Finite Group Databasebeta

← C2×#10594076 #11902631

Subgroups — C2×#10594076 #11902631

Order 1152.

3401 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64087C211yesmaximal, characteristic, complemented
4C2×C3×#885C211yesmaximal, characteristic, complemented
5C2×C3×#884C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63970C211yesmaximal, characteristic, complemented
8C2×#63959C211yesmaximal, characteristic, complemented
9C2×#63913C211yesmaximal, characteristic, complemented
10C2×#63893C211yesmaximal, characteristic, complemented
11C2×Dic3×D12C211yesmaximal, characteristic, complemented
12C2×#63887C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63879C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594076C2116yesmaximal, direct product factor
17C2×#5677—31nomaximal
18C2×#5598—31nomaximal
19C23×C3⋊Dic3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×#627C2211yescharacteristic
28C22×#627C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C2×#3805—28no—
32C2×#3805C2218yescomplemented
33C22×D3×Dic3C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic
35C22×D3×Dic3C2211yescharacteristic
36C22×D3×Dic3C2211yescharacteristic
37C2×D3×Dic6—28no—
38C2×D3×Dic6C2218yescomplemented
39C2×C32×C22⋊C4C2211yescharacteristic
40C2×#3757C2211yescharacteristic
41C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
42C2×#3750C2211yescharacteristic
43C2×#3750C2211yescharacteristic
44#64087C2218yescomplemented
45C2×C3×#217C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×C4×Dic3C2211yescharacteristic
51C3×#885C2218yescomplemented
52C3×#884C2218yescomplemented
53#67⋊Dic3C2218yescomplemented
54#63970C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61#63959C2218yescomplemented
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64#63913C2218yescomplemented
65#63893C2218yescomplemented
66Dic3×D12C2218yescomplemented
67#63887C2218yescomplemented
68#63885C2218yescomplemented
69#63879C2218yescomplemented
70#63837C2218yescomplemented
71C22×D3×Q8—31no—
72C22×#237—31no—
73C22×#237—31no—
74C23×Dic6—31no—
75C2×C3×#124—31no—
76C2×C3×#121—31no—
77C2×#946—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#938—31no—
81C2×#936—31no—
82C2×D4×Dic3—31no—
83C2×D4×Dic3—31no—
84C2×C4×#67—31no—
85#5677—316no—
86#5598—316no—
87C2×#897—31no—
88C2×#887—31no—
89C2×#885—31no—
90C2×#885—31no—
91C2×#885—31no—
92C2×#885D311yescharacteristic, complemented
93C2×#884—31no—
94C2×#884D311yescharacteristic, complemented
95C2×#67⋊C4—31no—
96C2×#67⋊C4—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—31no—
101C2×#878—61no—
102C2×C4×D12—31no—
103C2×C4×Dic6—31no—
104C24×C32C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3—24no—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2314yes—
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C2×#634—24no—
117C2×#634C2314yes—
118C2×C3×#67—24no—
119C2×C3×#67—24no—
120C2×C3×#67—24no—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×D12—24no—
130C2×C3×D12C2314yes—
131C2×C3×C4×D3—24no—
132C2×C3×C4×D3C2314yes—
133C2×C3×Dic6—24no—
134C2×C3×Dic6C2314yes—
