Finite Group Databasebeta

← C2×#10594917 #11902530

Subgroups — C2×#10594917 #11902530

Order 1152.

3709 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×C3×#929C211yesmaximal, characteristic, complemented
4C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63966C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63897C211yesmaximal, characteristic, complemented
10#10594917C2116yesmaximal, direct product factor
11C2×#63896C211yesmaximal, characteristic, complemented
12C2×#63883C211yesmaximal, characteristic, complemented
13C2×#63881C211yesmaximal, characteristic, complemented
14C2×#63865C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16C2×#63840C211yesmaximal, characteristic, complemented
17C2×#5655—31nomaximal
18C2×#5507—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C2×#3828—28no—
23C2×#3828C2218yescomplemented
24C22×C4⋊(C3⋊D3)C2211yescharacteristic
25C22×C4×C3⋊D3C2211yescharacteristic
26C22×C4×C3⋊D3C2211yescharacteristic
27C22×#634C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic
29C23×C3×Dic3C2211yescharacteristic
30C23×C3×Dic3C2211yescharacteristic
31C22×#627C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C22×#624C2211yescharacteristic
36C2×#3804—28no—
37C2×#3804C2218yescomplemented
38C22×D3×Dic3C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C3×#929C2218yescomplemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2218yescomplemented
50#63978C2218yescomplemented
51C2×#3724C2211yescharacteristic
52#63966C2218yescomplemented
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×#3722C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×Dic32C2211yescharacteristic
62#63952C2218yescomplemented
63#63910C2218yescomplemented
64#63897C2218yescomplemented
65#63896C2218yescomplemented
66#63883C2218yescomplemented
67#63881C2218yescomplemented
68#63865C2218yescomplemented
69#63853C2218yescomplemented
70#63840C2218yescomplemented
71C22×#237—31no—
72C22×#235—31no—
73C22×#235—31no—
74C22×#235—31no—
75C22×#235—61no—
76C2×C3×#123—31no—
77C22×C3×C4⋊C4—31no—
78C2×#939—31no—
79C2×#930—31no—
80C2×#929—31no—
81C2×#929D311yescharacteristic, complemented
82C2×C4×#67—31no—
83C22×Dic3⋊C4D311yescharacteristic, complemented
84#5655—316no—
85C2×#896—31no—
86C2×#896—31no—
87C2×#896—31no—
88#5507—316no—
89C2×#895—31no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#894—31no—
93C2×#893—31no—
94C2×D3×C4⋊C4—31no—
95C2×D3×C4⋊C4—31no—
96C2×#888—31no—
97C2×#888—31no—
98C2×#886—31no—
99C2×#884—31no—
100C2×#883—31no—
101C2×#67⋊C4—31no—
102C2×#67⋊C4—31no—
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×C32×C4—24no—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2314yes—
112C2×#638—24no—
113C2×#638D418yescomplemented
114C2×#638C2314yes—
115C2×#638C2314yes—
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118#3828—232no—
119C2×C4⋊(C3⋊D3)—24no—
120C2×C4⋊(C3⋊D3)C2314yes—
121C2×C4×C3⋊D3—24no—
122C2×C4×C3⋊D3—24no—
123C2×C4×C3⋊D3C2314yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634—24no—
126C2×#634C2314yes—
127C2×C3×#67—24no—
128C2×C3×#67C2314yes—
129C22×C3×Dic3—24no—
130C22×C3×Dic3—24no—
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2314yes—
138C22×C3×Dic3C2314yes—
139C22×C3×Dic3C2311yescharacteristic
140C2×#627—24no—
