Finite Group Databasebeta

← C2×#10593926 #11900848

Subgroups — C2×#10593926 #11900848

Order 1152.

2485 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×C4×#627C211yesmaximal, characteristic, complemented
5C2×C4×#627C211yesmaximal, characteristic, complemented
6C2×#63899C211yesmaximal, characteristic
7C2×#63896C211yesmaximal, characteristic
8C2×#63893C211yesmaximal, characteristic
9C2×#63887C211yesmaximal, characteristic
10C2×C4×D3×Dic3C211yesmaximal, characteristic
11C2×#63855C211yesmaximal, characteristic
12C2×#63846C211yesmaximal, characteristic, complemented
13C2×#63845C211yesmaximal, characteristic, complemented
14C2×#63840C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10593926C2116yesmaximal, direct product factor
17C2×#5578—31nomaximal
18C2×#5517—31nomaximal
19C22×#634C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C2×C32×C42C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C4×#634C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#872C2218yes—
44C3×C4×Dic6C2218yescomplemented
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57C4×#627C2218yescomplemented
58C4×#627C2218yescomplemented
59#63899C2218yes—
60#63896C2218yes—
61#63893C2218yes—
62#63887C2218yes—
63C4×D3×Dic3C2218yes—
64#63855C2218yes—
65#63846C2218yescomplemented
66#63845C2218yescomplemented
67#63840C2218yescomplemented
68#63839C2218yescomplemented
69C2×C3×C4×Q8—31no—
70C2×C3×#117—31no—
71C2×#946—31no—
72C2×#944—31no—
73C2×#926—31no—
74C22×C4×Dic3—31no—
75#5578—316no—
76#5517—316no—
77C2×#897—31no—
78C2×#896—31no—
79C2×#896—31no—
80C2×#890—31no—
81C2×#890—31no—
82C2×#889—31no—
83C2×#889—31no—
84C2×#888—31no—
85C2×#888—31no—
86C2×#888—31no—
87C2×#878—31no—
88C2×#878—31no—
89C2×#878—31no—
90C2×#878—31no—
91C2×#872—31no—
92C2×#872D311yescharacteristic
93C2×C42×D3—31no—
94C2×C4×Dic6—31no—
95C2×C4×Dic6—31no—
96C2×C4×Dic6—31no—
97C2×C4×Dic6—31no—
98C2×C4×Dic6—31no—
99C2×C4×Dic6—31no—
100C2×C4×Dic6—61no—
101C2×C4×Dic6D311yescharacteristic, complemented
102C23×C3×D3C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×#634—24no—
111C2×#634C2314yes—
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×C4×D3Q818yescomplemented
120C2×C3×C4×D3C2314yes—
121C2×C3×Dic6—24no—
122C2×C3×Dic6C2314yes—
123C2×#627—24no—
124C2×#627—24no—
125C2×#627C2314yes—
126C2×#627C2314yes—
127C2×D3×Dic3—24no—
128C2×D3×Dic3—24no—
129C2×D3×Dic3C2314yes—
130C2×D3×Dic3C2314yes—
131C32×C42C2314yes—
132C4⋊(C3⋊Dic3)C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135C4×C3⋊Dic3C2314yes—
136C4×C3⋊Dic3C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×C4×Dic3C2314yes—
145C3×C4×Dic3C2314yes—
146C3×C4×Dic3C2314yes—
147#3724C2314yes—
148#3724C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157Dic32C2314yes—
158Dic32C2314yes—
159C2×#533—91noSylow
160C22×C3×Q8—31no—
161C23×C3×C4—31no—
162C23×Dic3—31no—
163C23×Dic3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3C2×D311yescharacteristic
