Finite Group Databasebeta

← C2×#10595264 #11910188

Subgroups — C2×#10595264 #11910188

Order 1152.

3019 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6C2×#63979C211yesmaximal, characteristic, complemented
7C2×#63978C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C2×#63970C211yesmaximal, characteristic, complemented
10C2×#63966C211yesmaximal, characteristic, complemented
11C2×#63956C211yesmaximal, characteristic, complemented
12#10595264C2116yesmaximal, direct product factor
13C2×#63906C211yesmaximal, characteristic, complemented
14C2×#63890C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16C2×#63848C211yesmaximal, characteristic, complemented
17C2×#5620—31nomaximal
18C2×#5620—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C22×C3×#67C2211yescharacteristic, complemented
27C23×C3×Dic3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#625C2211yescharacteristic, complemented
34C22×D3×Dic3C2211yescharacteristic, complemented
35C2×#3757C2211yescharacteristic
36#64146C2218yescomplemented
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic, complemented
42C3×#939C2218yescomplemented
43C3×#938C2218yescomplemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47#63981C2218yescomplemented
48#63981C2218yescomplemented
49#63979C2218yescomplemented
50#63978C2218yescomplemented
51#63971C2218yescomplemented
52#63970C2218yescomplemented
53C2×#3724C2211yescharacteristic, complemented
54#63966C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic
59C2×#3722C2211yescharacteristic
60C2×#3722C2211yescharacteristic
61C2×#3722C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63956C2218yescomplemented
64C2×Dic32C2211yescharacteristic, complemented
65#63906C2218yescomplemented
66#63890C2218yescomplemented
67#63850C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×#121—31no—
71C2×#940—31no—
72C2×#940—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#939D311yescharacteristic, complemented
77C2×#938—31no—
78C2×#938D311yescharacteristic, complemented
79C2×#937—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#937—31no—
83C2×#937—61no—
84C2×#930—31no—
85C2×#930—31no—
86C2×#929—31no—
87C2×#929—31no—
88#5620—316no—
89#5620—316no—
90C2×#898—31no—
91C2×#898—31no—
92C2×#894—31no—
93C2×#894—31no—
94C2×#886—31no—
95C2×#886—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#879—31no—
101C2×#879—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3—42no—
105C23×C3⋊D3—42no—
106C23×C3⋊D3—42no—
107C23×C3⋊D3C2311yescharacteristic
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C2×C32×D4—42no—
113C2×C32×D4C2314yes—
114C22×C32×C4C2311yescharacteristic
115C2×#638—42no—
116C2×#638—42no—
117C2×#638C2314yes—
118C2×#638C2314yes—
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121C2×C3×#67—42no—
122C2×C3×#67—42no—
123C2×C3×#67—42no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yescomplemented
128C2×C3×#67C2314yescomplemented
129C22×C3×Dic3—42no—
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2314yescomplemented
137C2×C3×C4×D3—42no—
138C2×C3×C4×D3C2314yescomplemented
139C2×#626—42no—
140C2×#626—42no—
141C2×#626—42no—
142C2×#626—42no—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#626C2314yes—
146C2×#626C2314yes—
147C2×#625—42no—
148C2×#625C2314yescomplemented
149C2×D3×Dic3—42no—
150C2×D3×Dic3C2314yescomplemented
151#3757C2314yes—
152#3752C2314yes—
153#3752C2314yes—
154C3×#217C2314yes—
155C3×#217C2314yes—
156C3×#217C2314yescomplemented
157C3×(C2×D3)⋊C4C2314yescomplemented
158C3×C4⋊Dic3C2314yescomplemented
159C3×Dic3⋊C4C2314yescomplemented
160#3724C2314yescomplemented
161Dic3⋊Dic3C2314yescomplemented