141C2×#627C2314yes—
142C2×#626—24no—
143C2×#626—24no—
144C2×#626C2314yes—
145C2×#626C2314yes—
146C2×#624—24no—
147C2×#624—24no—
148C2×#624C2314yes—
149C2×#624C2314yes—
150#3804—232no—
151C2×D3×Dic3—24no—
152C2×D3×Dic3C2314yes—
153C3×#217C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162#3724C2314yes—
163Dic3⋊Dic3C2314yes—
164Dic3⋊Dic3C2314yes—
165Dic3⋊Dic3C2314yes—
166#3722C2314yes—
167#3722C2314yes—
168#3722C2314yes—
169#3722C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171Dic32C2314yes—
172C2×#547—91noSylow
173C22×C3×D4—31no—
174C23×C3×C4—21no—
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C23×C3×C4C2×D311yescharacteristic
178C23×C3×C4C2×D311yescharacteristic
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—61no—
186C22×#67—61no—
187C22×#67C2×D311yescharacteristic
188C23×Dic3—31no—
189C23×Dic3C2×D311yescharacteristic
190C23×Dic3C2×D311yescharacteristic
191C2×#237—38no—
192C2×#237—68no—
193C2×#235—38no—
194C2×#235—38no—
195C2×#235—38no—
196C2×#235—68no—
197C2×#235—68no—
198C2×#235—68no—
199C2×#235—68no—
200C2×#235—616no—
201C22×D12—31no—
202C22×D12—31no—
203C22×D12—31no—
204C22×D12—31no—
205C22×D12—61no—
206C22×C4×D3—31no—
207C22×C4×D3—31no—
208C22×C4×D3—31no—
209C22×C4×D3—31no—
210C22×C4×D3—31no—
211C22×C4×D3—31no—
212C22×C4×D3—31no—
213C22×C4×D3—31no—
214C22×C4×D3—31no—
215C22×C4×D3—61no—
216C22×C4×D3—61no—
217C22×Dic6—31no—
218C22×Dic6—31no—
219C22×Dic6—31no—
220C22×Dic6—31no—
221C22×Dic6—61no—
222C3×#123—38no—
223C2×C3×C4⋊C4—31no—
224C2×C3×C4⋊C4—31no—
225C2×C3×C4⋊C4—31no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4—38no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×#217—31no—
234C2×#217C2×D311yescharacteristic
235#939—38no—
236#930—38no—
237#929—38no—
238#929C2×D318yescomplemented
239C4×#67—38no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4C2×D311yescharacteristic
250C2×(C2×D3)⋊C4C2×D311yescharacteristic
251C2×C4⋊Dic3—31no—
252C2×C4⋊Dic3—31no—
253C2×C4⋊Dic3—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4C2×D311yescharacteristic
260C2×Dic3⋊C4C2×D311yescharacteristic
261C2×Dic3⋊C4C2×D311yescharacteristic
262C2×Dic3⋊C4C2×D311yescharacteristic
263C2×Dic3⋊C4C2×D311yescharacteristic
264C2×Dic3⋊C4C2×D311yescharacteristic
265C2×Dic3⋊C4C2×D318yescomplemented
266C2×C4×Dic3—31no—
267C2×C4×Dic3—31no—
268#896—38no—
269#896—38no—
270#896—38no—
271#895—38no—
272#894—38no—
273#894—38no—
274#894—38no—
275#893—38no—
276D3×C4⋊C4—38no—
277D3×C4⋊C4—38no—
278#888—38no—
279#888—38no—
280#886—38no—
281#884—38no—
282#883—38no—
283#67⋊C4—38no—
284#67⋊C4—38no—
285#878—38no—
286C23×C32—22no—
287C23×C32—22no—
288C23×C32C2×D414yes—
289C23×C32C2412yes—
290C23×C32C2411yescharacteristic
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3—22no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3—22no—
296C22×C3⋊D3C2×D414yes—
297C22×C3⋊D3C2412yes—
298C22×C3⋊D3C2412yes—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3C2412yes—
303C2×C32×C4—22no—
304C2×C32×C4—22no—
305C2×C32×C4—28no—
306C2×C32×C4C2412yes—
307C2×C32×C4C2412yes—
308#638—28no—
309#638C2×D4116yescomplemented
310C2×C3⋊Dic3—22no—
311C2×C3⋊Dic3C2×D414yes—
312C2×C3⋊Dic3C2412yes—
313C2×C3⋊Dic3C2412yes—
314C4⋊(C3⋊D3)—28no—
315C4×C3⋊D3—28no—
316C4×C3⋊D3—28no—
317#634—28no—