167C22×Dic6—31no—
168C22×Dic6—31no—
169C22×Dic6—31no—
170C22×Dic6—31no—
171C22×Dic6—31no—
172C22×Dic6—31no—
173C22×Dic6—61no—
174C22×Dic6C2×D311yescharacteristic
175C3×C4×Q8—38no—
176C3×#117—38no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C42—21no—
185C2×C3×C42—31no—
186C2×C3×C42—31no—
187C2×C3×C42—31no—
188C2×C3×C42C2×D311yescharacteristic
189C2×C3×C42C2×D311yescharacteristic
190C2×#217—31no—
191C2×#217—31no—
192#946—38no—
193#944—38no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4C2×D311yescharacteristic
197C2×(C2×D3)⋊C4C2×D311yescharacteristic
198#926—38no—
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—31no—
202C2×C4⋊Dic3—31no—
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—61no—
208C2×C4⋊Dic3C2×D311yescharacteristic
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—61no—
224C2×Dic3⋊C4—61no—
225C2×Dic3⋊C4C2×D311yescharacteristic
226C2×Dic3⋊C4C2×D311yescharacteristic
227C2×Dic3⋊C4C2×D311yescharacteristic
228C2×Dic3⋊C4C2×D311yescharacteristic
229C2×C4×Dic3—31no—
230C2×C4×Dic3—31no—
231C2×C4×Dic3—31no—
232C2×C4×Dic3—31no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3—38no—
238C2×C4×Dic3—61no—
239C2×C4×Dic3—61no—
240C2×C4×Dic3C2×D311yescharacteristic
241C2×C4×Dic3C2×D311yescharacteristic
242C2×C4×Dic3C2×D311yescharacteristic
243#897—38no—
244#896—38no—
245#896—38no—
246#890—38no—
247#890—38no—
248#889—38no—
249#889—38no—
250#888—38no—
251#888—38no—
252#888—38no—
253#878—38no—
254#878—38no—
255#878—38no—
256#878—38no—
257#872—38no—
258#872C2×D318yes—
259C42×D3—38no—
260C4×Dic6—38no—
261C4×Dic6—38no—
262C4×Dic6—38no—
263C4×Dic6—38no—
264C4×Dic6—38no—
265C4×Dic6—38no—
266C4×Dic6—68no—
267C4×Dic6C2×D318yescomplemented
268C23×C32C2411yescharacteristic
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3C2×Q814yes—
272C22×C3×D3C2412yes—
273C2×C32×C4—22no—
274C2×C32×C4—22no—
275C2×C32×C4C2×Q814yes—
276C2×C32×C4C2412yes—
277C2×C32×C4C2412yes—
278C2×C32×C4C2412yes—
279C2×C3⋊Dic3—22no—
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3#4114yes—
283C2×C3⋊Dic3C2412yes—
284C2×C3⋊Dic3C2412yes—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287#634—28no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3C2×Q814yes—
294C2×C3×Dic3#4114yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C3×C4×D3C2×Q8116yescomplemented
303C3×Dic6—28no—
304#627—28no—
305#627—28no—
306D3×Dic3—28no—
307D3×Dic3—28no—
308#533—916no—
309C2×C4⋊Q8—91no—
310C2×C4⋊Q8—91no—
311C2×#125—91no—
312C2×#125—91no—
313C2×C22⋊Q8—91no—
314C2×C22⋊Q8—91no—
315C2×C22⋊Q8—91no—
316C2×C22⋊Q8—91no—
317C2×C4×Q8—31no—
318C2×C4×Q8—91no—
319C2×C4×Q8—91no—
320C2×C4×Q8—91no—
321C2×#117—31no—
322C2×#117—91no—
323C22×C42—91no—
324C24×C3—31no—
325C23×D3C22×D311yescharacteristic
326C2×C3×Q8—34no—
327C2×C3×Q8—64no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—38no—
334C22×C3×C4—34no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—34no—
