Finite Group Databasebeta

← C2×#10594378 #11902682

Subgroups — C2×#10594378 #11902682

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
1C22×#3797C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64105C211yesmaximal, characteristic, complemented
4C2×C3×#896C211yesmaximal, characteristic, complemented
5C2×C3×#888C211yesmaximal, characteristic, complemented
6C2×#63904C211yesmaximal, characteristic
7C2×#63899C211yesmaximal, characteristic, complemented
8C2×#63895C211yesmaximal, characteristic, complemented
9C2×#63888C211yesmaximal, characteristic, complemented
10C2×#63887C211yesmaximal, characteristic, complemented
11C2×#63881C211yesmaximal, characteristic
12C2×#63880C211yesmaximal, characteristic
13C2×#63840C211yesmaximal, characteristic, complemented
14C2×#63839C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594378C2116yesmaximal, direct product factor
17C2×#5727—31nomaximal
18C2×#5632—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#627C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#624C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C22×D3×Dic3C2211yescharacteristic
33C2×#3797—28no—
34C2×#3797C2218yescomplemented
35C2×D3×Dic6—28no—
36C2×D3×Dic6C2218yescomplemented
37C2×C32×C4⋊C4C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3750C2211yescharacteristic
41C2×#3750C2211yescharacteristic
42#64105C2218yescomplemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×C4⋊Dic3C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×C4×Dic3C2211yescharacteristic
51C3×#896C2218yescomplemented
52C3×#888C2218yescomplemented
53C2×#3724C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63904C2218yes—
62#63899C2218yescomplemented
63#63895C2218yescomplemented
64#63888C2218yescomplemented
65#63887C2218yescomplemented
66#63881C2218yes—
67#63880C2218yes—
68#63840C2218yescomplemented
69#63839C2218yescomplemented
70#63837C2218yescomplemented
71C22×D3×Q8—31no—
72C22×D3×Q8—31no—
73C22×D3×Q8—31no—
74C23×Dic6—31no—
75C2×C3×C4⋊Q8—31no—
76C2×C3×C22⋊Q8—31no—
77C2×#946—31no—
78C2×#946—31no—
79C2×#944—31no—
80C2×C4×#67—31no—
81#5727—316no—
82#5632—316no—
83C2×#897—31no—
84C2×#896—31no—
85C2×#896—31no—
86C2×#896—31no—
87C2×#896—31no—
88C2×#896—31no—
89C2×#896—61no—
90C2×#896D311yescharacteristic, complemented
91C2×#893—31no—
92C2×#893—31no—
93C2×#888—31no—
94C2×#888—31no—
95C2×#888—31no—
96C2×#888D311yescharacteristic, complemented
97C2×#887—31no—
98C2×#67⋊C4—31no—
99C2×#67⋊C4—31no—
100C2×#878—31no—
101C2×#878—31no—
102C2×C4×D12—31no—
103C2×C4×Dic6—31no—
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×C4×C3⋊D3—24no—
113C2×C4×C3⋊D3C2314yes—
114C2×#634—24no—
115C2×#634C2314yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×C4×D3—24no—
124C2×C3×C4×D3C2314yes—
125C2×C3×Dic6—24no—
126C2×C3×Dic6—24no—
127C2×C3×Dic6—24no—
128C2×C3×Dic6C2314yes—
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2314yes—
131C2×#627—24no—
132C2×#627—24no—
133C2×#627D418yescomplemented
134C2×#627C2314yes—
135C2×#627C2314yes—
136C2×#627C2314yes—
137C2×#626Q818yescomplemented
138C2×#626C2314yes—
139C2×#624—24no—
140C2×#624—24no—
141C2×#624C2314yes—
142C2×#624C2314yes—
143C2×D3×Dic3—24no—
144C2×D3×Dic3—24no—
145C2×D3×Dic3C2314yes—
146C2×D3×Dic3C2314yes—
147#3797—232no—
148D3×Dic6—232no—
149C32×C4⋊C4C2314yes—
150#3752C2314yes—
151#3752C2314yes—
152#3750C2314yes—