162Dic3⋊Dic3C2314yescomplemented
163Dic3⋊Dic3C2314yescomplemented
164#3722C2314yes—
165#3722C2314yes—
166#3722C2314yes—
167#3722C2314yes—
168(C2×D3)⋊Dic3C2314yescomplemented
169Dic32C2314yescomplemented
170C2×#560—91noSylow
171C24×D3—31no—
172C24×D3—31no—
173C24×D3—61no—
174C22×C3×D4—21no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4C2×D311yescharacteristic
180C22×C3×D4C2×D311yescharacteristic
181C23×C3×C4—31no—
182C23×C3×C4—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—61no—
194C22×#67—61no—
195C22×#67C2×D311yescharacteristic
196C22×#67C2×D311yescharacteristic
197C22×#67C2×D311yescharacteristic, complemented
198C22×#67C2×D311yescharacteristic, complemented
199C23×Dic3—31no—
200C23×Dic3C2×D311yescharacteristic, complemented
201C22×D12—31no—
202C22×D12—31no—
203C22×D12—31no—
204C22×D12—31no—
205C22×C4×D3—31no—
206C22×C4×D3C2×D311yescharacteristic, complemented
207C3×#121—38no—
208C3×#121—38no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C22⋊C4—31no—
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217—31no—
218C2×#217—61no—
219C2×#217C2×D311yescharacteristic
220C2×#217C2×D311yescharacteristic
221C2×#217C2×D311yescharacteristic, complemented
222#940—38no—
223#940—38no—
224#939—38no—
225#939—38no—
226#939—38no—
227#939C2×D318yescomplemented
228#938—38no—
229#938C2×D318yescomplemented
230#937—38no—
231#937—38no—
232#937—38no—
233#937—38no—
234#937—68no—
235#930—38no—
236#930—38no—
237#929—38no—
238#929—38no—
239C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—61no—
253C2×(C2×D3)⋊C4—61no—
254C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
255C2×C4⋊Dic3—31no—
256C2×C4⋊Dic3—31no—
257C2×C4⋊Dic3—31no—
258C2×C4⋊Dic3C2×D311yescharacteristic, complemented
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—31no—
262C2×Dic3⋊C4—31no—
263C2×Dic3⋊C4—31no—
264C2×Dic3⋊C4C2×D311yescharacteristic, complemented
265C2×C4×Dic3—31no—
266C2×C4×Dic3—31no—
267#898—38no—
268#898—38no—
269#894—38no—
270#894—38no—
271#886—38no—
272#886—38no—
273#884—38no—
274#884—38no—
275#882—38no—
276#882—38no—
277#879—38no—
278#879—38no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32—22no—
283C23×C32—22no—
284C23×C32—22no—
285C23×C32C2412yes—
286C23×C32C2412yes—
287C23×C32C2411yescharacteristic
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3—22no—
294C22×C3⋊D3—44no—
295C22×C3⋊D3—44no—
296C22×C3⋊D3—44no—
297C22×C3⋊D3—416no—
298C22×C3⋊D3C2412yes—
299C22×C3⋊D3C2412yes—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C32×D4—44no—
309C2×C32×C4—22no—
310C2×C32×C4C2412yes—
311#638—44no—
312#638—44no—
313C2×C3⋊Dic3—22no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3C2412yes—
316C2×C3⋊Dic3C2412yes—
317C3×#67—44no—
318C3×#67—44no—
319C3×#67—44no—
320C3×#67—44no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—44no—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C3×C4×D3—44no—
335#626—44no—
336#626—44no—
337#626—44no—
338#626—44no—
339#625—44no—
340D3×Dic3—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—91no—
344C2×#126—91no—
345C2×#123—91no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#121—31no—
349C2×#121—31no—
350C2×#121—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×#121—91no—
354C2×#120—91no—
355C2×#120—91no—
356C2×#120—91no—
357C24×C3—21no—
358C24×C3—21no—
359C24×C3—31no—
360C24×C3—31no—
361C24×C3C22×D311yescharacteristic
362C24×C3C22×D311yescharacteristic
363C24×C3C22×D311yescharacteristic
364C24×C3C22×D311yescharacteristic
365C23×D3—31no—
366C23×D3—31no—
367C23×D3—31no—
368C23×D3—31no—
369C23×D3—34no—
370C23×D3—34no—
371C23×D3—61no—
372C23×D3—61no—
373C23×D3—64no—
374C23×D3—122no—
375C23×D3—122no—