135C2×#627—24no—
136C2×#627D418yescomplemented
137C2×#627C2314yes—
138C2×#627C2314yes—
139C2×#625—24no—
140C2×#625—24no—
141C2×#625C2314yes—
142C2×#625C2314yes—
143#3805—232no—
144C2×D3×Dic3—24no—
145C2×D3×Dic3—24no—
146C2×D3×Dic3—24no—
147C2×D3×Dic3—24no—
148C2×D3×Dic3C2314yes—
149C2×D3×Dic3C2314yes—
150C2×D3×Dic3C2314yes—
151C2×D3×Dic3C2314yes—
152D3×Dic6—232no—
153C32×C22⋊C4C2314yes—
154#3757C2314yes—
155C4⋊(C3⋊Dic3)C2314yes—
156#3750C2314yes—
157#3750C2314yes—
158C3×#217C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×C4×Dic3C2314yes—
164Dic3⋊Dic3C2314yes—
165Dic3⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yes—
170Dic32C2314yes—
171Dic32C2314yes—
172C2×#548—91noSylow
173C22×C3×Q8—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C23×C3×C4—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67C2×D311yescharacteristic
184C22×#67C2×D311yescharacteristic
185C22×#67C2×D311yescharacteristic
186C23×Dic3—31no—
187C23×Dic3—31no—
188C23×Dic3—31no—
189C23×Dic3—31no—
190C23×Dic3—31no—
191C23×Dic3—31no—
192C23×Dic3—61no—
193C2×D3×Q8—38no—
194C2×D3×Q8—68no—
195C2×#237—38no—
196C2×#237—38no—
197C2×#237—68no—
198C2×#237—68no—
199C22×D12C2×D311yescharacteristic
200C22×C4×D3—31no—
201C22×C4×D3—31no—
202C22×C4×D3—31no—
203C22×C4×D3—31no—
204C22×C4×D3C2×D311yescharacteristic
205C22×Dic6—31no—
206C22×Dic6—31no—
207C22×Dic6—31no—
208C22×Dic6—31no—
209C22×Dic6—31no—
210C22×Dic6—31no—
211C22×Dic6—38no—
212C22×Dic6—61no—
213C22×Dic6—68no—
214C22×Dic6C2×D311yescharacteristic
215C3×#124—38no—
216C3×#121—38no—
217C2×C3×C4⋊C4—31no—
218C2×C3×C22⋊C4—21no—
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4—31no—
221C2×C3×C22⋊C4—31no—
222C2×C3×C22⋊C4—31no—
223C2×C3×C22⋊C4C2×D311yescharacteristic
224C2×C3×C22⋊C4C2×D311yescharacteristic
225C2×C3×C42—31no—
226C2×#217—31no—
227C2×#217—31no—
228C2×#217—31no—
229C2×#217—31no—
230C2×#217—31no—
231C2×#217—31no—
232C2×#217—61no—
233C2×#217C2×D311yescharacteristic
234#946—38no—
235#939—38no—
236#939—38no—
237#938—38no—
238#936—38no—
239D4×Dic3—38no—
240D4×Dic3—38no—
241C4×#67—38no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4C2×D311yescharacteristic
247C2×(C2×D3)⋊C4C2×D311yescharacteristic
248C2×(C2×D3)⋊C4C2×D311yescharacteristic
249C2×C4⋊Dic3—31no—
250C2×C4⋊Dic3—31no—
251C2×C4⋊Dic3—31no—
252C2×C4⋊Dic3—31no—
253C2×C4⋊Dic3—61no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—61no—
261C2×Dic3⋊C4—61no—
262C2×Dic3⋊C4C2×D311yescharacteristic
263C2×C4×Dic3—31no—
264C2×C4×Dic3—31no—
265C2×C4×Dic3—31no—
266C2×C4×Dic3—31no—
267C2×C4×Dic3C2×D311yescharacteristic
268#897—38no—
269#887—38no—
270#885—38no—
271#885—38no—
272#885—38no—
273#885C2×D318yescomplemented
274#884—38no—
275#884C2×D318yescomplemented
276#67⋊C4—38no—
277#67⋊C4—38no—
278#878—38no—
279#878—38no—
280#878—38no—
281#878—38no—
282#878—68no—
283C4×D12—38no—
284C4×Dic6—38no—
285C23×C32—22no—
286C23×C32—22no—
287C23×C32—22no—
288C23×C32C2412yes—
289C23×C32C2411yescharacteristic
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3#4114yescomplemented
299C22×C3×D3C2412yes—
300C22×C3×D3C2412yes—