318C3×#67—28no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—28no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—28no—
327C2×C3×Dic3#4114yescomplemented
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335#627—28no—
336#626—28no—
337#626—28no—
338#624—28no—
339#624—28no—
340D3×Dic3—28no—
341C22×#41—91no—
342C22×#41—91no—
343#547—916no—
344C2×C4⋊Q8—91no—
345C2×#123—31no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#123—91no—
349C2×C22⋊Q8—91no—
350C2×C22⋊Q8—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×C4×D4—91no—
354C2×C4×D4—91no—
355C22×C4⋊C4—31no—
356C22×C4⋊C4—91no—
357C24×C3—21no—
358C24×C3—31no—
359C24×C3C22×D311yescharacteristic
360C24×C3C22×D311yescharacteristic
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—61no—
366C23×D3—61no—
367C23×D3C22×D311yescharacteristic
368C2×C3×D4—34no—
369C2×C3×D4—64no—
370C22×C3×C4—28no—
371C22×C3×C4—24no—
372C22×C3×C4—24no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—24no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—34no—
384C22×C3×C4—34no—
385C22×C3×C4—64no—
386C22×C3×C4—64no—
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D314yes—
392C22×C3×C4C22×D314yes—
393C2×#67—24no—
394C2×#67—38no—
395C2×#67—38no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—34no—
399C2×#67—34no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—68no—
403C2×#67—64no—
404C2×#67—64no—
405C2×#67—64no—
406C2×#67—68no—
407C2×#67—64no—
408C2×#67—64no—
409C2×#67—64no—
410C2×#67C22×D314yes—
411C22×Dic3—24no—
412C22×Dic3—24no—
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—31no—
417C22×Dic3—34no—
418C22×Dic3—61no—
419C22×Dic3—61no—
420C22×Dic3—64no—
421C22×Dic3C22×D314yes—
422C22×Dic3C22×D314yes—
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D311yescharacteristic
428C22×Dic3C22×D311yescharacteristic
429C22×Dic3C22×D311yescharacteristic
430#237—632no—
431#235—632no—
432#235—632no—
433#235—632no—
434#235—664no—
435C2×D12—34no—
436C2×D12—34no—
437C2×D12—34no—
438C2×D12—34no—
439C2×D12—64no—
440C2×D12—64no—
441C2×D12—64no—
442C2×D12—68no—
443C2×D12—64no—
444C2×D12—64no—
445C2×C4×D3—34no—
446C2×C4×D3—34no—
447C2×C4×D3—34no—
448C2×C4×D3—34no—
449C2×C4×D3—34no—
450C2×C4×D3—34no—
451C2×C4×D3—34no—
452C2×C4×D3—34no—
453C2×C4×D3—34no—
454C2×C4×D3—64no—
455C2×C4×D3—64no—
456C2×C4×D3—64no—
457C2×C4×D3—64no—
458C2×C4×D3—64no—
459C2×C4×D3—64no—
460C2×C4×D3—64no—
461C2×C4×D3—64no—
462C2×C4×D3—64no—
463C2×C4×D3—64no—
464C2×C4×D3—68no—
465C2×C4×D3—68no—
466C2×C4×D3—64no—
467C2×Dic6—34no—
468C2×Dic6—34no—
469C2×Dic6—34no—
470C2×Dic6—34no—
471C2×Dic6—64no—
472C2×Dic6—64no—
473C2×Dic6—64no—
474C2×Dic6—64no—
475C2×Dic6—64no—
476C2×Dic6—68no—
477C3×C4⋊C4—34no—
478C3×C4⋊C4—34no—
479C3×C4⋊C4—34no—
480C3×C4⋊C4—34no—
481C3×C4⋊C4—34no—
482C3×C4⋊C4—34no—
483C3×C22⋊C4—34no—
484C3×C22⋊C4—34no—
485C3×C22⋊C4—34no—
486#217—34no—
487#217C22×D314yes—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4C22×D314yes—
498(C2×D3)⋊C4C22×D314yes—
499C4⋊Dic3—34no—
500C4⋊Dic3—34no—
501C4⋊Dic3—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4C22×D314yes—
508Dic3⋊C4C22×D314yes—
509Dic3⋊C4C22×D314yes—
510Dic3⋊C4C22×D314yes—
511Dic3⋊C4C22×D314yes—
512Dic3⋊C4C22×D314yes—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C22×C32—28no—