376C23×D3—122no—
377C23×D3—122no—
378C23×D3—122no—
379C23×D3—122no—
380C23×D3—124no—
381C23×D3—124no—
382C23×D3—124no—
383C23×D3C22×D311yescharacteristic
384C23×D3C22×D311yescharacteristic
385C2×C3×D4—24no—
386C2×C3×D4—34no—
387C2×C3×D4—34no—
388C2×C3×D4—34no—
389C2×C3×D4—34no—
390C2×C3×D4—42no—
391C2×C3×D4—42no—
392C2×C3×D4—44no—
393C2×C3×D4—122no—
394C2×C3×D4—122no—
395C2×C3×D4—122no—
396C2×C3×D4—122no—
397C2×C3×D4C22×D314yes—
398C2×C3×D4C22×D314yes—
399C22×C3×C4—21no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—31no—
405C22×C3×C4—31no—
406C22×C3×C4—34no—
407C22×C3×C4—34no—
408C22×C3×C4—122no—
409C22×C3×C4—122no—
410C22×C3×C4C22×D311yescharacteristic
411C22×C3×C4C22×D311yescharacteristic
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—34no—
421C2×#67—34no—
422C2×#67—42no—
423C2×#67—42no—
424C2×#67—42no—
425C2×#67—42no—
426C2×#67—64no—
427C2×#67—64no—
428C2×#67—122no—
429C2×#67—122no—
430C2×#67—122no—
431C2×#67—122no—
432C2×#67—122no—
433C2×#67—122no—
434C2×#67—122no—
435C2×#67—122no—
436C2×#67—122no—
437C2×#67—122no—
438C2×#67—124no—
439C2×#67—124no—
440C2×#67C22×D314yes—
441C2×#67C22×D314yes—
442C2×#67C22×D314yescomplemented
443C2×#67C22×D314yescomplemented
444C22×Dic3—31no—
445C22×Dic3—31no—
446C22×Dic3—31no—
447C22×Dic3—31no—
448C22×Dic3—34no—
449C22×Dic3—42no—
450C22×Dic3—61no—
451C22×Dic3—61no—
452C22×Dic3—122no—
453C22×Dic3C22×D311yescharacteristic
454C22×Dic3C22×D311yescharacteristic
455C22×Dic3C22×D311yescharacteristic
456C22×Dic3C22×D311yescharacteristic
457C22×Dic3C22×D311yescharacteristic
458C22×Dic3C22×D311yescharacteristic
459C22×Dic3C22×D314yescomplemented
460C2×D12—34no—
461C2×D12—34no—
462C2×D12—34no—
463C2×D12—34no—
464C2×D12—122no—
465C2×D12—122no—
466C2×D12—122no—
467C2×D12—122no—
468C2×C4×D3—34no—
469C2×C4×D3—42no—
470C2×C4×D3—122no—
471C2×C4×D3C22×D314yescomplemented
472C3×C4⋊C4—34no—
473C3×C4⋊C4—34no—
474C3×C22⋊C4—34no—
475C3×C22⋊C4—34no—
476C3×C22⋊C4—34no—
477C3×C22⋊C4—34no—
478#217—34no—
479#217—34no—
480#217—34no—
481#217—64no—
482#217C22×D314yes—
483#217C22×D314yes—
484#217C22×D314yescomplemented
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
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)⋊C4—34no—
498(C2×D3)⋊C4—64no—
499(C2×D3)⋊C4—64no—
500(C2×D3)⋊C4C22×D314yescomplemented
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—34no—
504C4⋊Dic3C22×D314yescomplemented
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4C22×D314yescomplemented
511C4×Dic3—34no—
512C4×Dic3—34no—
513C22×C32—22no—
514C22×C32—22no—
515C22×C32—22no—
516C22×C32—22no—
517C22×C32—22no—
518C22×C32—22no—
519C22×C32—44no—
520C22×C32—44no—
521C22×C32H(5,𝔽2)12yes—
522C22×C32H(5,𝔽2)12yes—
523C22×C32H(5,𝔽2)12yes—
524C22×C32C2511yescharacteristic
525C2×C3⋊D3—22no—
526C2×C3⋊D3—22no—
527C2×C3⋊D3—22no—
528C2×C3⋊D3—22no—
529C2×C3⋊D3—22no—
530C2×C3⋊D3—22no—
531C2×C3⋊D3—416no—
532C2×C3⋊D3—44no—
533C2×C3⋊D3—44no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—44no—
541C2×C3×D3—44no—
542C32×C4—22no—
543C3⋊Dic3—22no—
544C3⋊Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3—22no—
550C3×Dic3—22no—
551C25—91no—
552C22×D4—31no—
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—31no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—91no—
562C22×D4—91no—
563C22×D4D3211yescharacteristic
564C23×C4—31no—
565C23×C4—31no—
566C23×C4—91no—
567#127—98no—
568#126—98no—
569#126—98no—
570#123—98no—
571#123—98no—
572#123—98no—
573#121—38no—
574#121—38no—
575#121—98no—
576#121—98no—
577#121—98no—
578#121—98no—
579#120—98no—
580#120—98no—
581#120—98no—
582C2×C4⋊C4—31no—
583C2×C4⋊C4—31no—
584C2×C4⋊C4—91no—
585C2×C4⋊C4—91no—
586C2×C4⋊C4—91no—