301C22×C3×D3C2412yes—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—28no—
310C2×C3⋊Dic3C2×D414yes—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C2×C3⋊Dic3C2412yes—
314C2×C3⋊Dic3C2412yes—
315#634—28no—
316C3×#67—28no—
317C3×#67—28no—
318C3×#67—28no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3C2×D414yes—
323C2×C3×Dic3C2×D414yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C3×D12—28no—
330C3×C4×D3—28no—
331C3×Dic6—28no—
332#627—28no—
333#627C2×D4116yescomplemented
334#625—28no—
335#625—28no—
336D3×Dic3—28no—
337D3×Dic3—28no—
338D3×Dic3—28no—
339D3×Dic3—28no—
340C22×#41—91no—
341C23×Q8—91no—
342#548—916no—
343C2×#124—31no—
344C2×#124—91no—
345C2×#124—91no—
346C2×C22⋊Q8—91no—
347C2×C22⋊Q8—91no—
348C2×C22⋊Q8—91no—
349C2×#121—31no—
350C2×#121—91no—
351C2×#121—91no—
352C2×C4×Q8—91no—
353C2×C4×D4—91no—
354C2×C4×D4—91no—
355C2×C4×D4—91no—
356C24×C3—21no—
357C24×C3—31no—
358C24×C3—31no—
359C24×C3—31no—
360C24×C3C22×D311yescharacteristic
361C24×C3C22×D311yescharacteristic
362C23×D3C22×D311yescharacteristic
363C23×D3C22×D311yescharacteristic
364C23×D3C22×D311yescharacteristic
365C2×C3×Q8—34no—
366C2×C3×Q8—64no—
367C2×C3×D4—34no—
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—64no—
372C2×C3×D4—64no—
373C2×C3×D4—64no—
374C2×C3×D4—64no—
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—34no—
383C22×C3×C4—64no—
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C2×#67—24no—
389C2×#67—24no—
390C2×#67—24no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—64no—
396C2×#67—64no—
397C2×#67—64no—
398C2×#67—64no—
399C2×#67C22×D314yes—
400C2×#67C22×D314yes—
401C2×#67C22×D314yes—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—34no—
405C22×Dic3—34no—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—34no—
413C22×Dic3—34no—
414C22×Dic3—34no—
415C22×Dic3—34no—
416C22×Dic3—61no—
417C22×Dic3—64no—
418C22×Dic3—61no—
419C22×Dic3—61no—
420C22×Dic3—61no—
421C22×Dic3—64no—
422C22×Dic3—64no—
423C22×Dic3—64no—
424C22×Dic3—64no—
425C22×Dic3—64no—
426C22×Dic3—64no—
427C22×Dic3—124no—
428C22×Dic3C22×D311yescharacteristic
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D311yescharacteristic
432C22×Dic3C22×D311yescharacteristic
433D3×Q8—632no—
434#237—632no—
435#237—632no—
436C2×D12—24no—
437C2×D12C22×D314yes—
438C2×C4×D3—24no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—34no—
443C2×C4×D3—64no—
444C2×C4×D3—64no—
445C2×C4×D3—64no—
446C2×C4×D3—64no—
447C2×C4×D3C22×D314yes—
448C2×Dic6—24no—
449C2×Dic6—38no—
450C2×Dic6—38no—
451C2×Dic6—34no—
452C2×Dic6—34no—
453C2×Dic6—34no—
454C2×Dic6—34no—
455C2×Dic6—34no—
456C2×Dic6—34no—
457C2×Dic6—64no—
458C2×Dic6—632no—
459C2×Dic6—64no—
460C2×Dic6—64no—
461C2×Dic6—64no—
462C2×Dic6—64no—
463C2×Dic6—124no—
464C2×Dic6C22×D314yes—
465C3×C4⋊C4—34no—
466C3×C22⋊C4—24no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471C3×C22⋊C4C22×D314yes—
472C3×C22⋊C4C22×D314yes—
473C3×C42—34no—
474#217—34no—
475#217—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480#217—64no—
481#217C22×D314yes—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4C22×D314yes—