516C22×C32—22no—
517C22×C32—22no—
518C22×C32C22×D414yes—
519C22×C32C22×D412yes—
520C22×C32C2×#4112yes—
521C22×C322−1+412yes—
522C22×C32C2511yescharacteristic
523C2×C3⋊D3—22no—
524C2×C3⋊D3—28no—
525C2×C3⋊D3—22no—
526C2×C3⋊D3—22no—
527C2×C3⋊D3—22no—
528C2×C3⋊D3—22no—
529C2×C3⋊D3—44no—
530C2×C3⋊D3C22×D414yes—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—44no—
535C32×C4—22no—
536C32×C4—22no—
537C3⋊Dic3—22no—
538C3⋊Dic3C22×D414yes—
539C3×Dic3—22no—
540C3×Dic3—22no—
541C3×Dic3—22no—
542C3×Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3C2×#4114yescomplemented
546C2×#41—98no—
547C2×#41—98no—
548C2×#41—188no—
549C2×#41—188no—
550C22×Q8—91no—
551C22×Q8—91no—
552C22×D4—31no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C23×C4—31no—
559C23×C4—31no—
560C23×C4—91no—
561C23×C4—91no—
562C23×C4—91no—
563C23×C4—91no—
564C23×C4—91no—
565C23×C4D3211yescharacteristic
566C4⋊Q8—98no—
567#123—38no—
568#123—98no—
569#123—98no—
570#123—98no—
571C22⋊Q8—98no—
572C22⋊Q8—98no—
573#121—98no—
574#121—98no—
575C4×D4—98no—
576C4×D4—98no—
577C2×C4⋊C4—31no—
578C2×C4⋊C4—31no—
579C2×C4⋊C4—31no—
580C2×C4⋊C4—31no—
581C2×C4⋊C4—38no—
582C2×C4⋊C4—31no—
583C2×C4⋊C4—31no—
584C2×C4⋊C4—98no—
585C2×C4⋊C4—91no—
586C2×C4⋊C4—91no—
587C2×C4⋊C4—91no—
588C2×C4⋊C4—91no—
589C2×C22⋊C4—31no—
590C2×C22⋊C4—31no—
591C2×C22⋊C4—31no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4—91no—
596C2×C22⋊C4—91no—
597C2×C42—91no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—21no—
604C23×C3—24no—
605C23×C3—32no—
606C23×C3—42no—
607C23×C3—42no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—62no—
611C23×C3D3×D414yes—
612C23×C3D3×D414yes—
613C23×C3C23×D312yes—
614C23×C3C23×D312yes—
615C23×C3C23×D311yescharacteristic
616C23×C3C23×D311yescharacteristic
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—34no—
621C22×D3—34no—
622C22×D3—32no—
623C22×D3—32no—
624C22×D3—32no—
625C22×D3—32no—
626C22×D3—64no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—64no—
634C22×D3—62no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3—122no—
643C22×D3—122no—
644C22×D3C23×D312yes—
645C3×D4—68no—
646C2×C3×C4—24no—
647C2×C3×C4—24no—
648C2×C3×C4—216no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—28no—
654C2×C3×C4—28no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—34no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—68no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—68no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4C23×D312yes—
674C2×C3×C4C23×D312yes—
675C2×C3×C4C23×D312yes—
676C2×C3×C4C23×D312yes—
677#67—28no—
678#67—316no—
679#67—316no—
680#67—616no—
681#67—68no—
682#67—616no—
683#67—68no—
684#67—68no—
685#67—68no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—28no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—28no—
694C2×Dic3—34no—
695C2×Dic3—34no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—64no—
701C2×Dic3—62no—
702C2×Dic3—62no—
703C2×Dic3—68no—
704C2×Dic3—64no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3#23514yescomplemented
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D312yes—
711C2×Dic3C23×D312yes—
712C2×Dic3C23×D312yes—
713C2×Dic3C23×D312yes—
714C2×Dic3C23×D312yes—
715D12—68no—
716D12—68no—
717D12—616no—