355C22×Dic3—34no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—64no—
361C22×Dic3—64no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C2×C4×D3—34no—
370C2×C4×D3—34no—
371C2×C4×D3—64no—
372C2×C4×D3—64no—
373C2×C4×D3Dic618yescomplemented
374C2×C4×D3C22×D314yes—
375C2×Dic6—24no—
376C2×Dic6—34no—
377C2×Dic6—34no—
378C2×Dic6—34no—
379C2×Dic6—34no—
380C2×Dic6—34no—
381C2×Dic6—34no—
382C2×Dic6—64no—
383C2×Dic6—64no—
384C2×Dic6—64no—
385C2×Dic6—64no—
386C2×Dic6—64no—
387C2×Dic6—64no—
388C2×Dic6—68no—
389C2×Dic6—64no—
390C2×Dic6C22×D314yes—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—34no—
398C3×C42—24no—
399C3×C42—34no—
400C3×C42—34no—
401C3×C42—34no—
402C3×C42C22×D314yes—
403C3×C42C22×D314yes—
404#217—34no—
405#217—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4C22×D314yes—
409(C2×D3)⋊C4C22×D314yes—
410C4⋊Dic3—34no—
411C4⋊Dic3—34no—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3—34no—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—64no—
419C4⋊Dic3C22×D314yes—
420Dic3⋊C4—34no—
421Dic3⋊C4—34no—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—64no—
435Dic3⋊C4—64no—
436Dic3⋊C4C22×D314yes—
437Dic3⋊C4C22×D314yes—
438Dic3⋊C4C22×D314yes—
439Dic3⋊C4C22×D314yes—
440C4×Dic3—34no—
441C4×Dic3—34no—
442C4×Dic3—34no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—64no—
449C4×Dic3—64no—
450C4×Dic3C22×D314yes—
451C4×Dic3C22×D314yes—
452C4×Dic3C22×D314yes—
453C22×C32C22×Q812yes—
454C22×C32C2×#4112yes—
455C22×C32C2×#4112yes—
456C22×C32C2511yescharacteristic
457C2×C3×D3—28no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3C22×Q814yes—
461C32×C4—22no—
462C32×C4—22no—
463C32×C4C22×Q814yes—
464C3⋊Dic3—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3C2×#4114yes—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3C22×Q814yes—
474C3×Dic3C2×#4114yes—
475C22×Q8—31no—
476C22×Q8—91no—
477C22×Q8—91no—
478C22×Q8—91no—
479C23×C4—31no—
480C23×C4—91no—
481C23×C4—91no—
482C4⋊Q8—98no—
483C4⋊Q8—98no—
484#125—98no—
485#125—98no—
486C22⋊Q8—98no—
487C22⋊Q8—98no—
488C22⋊Q8—98no—
489C22⋊Q8—98no—
490C4×Q8—38no—
491C4×Q8—98no—
492C4×Q8—98no—
493C4×Q8—98no—
494#117—38no—
495#117—98no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—91no—
507C2×C4⋊C4—91no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—91no—
511C2×C4⋊C4—91no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C42—31no—
517C2×C42—31no—
518C2×C42—31no—
519C2×C42—98no—
520C2×C42—91no—
521C2×C42—91no—
522C2×C42—91no—
523C2×C42—91no—
524C2×C42D3211yescharacteristic
525C23×C3—21no—
526C23×C3—34no—
527C23×C3—32no—
528C23×C3—62no—
529C23×C3—62no—
530C23×C3C23×D311yescharacteristic
531C23×C3C23×D311yescharacteristic
532C22×D3—22no—
533C22×D3—22no—
534C22×D3C2×Dic614yes—
535C22×D3C23×D312yes—
536C3×Q8—68no—
537C2×C3×C4—24no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—24no—
546C2×C3×C4—34no—