153#3750C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×C4⋊Dic3C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×C4×Dic3C2314yes—
162#3724C2314yes—
163Dic3⋊Dic3C2314yes—
164Dic3⋊Dic3C2314yes—
165Dic3⋊Dic3C2314yes—
166#3722C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168Dic32C2314yes—
169Dic32C2314yes—
170C2×D4×Q8—91noSylow
171C22×C3×Q8—31no—
172C22×C3×Q8—31no—
173C22×C3×Q8—31no—
174C23×C3×C4—31no—
175C22×#67—31no—
176C23×Dic3—31no—
177C23×Dic3—31no—
178C2×D3×Q8—38no—
179C2×D3×Q8—38no—
180C2×D3×Q8—38no—
181C2×D3×Q8—68no—
182C2×D3×Q8—68no—
183C2×D3×Q8—68no—
184C22×D12—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—61no—
194C22×C4×D3C2×D311yescharacteristic
195C22×Dic6—31no—
196C22×Dic6—31no—
197C22×Dic6—31no—
198C22×Dic6—31no—
199C22×Dic6—31no—
200C22×Dic6—31no—
201C22×Dic6—31no—
202C22×Dic6—31no—
203C22×Dic6—38no—
204C22×Dic6—61no—
205C22×Dic6—68no—
206C22×Dic6C2×D311yescharacteristic
207C22×Dic6C2×D311yescharacteristic
208C22×Dic6C2×D311yescharacteristic
209C3×C4⋊Q8—38no—
210C3×C22⋊Q8—38no—
211C2×C3×C4⋊C4—21no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C4⋊C4—31no—
214C2×C3×C4⋊C4—31no—
215C2×C3×C4⋊C4—31no—
216C2×C3×C4⋊C4—31no—
217C2×C3×C4⋊C4C2×D311yescharacteristic
218C2×C3×C4⋊C4C2×D311yescharacteristic
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4—31no—
221C2×C3×C42—31no—
222C2×#217—31no—
223#946—38no—
224#946—38no—
225#944—38no—
226C4×#67—38no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—61no—
235C2×(C2×D3)⋊C4—61no—
236C2×(C2×D3)⋊C4C2×D311yescharacteristic
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×C4⋊Dic3—31no—
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3C2×D311yescharacteristic
242C2×Dic3⋊C4—31no—
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—61no—
252C2×Dic3⋊C4—61no—
253C2×Dic3⋊C4C2×D311yescharacteristic
254C2×Dic3⋊C4C2×D311yescharacteristic
255C2×Dic3⋊C4C2×D311yescharacteristic
256C2×Dic3⋊C4C2×D311yescharacteristic
257C2×C4×Dic3—31no—
258C2×C4×Dic3—31no—
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3C2×D311yescharacteristic
262#897—38no—
263#896—38no—
264#896—38no—
265#896—38no—
266#896—38no—
267#896—38no—
268#896—68no—
269#896C2×D318yescomplemented
270#893—38no—
271#893—38no—
272#888—38no—
273#888—38no—
274#888—38no—
275#888C2×D318yescomplemented
276#887—38no—
277#67⋊C4—38no—
278#67⋊C4—38no—
279#878—38no—
280#878—38no—
281C4×D12—38no—
282C4×Dic6—38no—
283C23×C32C2411yescharacteristic
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3C2×Q814yescomplemented
287C22×C3⋊D3C2412yes—
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×C4—22no—
295C2×C32×C4C2412yes—
296C2×C32×C4C2412yes—
297C2×C32×C4C2412yes—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3C2×D414yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
304C4×C3⋊D3—28no—
305#634—28no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3C2×D414yes—
311C2×C3×Dic3C2×D414yes—
312C2×C3×Dic3C2×Q814yescomplemented
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C3×C4×D3—28no—
321C3×Dic6—28no—
322C3×Dic6—28no—
323C3×Dic6—28no—
324#627—28no—
325#627—28no—
326#627C2×D4116yescomplemented
327#626C2×Q8116yescomplemented
328#624—28no—
329#624—28no—
330D3×Dic3—28no—
331D3×Dic3—28no—
332C23×Q8—91no—
333C23×Q8—91no—
334D4×Q8—916no—
335C2×C4⋊Q8—31no—
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—91no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C24×C3—31no—