718D12—68no—
719D12—68no—
720C4×D3—68no—
721C4×D3—68no—
722C4×D3—68no—
723C4×D3—68no—
724C4×D3—68no—
725C4×D3—68no—
726C4×D3—68no—
727C4×D3—68no—
728C4×D3—616no—
729C4×D3—616no—
730C4×D3—68no—
731Dic6—68no—
732Dic6—68no—
733Dic6—68no—
734Dic6—68no—
735Dic6—616no—
736C2×C32—24no—
737C2×C32#54714yescomplemented
738C2×C32C23×D411yescharacteristic
739C2×C32C22×#4111yescharacteristic
740C2×C32C2×2−1+411yescharacteristic
741C3⋊D3—24no—
742C3⋊D3—42no—
743C3×D3—42no—
744C24—31no—
745C24—91no—
746C24—91no—
747C24C2×D3211yescharacteristic
748#41—1832no—
749#41—1832no—
750C2×Q8—94no—
751C2×Q8—94no—
752C2×Q8—184no—
753C2×Q8—184no—
754C2×D4—34no—
755C2×D4—64no—
756C2×D4—94no—
757C2×D4—94no—
758C2×D4—94no—
759C2×D4—98no—
760C2×D4—94no—
761C2×D4—94no—
762C2×D4—184no—
763C2×D4—184no—
764C2×D4—184no—
765C2×D4—184no—
766C22×C4—24no—
767C22×C4—31no—
768C22×C4—34no—
769C22×C4—34no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—64no—
777C22×C4—64no—
778C22×C4—94no—
779C22×C4—94no—
780C22×C4—94no—
781C22×C4—91no—
782C22×C4—91no—
783C22×C4—94no—
784C22×C4—94no—
785C22×C4—184no—
786C22×C4—184no—
787C22×C4—184no—
788C22×C4—184no—
789C22×C4—184no—
790C22×C4C2×D3214yes—
791C22×C4C2×D3211yescharacteristic
792C22×C4C2×D3211yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—34no—
795C4⋊C4—34no—
796C4⋊C4—34no—
797C4⋊C4—34no—
798C4⋊C4—34no—
799C4⋊C4—94no—
800C4⋊C4—94no—
801C4⋊C4—94no—
802C4⋊C4—94no—
803C22⋊C4—34no—
804C22⋊C4—34no—
805C22⋊C4—34no—
806C22⋊C4—94no—
807C22⋊C4—94no—
808C22⋊C4—94no—
809C22⋊C4—94no—
810C22⋊C4—94no—
811C42—94no—
812C22×C3—28no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—28no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—24no—
822C22×C3—21no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—48no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—124no—
830C22×C3C2×#23512yes—
831C22×C3C2×D3×D414yes—
832C22×C3C2×D3×D414yes—
833C22×C3C2×D3×D412yes—
834C22×C3C2×D3×D412yes—
835C22×C3#100712yes—
836C22×C3D3×#4112yes—
837C22×C3#101012yes—
838C22×C3C24×D311yescharacteristic
839C22×C3C24×D311yescharacteristic
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—34no—
844C2×D3—34no—
845C2×D3—44no—
846C2×D3—64no—
847C2×D3—68no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—68no—
853C2×D3—64no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—128no—
863C2×D3—122no—
864C2×D3—122no—
865C2×D3—128no—
866C2×D3—124no—
867C2×D3—124no—
868C3×C4—24no—
869C3×C4—24no—
870C3×C4—22no—
871C3×C4—22no—
872C3×C4—22no—
873C3×C4—22no—
874C3×C4—34no—
875C3×C4—62no—
876C3×C4—62no—
877C3×C4—62no—
878C3×C4—62no—
879C3×C4—62no—
880C3×C4—62no—
881Dic3—22no—
882Dic3—22no—
883Dic3—22no—
884Dic3—22no—
885Dic3—22no—
886Dic3—22no—
887Dic3—34no—
888Dic3—34no—
889Dic3—64no—
890Dic3—64no—
891Dic3—62no—
892Dic3—62no—
893Dic3C2×#23514yescomplemented
894C32C2×#54711yescharacteristic, complemented, Sylow
895C23—22no—
896C23—22no—
897C23—32no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—94no—
902C23—92no—
903C23—92no—
904C23—182no—
905C23—182no—
906C23—182no—
907C23—182no—
908C23—182no—
909C23#381114yes—
910C23C22×D3212yes—
911C23C22×D3211yescharacteristic
912Q8—188no—
913Q8—188no—
914D4—68no—
915D4—916no—
916D4—188no—
917D4—188no—
918D4—188no—