487(C2×D3)⋊C4C22×D314yes—
488(C2×D3)⋊C4C22×D314yes—
489C4⋊Dic3—34no—
490C4⋊Dic3—34no—
491C4⋊Dic3—34no—
492C4⋊Dic3—34no—
493C4⋊Dic3—64no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—64no—
501Dic3⋊C4—64no—
502Dic3⋊C4C22×D314yes—
503C4×Dic3—34no—
504C4×Dic3—34no—
505C4×Dic3—34no—
506C4×Dic3—34no—
507C4×Dic3C22×D314yes—
508C22×C32—22no—
509C22×C32—22no—
510C22×C32—22no—
511C22×C32—44no—
512C22×C32C22×D412yes—
513C22×C32C2×#4112yes—
514C22×C322−1+412yes—
515C22×C32C2511yescharacteristic
516C2×C3×D3—28no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—44no—
526C2×C3×D3—44no—
527C2×C3×D3C2×#4114yescomplemented
528C32×C4—22no—
529C32×C4—22no—
530C3⋊Dic3—22no—
531C3⋊Dic3—22no—
532C3⋊Dic3—22no—
533C3⋊Dic3C22×D414yes—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3C22×D414yes—
538C3×Dic3C22×D414yes—
539C2×#41—98no—
540C2×#41—188no—
541C22×Q8—31no—
542C22×Q8—91no—
543C22×Q8—91no—
544C22×Q8—98no—
545C22×Q8—91no—
546C22×Q8—188no—
547C22×D4—31no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—31no—
551C22×D4—91no—
552C22×D4—91no—
553C23×C4—31no—
554C23×C4—91no—
555C23×C4—91no—
556C23×C4—91no—
557C23×C4—91no—
558C23×C4—91no—
559#124—38no—
560#124—98no—
561#124—98no—
562C22⋊Q8—98no—
563C22⋊Q8—98no—
564C22⋊Q8—98no—
565#121—38no—
566#121—98no—
567#121—98no—
568C4×Q8—98no—
569C4×D4—98no—
570C4×D4—98no—
571C4×D4—98no—
572C2×C4⋊C4—31no—
573C2×C4⋊C4—91no—
574C2×C4⋊C4—91no—
575C2×C4⋊C4—91no—
576C2×C4⋊C4—91no—
577C2×C4⋊C4—91no—
578C2×C22⋊C4—31no—
579C2×C22⋊C4—31no—
580C2×C22⋊C4—31no—
581C2×C22⋊C4—31no—
582C2×C22⋊C4—91no—
583C2×C22⋊C4—91no—
584C2×C22⋊C4—91no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4—91no—
587C2×C22⋊C4D3211yescharacteristic
588C2×C42—31no—
589C2×C42—91no—
590C2×C42—91no—
591C23×C3—24no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—21no—
600C23×C3—34no—
601C23×C3—32no—
602C23×C3—32no—
603C23×C3—32no—
604C23×C3—42no—
605C23×C3—42no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—62no—
611C23×C3—62no—
612C23×C3—62no—
613C23×C3—62no—
614C23×C3C23×D312yes—
615C23×C3C23×D312yes—
616C23×C3C23×D311yescharacteristic
617C23×C3C23×D311yescharacteristic
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3#23714yescomplemented
627C22×D3C23×D312yes—
628C22×D3C23×D312yes—
629C22×D3C23×D312yes—
630C3×Q8—68no—
631C3×D4—68no—
632C3×D4—68no—
633C3×D4—68no—
634C3×D4—68no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—34no—
642C2×C3×C4—34no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—42no—
649C2×C3×C4—42no—
650C2×C3×C4—68no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D312yes—
657C2×C3×C4C23×D312yes—
658#67—28no—
659#67—28no—
660#67—28no—
661#67—68no—
662#67—68no—
663#67—68no—
664#67—68no—
665C2×Dic3—22no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—34no—
669C2×Dic3—34no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—64no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—68no—
684C2×Dic3—68no—
685C2×Dic3—68no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—68no—
693C2×Dic3—68no—
694C2×Dic3—68no—
695C2×Dic3—128no—