547C2×C3×C4—34no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—316no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—42no—
557C2×C3×C4—62no—
558C2×C3×C4—62no—
559C2×C3×C4—62no—
560C2×C3×C4—62no—
561C2×C3×C4—62no—
562C2×C3×C4C2×Dic614yes—
563C2×C3×C4D3×Q814yes—
564C2×C3×C4C23×D312yes—
565C2×C3×C4C23×D312yes—
566C2×C3×C4C23×D312yes—
567C2×C3×C4C23×D312yes—
568C2×C3×C4C23×D312yes—
569C2×C3×C4C23×D312yes—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—34no—
576C2×Dic3—34no—
577C2×Dic3—32no—
578C2×Dic3—32no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—32no—
582C2×Dic3—32no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—64no—
586C2×Dic3—62no—
587C2×Dic3—62no—
588C2×Dic3—62no—
589C2×Dic3—62no—
590C2×Dic3—68no—
591C2×Dic3—64no—
592C2×Dic3—62no—
593C2×Dic3—62no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—68no—
599C2×Dic3—122no—
600C2×Dic3—122no—
601C2×Dic3C2×Dic614yes—
602C2×Dic3#23514yes—
603C2×Dic3C23×D312yes—
604C2×Dic3C23×D312yes—
605C2×Dic3C23×D312yes—
606C2×Dic3C23×D312yes—
607C2×Dic3C23×D312yes—
608C2×Dic3C23×D312yes—
609C2×Dic3C23×D312yes—
610C4×D3—68no—
611C4×D3—68no—
612C4×D3C2×Dic6116yescomplemented
613Dic6—28no—
614Dic6—68no—
615Dic6—68no—
616Dic6—68no—
617Dic6—68no—
618Dic6—68no—
619Dic6—616no—
620Dic6—68no—
621C2×C32#53314yescomplemented
622C2×C32C23×Q811yescharacteristic
623C2×C32C22×#4111yescharacteristic
624C2×C32C22×#4111yescharacteristic
625C3×D3—24no—
626C24—31no—
627C2×Q8—34no—
628C2×Q8—64no—
629C2×Q8—94no—
630C2×Q8—94no—
631C2×Q8—94no—
632C2×Q8—184no—
633C2×Q8—184no—
634C2×Q8—184no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—34no—
638C22×C4—38no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—94no—
645C22×C4—94no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—184no—
651C22×C4—184no—
652C22×C4C2×D3211yescharacteristic
653C22×C4C2×D3211yescharacteristic
654C22×C4C2×D3211yescharacteristic
655C4⋊C4—34no—
656C4⋊C4—34no—
657C4⋊C4—34no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—94no—
661C4⋊C4—94no—
662C4⋊C4—94no—
663C4⋊C4—94no—
664C4⋊C4—94no—
665C4⋊C4—94no—
666C4⋊C4—94no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C22⋊C4—34no—
672C22⋊C4—34no—
673C22⋊C4—94no—
674C22⋊C4—94no—
675C42—34no—
676C42—34no—
677C42—34no—
678C42—94no—
679C42—94no—
680C42—94no—
681C42—94no—
682C42C2×D3214yes—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—21no—
687C22×C3—34no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—68no—
691C22×C3C22×Dic612yes—
692C22×C3C2×#23512yes—
693C22×C3C2×D3×Q812yes—
694C22×C3D3×#4112yes—
695C22×C3D3×#4112yes—
696C22×C3D3×#4112yes—
697C22×C3C24×D311yescharacteristic
698C22×C3C24×D311yescharacteristic
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—28no—
702C2×D3C22×Dic614yes—
703C3×C4—24no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—24no—
709C3×C4—34no—
710C3×C4—34no—
711C3×C4—42no—
712C3×C4—62no—
713C3×C4—62no—
714C3×C4—62no—
715C3×C4—62no—
716C3×C4—62no—