919D4—188no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—28no—
923C2×C4—34no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—32no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—68no—
932C2×C4—62no—
933C2×C4—62no—
934C2×C4—62no—
935C2×C4—62no—
936C2×C4—62no—
937C2×C4—68no—
938C2×C4—62no—
939C2×C4—94no—
940C2×C4—92no—
941C2×C4—92no—
942C2×C4—188no—
943C2×C4—188no—
944C2×C4—188no—
945C2×C4—188no—
946C2×C4—188no—
947C2×C4—182no—
948C2×C4C22×D3212yes—
949C2×C4C22×D3212yes—
950C2×C3—24no—
951C2×C3—24no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—24no—
956C2×C3—44no—
957C2×C3—122no—
958C2×C3#550714yescomplemented
959C2×C3#565514yescomplemented
960C2×C3C22×#23511yescharacteristic
961C2×C3C22×D3×D411yescharacteristic
962C2×C3C22×D3×D411yescharacteristic
963C2×C3C2×#100711yescharacteristic
964C2×C3C2×D3×#4111yescharacteristic
965C2×C3C2×#101011yescharacteristic
966D3—42no—
967D3—64no—
968D3—64no—
969D3—124no—
970D3—124no—
971D3—122no—
972D3—122no—
973C22—22no—
974C22—22no—
975C22—28no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—94no—
980C22—124no—
981C22—182no—
982C22—182no—
983C22—188no—
984C22—182no—
985C22—182no—
986C22—182no—
987C22—364no—
988C22#6429712yes—
989C22D3×#23512yes—
990C22C2×#381114yes—
991C22C2×#381112yes—
992C22C23×D3211yescharacteristic
993C4—22no—
994C4—22no—
995C4—34no—
996C4—62no—
997C4—62no—
998C4—62no—
999C4—62no—
1000C4—62no—
1001C4—62no—
1002C4—94no—
1003C4—182no—
1004C3—21no—
1005C3C2×#550711yescharacteristic, complemented
1006C3C2×#565511yescharacteristic, complemented
1007C2—24no—
1008C2—122no—
1009C2—184no—
1010C2—362no—
1011C2#1059491714yesdirect product factor
1012C2C2×#6429711yescharacteristic
1013C2C2×D3×#23511yescharacteristic
1014C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C22×#3804C2semidirect
3. C2×C3×#929C2semidirect
4. C22×C3×Dic3⋊C4C2semidirect
5. C2×#63978C2semidirect
6. C2×#63966C2semidirect
7. C2×#63952C2semidirect
8. C2×#63910C2semidirect
9. C2×#63897C2semidirect
10. #10594917C2direct (N × H)
11. C2×#63896C2semidirect
12. C2×#63883C2semidirect
13. C2×#63881C2semidirect
14. C2×#63865C2semidirect
15. C2×#63853C2semidirect
16. C2×#63840C2semidirect
23. C2×#3828C22semidirect
37. C2×#3804C22semidirect
40. C3×#929C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. #63978C22semidirect
52. #63966C22semidirect
62. #63952C22semidirect
63. #63910C22semidirect
64. #63897C22semidirect
65. #63896C22semidirect
66. #63883C22semidirect
67. #63881C22semidirect
68. #63865C22semidirect
69. #63853C22semidirect
70. #63840C22semidirect
81. C2×#929D3semidirect
83. C22×Dic3⋊C4D3semidirect
113. C2×#638D4semidirect
238. #929C2×D3semidirect
265. C2×Dic3⋊C4C2×D3semidirect
309. #638C2×D4semidirect
327. C2×C3×Dic3#41semidirect
545. C3×Dic3C2×#41semidirect
707. C2×Dic3#235semidirect
737. C2×C32#547semidirect
893. Dic3C2×#235semidirect
894. C32C2×#547semidirect
958. C2×C3#5507semidirect
959. C2×C3#5655semidirect
1005. C3C2×#5507semidirect
1006. C3C2×#5655semidirect
1011. C2#10594917direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×#38042
C2×C3×#9292
C22×C3×Dic3⋊C42
C2×#639782
C2×#639662
C2×#639522
C2×#639102
C2×#638972
#105949172
C2×#638962
C2×#638832
C2×#638812
C2×#638652
C2×#638532
C2×#638402
C2×#56553
C2×#55073