349C23×D3—31no—
350C23×D3—31no—
351C23×D3—61no—
352C23×D3C22×D311yescharacteristic
353C2×C3×Q8—34no—
354C2×C3×Q8—34no—
355C2×C3×Q8—34no—
356C2×C3×Q8—64no—
357C2×C3×Q8—64no—
358C2×C3×Q8—64no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—34no—
370C22×C3×C4—64no—
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—38no—
378C2×#67—34no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—34no—
386C22×Dic3—34no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—64no—
391C22×Dic3—64no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399D3×Q8—632no—
400D3×Q8—632no—
401D3×Q8—632no—
402C2×D12—38no—
403C2×D12—34no—
404C2×C4×D3—24no—
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—64no—
414C2×C4×D3—64no—
415C2×C4×D3—64no—
416C2×C4×D3—64no—
417C2×C4×D3—64no—
418C2×C4×D3—64no—
419C2×C4×D3—64no—
420C2×C4×D3—64no—
421C2×C4×D3—64no—
422C2×C4×D3—124no—
423C2×C4×D3C22×D314yes—
424C2×Dic6—24no—
425C2×Dic6—24no—
426C2×Dic6—24no—
427C2×Dic6—38no—
428C2×Dic6—38no—
429C2×Dic6—34no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—34no—
433C2×Dic6—34no—
434C2×Dic6—34no—
435C2×Dic6—34no—
436C2×Dic6—34no—
437C2×Dic6—64no—
438C2×Dic6—632no—
439C2×Dic6—64no—
440C2×Dic6—64no—
441C2×Dic6—64no—
442C2×Dic6—64no—
443C2×Dic6—64no—
444C2×Dic6—64no—
445C2×Dic6—124no—
446C2×Dic6C22×D314yes—
447C2×Dic6C22×D314yes—
448C2×Dic6C22×D314yes—
449C3×C4⋊C4—24no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4C22×D314yes—
456C3×C4⋊C4C22×D314yes—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C42—34no—
460#217—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—64no—
469(C2×D3)⋊C4—64no—
470(C2×D3)⋊C4C22×D314yes—
471(C2×D3)⋊C4C22×D314yes—
472C4⋊Dic3—34no—
473C4⋊Dic3—34no—
474C4⋊Dic3—34no—
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—64no—
486Dic3⋊C4—64no—
487Dic3⋊C4C22×D314yes—
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×C32C22×D412yes—
497C22×C32C22×Q812yes—
498C22×C322−1+412yes—
499C22×C32C2511yescharacteristic
500C2×C3⋊D3—28no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3C22×Q814yescomplemented
504C2×C3×D3—28no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3C22×Q814yescomplemented
508C32×C4—22no—
509C32×C4—22no—
510C32×C4—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—31no—
523C22×Q8—31no—
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—91no—
533C23×C4—31no—
534C23×C4—91no—
535C23×C4—91no—
536C23×C4—91no—
537C23×C4—91no—
538C23×C4—91no—
539C4⋊Q8—38no—
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—98no—
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—31no—
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⋊C4D3211yescharacteristic
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—91no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—91no—
570C2×C42—31no—
571C2×C42—91no—
572C2×C42—91no—
573C23×C3—21no—
574C23×C3—34no—
575C23×C3—32no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3C23×D311yescharacteristic
579C23×C3C23×D311yescharacteristic
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—34no—
583C22×D3—34no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—64no—
587C22×D3—62no—
588C22×D3—62no—
589C22×D3—62no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3D3×Q814yescomplemented
595C22×D3C23×D312yes—
596C3×Q8—68no—
597C3×Q8—68no—
598C3×Q8—68no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—34no—