696C2×Dic3—122no—
697C2×Dic3—122no—
698C2×Dic3—122no—
699C2×Dic3D3×D414yes—
700C2×Dic3D3×D414yes—
701C2×Dic3C23×D312yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706D12—28no—
707C4×D3—28no—
708C4×D3—68no—
709C4×D3—68no—
710C4×D3—68no—
711C4×D3—68no—
712Dic6—28no—
713Dic6—316no—
714Dic6—316no—
715Dic6—68no—
716Dic6—68no—
717Dic6—68no—
718Dic6—68no—
719Dic6—128no—
720C2×C32—42no—
721C2×C32#54814yescomplemented
722C2×C32C23×D411yescharacteristic
723C2×C32C22×#4111yescharacteristic
724C2×C32C2×2−1+411yescharacteristic
725C3×D3—24no—
726C3×D3—42no—
727C3×D3—42no—
728C24—31no—
729C24—31no—
730C24—31no—
731C24C2×D3211yescharacteristic
732#41—1832no—
733C2×Q8—34no—
734C2×Q8—64no—
735C2×Q8—94no—
736C2×Q8—98no—
737C2×Q8—94no—
738C2×Q8—94no—
739C2×Q8—184no—
740C2×Q8—184no—
741C2×Q8—1832no—
742C2×D4—34no—
743C2×D4—34no—
744C2×D4—34no—
745C2×D4—34no—
746C2×D4—64no—
747C2×D4—64no—
748C2×D4—64no—
749C2×D4—64no—
750C2×D4—94no—
751C2×D4—94no—
752C2×D4—184no—
753C2×D4—184no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—34no—
760C22×C4—64no—
761C22×C4—94no—
762C22×C4—94no—
763C22×C4—94no—
764C22×C4—94no—
765C22×C4—91no—
766C22×C4—94no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—184no—
771C22×C4—184no—
772C22×C4—184no—
773C22×C4—184no—
774C22×C4—184no—
775C22×C4C2×D3211yescharacteristic
776C22×C4C2×D3211yescharacteristic
777C4⋊C4—34no—
778C4⋊C4—94no—
779C4⋊C4—94no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C4⋊C4—94no—
783C22⋊C4—34no—
784C22⋊C4—34no—
785C22⋊C4—34no—
786C22⋊C4—34no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4C2×D3214yes—
793C42—34no—
794C42—94no—
795C42—94no—
796C22×C3—24no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—21no—
807C22×C3—34no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—48no—
811C22×C3—44no—
812C22×C3—44no—
813C22×C3—68no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—124no—
823C22×C3—124no—
824C22×C3C2×D3×D412yes—
825C22×C3C2×D3×D412yes—
826C22×C3C2×#23712yes—
827C22×C3D3×#4112yes—
828C22×C3#101012yes—
829C22×C3#101012yes—
830C22×C3C24×D311yescharacteristic
831C22×C3C24×D311yescharacteristic
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—28no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—44no—
842C2×D3—44no—
843C2×D3C2×#23714yescomplemented
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—34no—
849C3×C4—34no—
850C3×C4—42no—
851C3×C4—42no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—62no—
855Dic3—22no—
856Dic3—22no—
857Dic3—22no—
858Dic3—34no—
859Dic3—34no—
860Dic3—64no—
861Dic3—62no—
862Dic3—62no—
863Dic3—62no—
864Dic3—62no—
865Dic3—62no—
866Dic3—62no—
867Dic3—122no—
868Dic3—122no—
869Dic3—122no—
870Dic3C2×D3×D414yes—
871Dic3C2×D3×D414yes—
872C32C2×#54811yescharacteristic, complemented, Sylow
873C23—22no—
874C23—22no—
875C23—22no—
876C23—34no—
877C23—32no—
878C23—32no—
879C23—32no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23C22×D3212yes—
889C23C22×D3211yescharacteristic
890Q8—68no—
891Q8—916no—
892Q8—188no—
893Q8—188no—
894D4—68no—
895D4—68no—
896D4—68no—
897D4—68no—
898D4—188no—
