—
591C23×C3C23×D312yes—
592C23×C3C23×D312yes—
593C23×C3C23×D312yes—
594C23×C3C23×D311yescharacteristic
595C23×C3C23×D311yescharacteristic
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3C23×D312yes—
603C22×D3C23×D312yes—
604C3×D4—44no—
605C3×D4—44no—
606C3×D4—48no—
607C3×D4—124no—
608C3×D4—124no—
609C3×D4—124no—
610C3×D4—124no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—42no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—124no—
628C2×C3×C4—124no—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631#67—44no—
632#67—44no—
633#67—44no—
634#67—44no—
635#67—124no—
636#67—124no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—44no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—122no—
665C2×Dic3—122no—
666C2×Dic3—122no—
667C2×Dic3—122no—
668C2×Dic3—124no—
669C2×Dic3—124no—
670C2×Dic3—124no—
671C2×Dic3—128no—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C4×D3—44no—
679C4×D3—124no—
680Dic6—124no—
681Dic6—124no—
682Dic6—124no—
683Dic6—124no—
684C2×C32—42no—
685C2×C32—42no—
686C2×C32#56214yescomplemented
687C2×C32C2×H(5,𝔽2)11yescharacteristic
688C2×C32C2×H(5,𝔽2)11yescharacteristic
689C2×C32C2×2−1+411yescharacteristic
690C3×D3—42no—
691C3×D3—42no—
692C24—31no—
693C24—31no—
694C24C2×D3211yescharacteristic
695C24C2×D3211yescharacteristic
696C2×Q8—94no—
697C2×Q8—94no—
698C2×Q8—362no—
699C2×Q8—362no—
700C2×D4—34no—
701C2×D4—34no—
702C2×D4—34no—
703C2×D4—34no—
704C2×D4—42no—
705C2×D4—94no—
706C2×D4—122no—
707C2×D4—122no—
708C2×D4—122no—
709C2×D4—122no—
710C2×D4—362no—
711C2×D4C2×D3214yes—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—34no—
719C22×C4—34no—
720C22×C4—94no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—91no—
725C22×C4—94no—
726C22×C4—122no—
727C22×C4—122no—
728C22×C4—362no—
729C22×C4—362no—
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C42—94no—
754C22×C3—24no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—21no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—48no—
777C22×C3—44no—
778C22×C3—44no—
779C22×C3—44no—
780C22×C3—44no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—84no—
788C22×C3—124no—
789C22×C3—124no—
790C22×C3#100412yes—
791C22×C3#100412yes—
792C22×C3#100412yes—
793C22×C3#100412yes—
794C22×C3#101012yes—
795C22×C3#101012yes—
796C22×C3C24×D311yescharacteristic
797C22×C3C24×D311yescharacteristic
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—44no—
805C2×D3—44no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—42no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—62no—
815Dic3—22no—
816Dic3—22no—
817Dic3—22no—
818Dic3—22no—
819Dic3—22no—
820Dic3—22no—
821Dic3—62no—
822Dic3—62no—
823Dic3—62no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—62no—
829Dic3—122no—
830Dic3—122no—
831Dic3—122no—
832Dic3—122no—
833C32C2×#56211yescharacteristic, complemented, Sylow
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—32no—
841C23—32no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23C22×D3212yes—
849C23C22×D3212yes—
850C23C22×D3211yescharacteristic
851Q8—364no—
852Q8—364no—
853D4—44no—
854D4—124no—
855D4—124no—
856D4—124no—
857D4—124no—
858D4—364no—
859C2×C4—22no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—92no—
875C2×C4—92no—
876C2×C4—124no—
877C2×C4—124no—
878C2×C4—182no—
879C2×C4—182no—
880C2×C4—182no—
881C2×C4—182no—
882C2×C4—364no—
883C2×C4—364no—
884C2×C4C22×D3212yes—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—24no—
889C2×C3—44no—
890C2×C3—42no—
891C2×C3—42no—
892C2×C3—42no—
893C2×C3—42no—
894C2×C3—82no—
895C2×C3—122no—
896C2×C3—122no—
897C2×C3#562114yescomplemented
898C2×C3#562114yescomplemented
899C2×C3C2×#100411yescharacteristic
900C2×C3C2×#100411yescharacteristic
901C2×C3C2×#100411yescharacteristic
902C2×C3C2×#100411yescharacteristic
903C2×C3C2×#101011yescharacteristic
904C2×C3C2×#101011yescharacteristic
905D3—42no—
906D3—42no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—44no—
914C22—44no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—62no—
921C22—124no—
922C22—124no—
923C22#6430912yes—
924C22#6431312yes—
925C22#6433012yes—
926C22C23×D3211yescharacteristic
927C4—22no—
928C4—62no—
929C4—62no—
930C4—62no—
931C4—62no—
932C4—62no—
933C4—62no—
934C4—182no—
935C4—182no—
936C4—182no—
937C4—182no—
938C3—21no—
939C3C2×#562111yescharacteristic, complemented
940C3C2×#562111yescharacteristic, complemented
941C2—42no—
942C2—42no—
943C2—122no—
944C2—122no—
945C2#1059526014yesdirect product factor
946C2C2×#6430911yescharacteristic
947C2C2×#6431311yescharacteristic
948C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64144C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#938C2semidirect
4. C2×#63982C2semidirect
5. C2×#63980C2semidirect
6. C2×#63970C2semidirect
7. C2×#63969C2semidirect
8. C2×#63964C2semidirect
9. C2×#63961C2semidirect
10. C2×#63959C2semidirect
11. C2×#63959C2semidirect
12. #10595260C2direct (N × H)
13. C2×#63905C2semidirect
14. C2×#63899C2semidirect
15. C2×#63851C2semidirect
16. C2×#63847C2semidirect
34. #64144C22semidirect
40. C3×#939C22semidirect
41. C3×#938C22semidirect
45. #63982C22semidirect
46. #63980C22semidirect
47. #63970C22semidirect
48. #63969C22semidirect
55. #63964C22semidirect
56. #63961C22semidirect
62. #63959C22semidirect
63. #63959C22semidirect
65. #63905C22semidirect
66. #63899C22semidirect
67. #63851C22semidirect
68. #63847C22semidirect
74. C2×#939D3semidirect
76. C2×#938D3semidirect
219. #939C2×D3semidirect
221. #938C2×D3semidirect
686. C2×C32#562semidirect
833. C32C2×#562semidirect
897. C2×C3#5621semidirect
898. C2×C3#5621semidirect
939. C3C2×#5621semidirect
940. C3C2×#5621semidirect
945. C2#10595260direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9392
C2×C3×#9382
C2×#639822
C2×#639802
C2×#639702
C2×#639692
C2×#639642
C2×#639612
C2×#639592
#105952602
C2×#639052
C2×#638992
C2×#638512
C2×#638472
C2×#56213