609C2×C3×C4—34no—
610C2×C3×C4—34no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—42no—
619C2×C3×C4—42no—
620C2×C3×C4—42no—
621C2×C3×C4—68no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4C23×D312yes—
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C23×D312yes—
632#67—316no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—34no—
638C2×Dic3—34no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—64no—
646C2×Dic3—62no—
647C2×Dic3—62no—
648C2×Dic3—62no—
649C2×Dic3—68no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—68no—
655C2×Dic3—122no—
656C2×Dic3—122no—
657C2×Dic3D3×D414yes—
658C2×Dic3D3×D414yes—
659C2×Dic3D3×Q814yescomplemented
660C2×Dic3C23×D312yes—
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667D12—316no—
668C4×D3—28no—
669C4×D3—68no—
670C4×D3—68no—
671C4×D3—68no—
672C4×D3—68no—
673C4×D3—68no—
674C4×D3—68no—
675C4×D3—68no—
676C4×D3—68no—
677C4×D3—128no—
678Dic6—28no—
679Dic6—28no—
680Dic6—28no—
681Dic6—316no—
682Dic6—316no—
683Dic6—68no—
684Dic6—68no—
685Dic6—68no—
686Dic6—68no—
687Dic6—68no—
688Dic6—68no—
689Dic6—128no—
690C2×C32D4×Q814yescomplemented
691C2×C32C23×D411yescharacteristic
692C2×C32C23×Q811yescharacteristic
693C2×C32C2×2−1+411yescharacteristic
694C3⋊D3—24no—
695C3×D3—24no—
696C24—31no—
697C24—91no—
698C2×Q8—34no—
699C2×Q8—34no—
700C2×Q8—34no—
701C2×Q8—64no—
702C2×Q8—64no—
703C2×Q8—64no—
704C2×Q8—94no—
705C2×Q8—98no—
706C2×Q8—94no—
707C2×Q8—94no—
708C2×Q8—94no—
709C2×Q8—184no—
710C2×Q8—184no—
711C2×Q8—184no—
712C2×Q8—1832no—
713C2×Q8—1832no—
714C2×D4—94no—
715C2×D4—98no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—34no—
724C22×C4—64no—
725C22×C4—94no—
726C22×C4—94no—
727C22×C4—94no—
728C22×C4—94no—
729C22×C4—91no—
730C22×C4—91no—
731C22×C4—91no—
732C22×C4—94no—
733C22×C4—184no—
734C22×C4—184no—
735C22×C4—184no—
736C22×C4—184no—
737C22×C4—184no—
738C22×C4C2×D3211yescharacteristic
739C22×C4C2×D3211yescharacteristic
740C22×C4C2×D3211yescharacteristic
741C4⋊C4—34no—
742C4⋊C4—34no—
743C4⋊C4—34no—
744C4⋊C4—34no—
745C4⋊C4—34no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4C2×D3214yes—
753C22⋊C4—34no—
754C22⋊C4—34no—
755C22⋊C4—94no—
756C22⋊C4—94no—
757C22⋊C4—94no—
758C22⋊C4—94no—
759C42—34no—
760C42—94no—
761C42—94no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—21no—
766C22×C3—34no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—68no—
770C22×C3C2×D3×D412yes—
771C22×C3C2×D3×D412yes—
772C22×C3C2×D3×Q812yes—
773C22×C3C2×D3×Q812yes—
774C22×C3#100712yes—
775C22×C3#101012yes—
776C22×C3C24×D311yescharacteristic
777C22×C3C24×D311yescharacteristic
778C2×D3—28no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—34no—
782C2×D3—34no—
783C2×D3—64no—
784C2×D3—68no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—62no—
789C2×D3—68no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—128no—
793C2×D3C2×D3×Q814yescomplemented
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—34no—
801C3×C4—34no—
802C3×C4—34no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—42no—
806C3×C4—62no—
807C3×C4—62no—
808C3×C4—62no—
809C3×C4—62no—
810Dic3—22no—
811Dic3—22no—
812Dic3—22no—
813Dic3—22no—
814Dic3—34no—
815Dic3—34no—
816Dic3—64no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—62no—
821Dic3—122no—
822Dic3—122no—
823Dic3C2×D3×D414yes—
824Dic3C2×D3×D414yes—
825Dic3C2×D3×Q814yescomplemented