899D4—188no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—34no—
903C2×C4—34no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—68no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—94no—
914C2×C4—92no—
915C2×C4—92no—
916C2×C4—92no—
917C2×C4—92no—
918C2×C4—188no—
919C2×C4—188no—
920C2×C4—188no—
921C2×C4—188no—
922C2×C4—188no—
923C2×C4—182no—
924C2×C4—182no—
925C2×C4—182no—
926C2×C4C22×D3212yes—
927C2×C4C22×D3212yes—
928C2×C3—24no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—44no—
933C2×C3—42no—
934C2×C3—42no—
935C2×C3—64no—
936C2×C3—122no—
937C2×C3—122no—
938C2×C3#559814yescomplemented
939C2×C3#567714yescomplemented
940C2×C3C22×D3×D411yescharacteristic
941C2×C3C22×D3×D411yescharacteristic
942C2×C3C22×#23711yescharacteristic
943C2×C3C2×D3×#4111yescharacteristic
944C2×C3C2×#101011yescharacteristic
945C2×C3C2×#101011yescharacteristic
946D3—24no—
947D3—42no—
948D3—42no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—34no—
953C22—44no—
954C22—68no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—124no—
964C22—124no—
965C22#6429812yes—
966C22D32×D412yes—
967C22D3×#23712yes—
968C22C23×D3211yescharacteristic
969C4—22no—
970C4—22no—
971C4—34no—
972C4—34no—
973C4—62no—
974C4—62no—
975C4—62no—
976C4—94no—
977C4—182no—
978C4—182no—
979C4—182no—
980C3—21no—
981C3C2×#559811yescharacteristic, complemented
982C3C2×#567711yescharacteristic, complemented
983C2—42no—
984C2—64no—
985C2—122no—
986C2—122no—
987C2#1059407614yesdirect product factor
988C2C2×#6429811yescharacteristic
989C2C2×D32×D411yescharacteristic
990C2C2×D3×#23711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×#64087C2semidirect
4. C2×C3×#885C2semidirect
5. C2×C3×#884C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C2×#63970C2semidirect
8. C2×#63959C2semidirect
9. C2×#63913C2semidirect
10. C2×#63893C2semidirect
11. C2×Dic3×D12C2semidirect
12. C2×#63887C2semidirect
13. C2×#63885C2semidirect
14. C2×#63879C2semidirect
15. C2×#63837C2semidirect
16. #10594076C2direct (N × H)
32. C2×#3805C22semidirect
38. C2×D3×Dic6C22semidirect
44. #64087C22semidirect
51. C3×#885C22semidirect
52. C3×#884C22semidirect
53. #67⋊Dic3C22semidirect
54. #63970C22semidirect
61. #63959C22semidirect
64. #63913C22semidirect
65. #63893C22semidirect
66. Dic3×D12C22semidirect
67. #63887C22semidirect
68. #63885C22semidirect
69. #63879C22semidirect
70. #63837C22semidirect
92. C2×#885D3semidirect
94. C2×#884D3semidirect
136. C2×#627D4semidirect
273. #885C2×D3semidirect
275. #884C2×D3semidirect
298. C22×C3×D3#41semidirect
333. #627C2×D4semidirect
527. C2×C3×D3C2×#41semidirect
626. C22×D3#237semidirect
721. C2×C32#548semidirect
843. C2×D3C2×#237semidirect
872. C32C2×#548semidirect
938. C2×C3#5598semidirect
939. C2×C3#5677semidirect
981. C3C2×#5598semidirect
982. C3C2×#5677semidirect
987. C2#10594076direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C22×D3×Dic62
C2×#640872
C2×C3×#8852
C2×C3×#8842
C2×#67⋊Dic32
C2×#639702
C2×#639592
C2×#639132
C2×#638932
C2×Dic3×D122
C2×#638872
C2×#638852
C2×#638792
C2×#638372
#105940762
C2×#56773
C2×#55983