717C3×C4C22×Dic614yes—
718C3×C4C2×D3×Q814yes—
719Dic3—22no—
720Dic3—22no—
721Dic3—22no—
722Dic3—22no—
723Dic3—22no—
724Dic3—34no—
725Dic3—34no—
726Dic3—64no—
727Dic3—64no—
728Dic3—62no—
729Dic3—62no—
730Dic3—62no—
731Dic3—62no—
732Dic3—62no—
733Dic3—62no—
734Dic3—122no—
735Dic3—122no—
736Dic3C22×Dic614yes—
737Dic3C2×#23514yes—
738C32C2×#53311yescharacteristic, complemented, Sylow
739C23—34no—
740C23—32no—
741C23—62no—
742C23—62no—
743C23C22×D3211yescharacteristic
744Q8—68no—
745Q8—188no—
746Q8—188no—
747Q8—188no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—34no—
751C2×C4—34no—
752C2×C4—32no—
753C2×C4—32no—
754C2×C4—316no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—94no—
766C2×C4—92no—
767C2×C4—92no—
768C2×C4—92no—
769C2×C4—92no—
770C2×C4—188no—
771C2×C4—188no—
772C2×C4—182no—
773C2×C4—182no—
774C2×C4—182no—
775C2×C4D3×Dic614yes—
776C2×C4C22×D3212yes—
777C2×C4C22×D3212yes—
778C2×C4C22×D3212yes—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—24no—
783C2×C3—64no—
784C2×C3#551714yescomplemented
785C2×C3#557814yescomplemented
786C2×C3C23×Dic611yescharacteristic
787C2×C3C22×#23511yescharacteristic
788C2×C3C22×D3×Q811yescharacteristic
789C2×C3C2×D3×#4111yescharacteristic
790C2×C3C2×D3×#4111yescharacteristic
791C2×C3C2×D3×#4111yescharacteristic
792D3—24no—
793C22—34no—
794C22—62no—
795C22—62no—
796C22—68no—
797C22C2×D3×Dic612yes—
798C22D3×#23512yes—
799C22#6430612yes—
800C22C23×D3211yescharacteristic
801C4—22no—
802C4—22no—
803C4—34no—
804C4—34no—
805C4—62no—
806C4—62no—
807C4—62no—
808C4—62no—
809C4—62no—
810C4—94no—
811C4—182no—
812C4—182no—
813C4—182no—
814C4C2×D3×Dic614yes—
815C3—21no—
816C3C2×#551711yescharacteristic, complemented
817C3C2×#557811yescharacteristic, complemented
818C2—64no—
819C2#1059392614yesdirect product factor
820C2C22×D3×Dic611yescharacteristic
821C2C2×D3×#23511yescharacteristic
822C2C2×#6430611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. C2×C4×#627C2semidirect
5. C2×C4×#627C2semidirect
12. C2×#63846C2semidirect
13. C2×#63845C2semidirect
14. C2×#63840C2semidirect
15. C2×#63839C2semidirect
16. #10593926C2direct (N × H)
32. C4×#634C22semidirect
44. C3×C4×Dic6C22semidirect
57. C4×#627C22semidirect
58. C4×#627C22semidirect
65. #63846C22semidirect
66. #63845C22semidirect
67. #63840C22semidirect
68. #63839C22semidirect
101. C2×C4×Dic6D3semidirect
119. C2×C3×C4×D3Q8semidirect
267. C4×Dic6C2×D3semidirect
302. C3×C4×D3C2×Q8semidirect
373. C2×C4×D3Dic6semidirect
612. C4×D3C2×Dic6semidirect
621. C2×C32#533semidirect
738. C32C2×#533semidirect
784. C2×C3#5517semidirect
785. C2×C3#5578semidirect
816. C3C2×#5517semidirect
817. C3C2×#5578semidirect
819. C2#10593926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×#8722
C2×C3×C4×Dic62
C2×C4×#6272
C2×#638992
C2×#638962
C2×#638932
C2×#638872
C2×C4×D3×Dic32
C2×#638552
C2×#638462
C2×#638452
C2×#638402
C2×#638392
#105939262
C2×#55783
C2×#55173