826C32C2×D4×Q811yescharacteristic, complemented, Sylow
827C23—34no—
828C23—32no—
829C23—62no—
830C23—62no—
831C23—94no—
832C23—92no—
833C23—182no—
834C23—182no—
835C23C22×D3211yescharacteristic
836Q8—68no—
837Q8—68no—
838Q8—68no—
839Q8—916no—
840Q8—188no—
841Q8—188no—
842Q8—188no—
843D4—916no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—34no—
848C2×C4—34no—
849C2×C4—34no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—68no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—94no—
863C2×C4—92no—
864C2×C4—92no—
865C2×C4—92no—
866C2×C4—188no—
867C2×C4—188no—
868C2×C4—188no—
869C2×C4—188no—
870C2×C4—188no—
871C2×C4—182no—
872C2×C4—182no—
873C2×C4C22×D3212yes—
874C2×C4C22×D3212yes—
875C2×C4C22×D3212yes—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—24no—
879C2×C3—21no—
880C2×C3—64no—
881C2×C3#563214yescomplemented
882C2×C3#572714yescomplemented
883C2×C3C22×D3×D411yescharacteristic
884C2×C3C22×D3×D411yescharacteristic
885C2×C3C22×D3×Q811yescharacteristic
886C2×C3C22×D3×Q811yescharacteristic
887C2×C3C2×#100711yescharacteristic
888C2×C3C2×#101011yescharacteristic
889D3—24no—
890D3—64no—
891D3—64no—
892D3—124no—
893C22—34no—
894C22—62no—
895C22—62no—
896C22—68no—
897C22—94no—
898C22—182no—
899C22—182no—
900C22—188no—
901C22#6429712yes—
902C22D32×D412yes—
903C22D32×Q812yes—
904C22C23×D3211yescharacteristic
905C4—22no—
906C4—22no—
907C4—22no—
908C4—34no—
909C4—34no—
910C4—34no—
911C4—62no—
912C4—62no—
913C4—62no—
914C4—62no—
915C4—94no—
916C4—182no—
917C4—182no—
918C3—21no—
919C3C2×#563211yescharacteristic, complemented
920C3C2×#572711yescharacteristic, complemented
921C2—64no—
922C2—184no—
923C2#1059437814yesdirect product factor
924C2C2×#6429711yescharacteristic
925C2C2×D32×D411yescharacteristic
926C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3797C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×#64105C2semidirect
4. C2×C3×#896C2semidirect
5. C2×C3×#888C2semidirect
7. C2×#63899C2semidirect
8. C2×#63895C2semidirect
9. C2×#63888C2semidirect
10. C2×#63887C2semidirect
13. C2×#63840C2semidirect
14. C2×#63839C2semidirect
15. C2×#63837C2semidirect
16. #10594378C2direct (N × H)
34. C2×#3797C22semidirect
36. C2×D3×Dic6C22semidirect
42. #64105C22semidirect
51. C3×#896C22semidirect
52. C3×#888C22semidirect
62. #63899C22semidirect
63. #63895C22semidirect
64. #63888C22semidirect
65. #63887C22semidirect
68. #63840C22semidirect
69. #63839C22semidirect
70. #63837C22semidirect
90. C2×#896D3semidirect
96. C2×#888D3semidirect
133. C2×#627D4semidirect
137. C2×#626Q8semidirect
269. #896C2×D3semidirect
275. #888C2×D3semidirect
286. C22×C3⋊D3C2×Q8semidirect
290. C22×C3×D3C2×Q8semidirect
312. C2×C3×Dic3C2×Q8semidirect
326. #627C2×D4semidirect
327. #626C2×Q8semidirect
503. C2×C3⋊D3C22×Q8semidirect
507. C2×C3×D3C22×Q8semidirect
520. C3×Dic3C22×Q8semidirect
594. C22×D3D3×Q8semidirect
659. C2×Dic3D3×Q8semidirect
690. C2×C32D4×Q8semidirect
793. C2×D3C2×D3×Q8semidirect
825. Dic3C2×D3×Q8semidirect
826. C32C2×D4×Q8semidirect
881. C2×C3#5632semidirect
882. C2×C3#5727semidirect
919. C3C2×#5632semidirect
920. C3C2×#5727semidirect
923. C2#10594378direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×D3×Dic62
C2×#641052
C2×C3×#8962
C2×C3×#8882
C2×#639042
C2×#638992
C2×#638952
C2×#638882
C2×#638872
C2×#638812
C2×#638802
C2×#638402
C2×#638392
C2×#638372
#105943782
C2×#57273
C2×#56323