587C2×C4⋊C4—91no—
588C2×C22⋊C4—31no—
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×C22⋊C4—91no—
598C2×C22⋊C4—91no—
599C2×C22⋊C4—91no—
600C2×C42—91no—
601C23×C3—24no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—21no—
617C23×C3—32no—
618C23×C3—32no—
619C23×C3—42no—
620C23×C3—42no—
621C23×C3—42no—
622C23×C3—42no—
623C23×C3—42no—
624C23×C3—62no—
625C23×C3—62no—
626C23×C3—62no—
627C23×C3—62no—
628C23×C3—62no—
629C23×C3—62no—
630C23×C3C23×D312yes—
631C23×C3C23×D312yes—
632C23×C3C23×D312yes—
633C23×C3C23×D312yes—
634C23×C3C23×D311yescharacteristic
635C23×C3C23×D311yescharacteristic
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—32no—
645C22×D3—32no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—64no—
649C22×D3—64no—
650C22×D3—62no—
651C22×D3—62no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—62no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—62no—
658C22×D3—62no—
659C22×D3—62no—
660C22×D3—62no—
661C22×D3—62no—
662C22×D3—122no—
663C22×D3—122no—
664C22×D3—122no—
665C22×D3—122no—
666C22×D3—124no—
667C22×D3—124no—
668C22×D3—124no—
669C22×D3—124no—
670C22×D3—124no—
671C22×D3—124no—
672C22×D3—128no—
673C22×D3—128no—
674C22×D3—128no—
675C22×D3—1232no—
676C22×D3—1216no—
677C22×D3—1216no—
678C22×D3C23×D312yes—
679C22×D3C23×D312yes—
680C3×D4—44no—
681C3×D4—44no—
682C3×D4—48no—
683C3×D4—124no—
684C3×D4—124no—
685C3×D4—124no—
686C3×D4—124no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
690C2×C3×C4—32no—
691C2×C3×C4—32no—
692C2×C3×C4—32no—
693C2×C3×C4—32no—
694C2×C3×C4—32no—
695C2×C3×C4—32no—
696C2×C3×C4—42no—
697C2×C3×C4—62no—
698C2×C3×C4—62no—
699C2×C3×C4—62no—
700C2×C3×C4—62no—
701C2×C3×C4—62no—
702C2×C3×C4—62no—
703C2×C3×C4—124no—
704C2×C3×C4—124no—
705C2×C3×C4C23×D312yes—
706C2×C3×C4C23×D312yes—
707#67—44no—
708#67—44no—
709#67—44no—
710#67—44no—
711#67—124no—
712#67—124no—
713#67—124no—
714#67—124no—
715#67—124no—
716#67—124no—
717#67—124no—
718#67—124no—
719#67—124no—
720#67—124no—
721#67—128no—
722#67—128no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—22no—
726C2×Dic3—22no—
727C2×Dic3—22no—
728C2×Dic3—22no—
729C2×Dic3—32no—
730C2×Dic3—32no—
731C2×Dic3—32no—
732C2×Dic3—32no—
733C2×Dic3—44no—
734C2×Dic3—62no—
735C2×Dic3—62no—
736C2×Dic3—62no—
737C2×Dic3—62no—
738C2×Dic3—62no—
739C2×Dic3—62no—
740C2×Dic3—122no—
741C2×Dic3—122no—
742C2×Dic3—124no—
743C2×Dic3C23×D312yes—
744C2×Dic3C23×D312yes—
745C2×Dic3C23×D312yes—
746C2×Dic3C23×D312yes—
747C2×Dic3C23×D312yes—
748C2×Dic3C23×D312yes—
749D12—124no—
750D12—124no—
751D12—124no—
752D12—124no—
753C4×D3—44no—
754C4×D3—124no—
755C2×C32—42no—
756C2×C32—42no—
757C2×C32#56014yescomplemented
758C2×C32C2×H(5,𝔽2)11yescharacteristic
759C2×C32C2×H(5,𝔽2)11yescharacteristic
760C2×C32C2×H(5,𝔽2)11yescharacteristic
761C3⋊D3—42no—
762C3⋊D3—42no—
763C3×D3—42no—
764C3×D3—42no—
765C24—31no—
766C24—31no—
767C24—91no—
768C24—91no—
769C24—94no—
770C24—362no—
771C24—362no—
772C24—362no—
773C24C2×D3211yescharacteristic
774C24C2×D3211yescharacteristic
775C2×D4—34no—
776C2×D4—34no—
777C2×D4—34no—
778C2×D4—34no—
779C2×D4—42no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—94no—
784C2×D4—94no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—122no—
788C2×D4—122no—
789C2×D4—122no—
790C2×D4—122no—
791C2×D4—362no—
792C2×D4—362no—
793C2×D4—362no—
794C2×D4—362no—
795C2×D4—362no—
796C2×D4—362no—
797C2×D4—362no—
798C2×D4C2×D3214yes—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—31no—
804C22×C4—31no—
805C22×C4—34no—
806C22×C4—34no—
807C22×C4—94no—
808C22×C4—91no—
809C22×C4—91no—
810C22×C4—122no—
811C22×C4—122no—
812C22×C4—362no—
813C22×C4C2×D3211yescharacteristic
814C4⋊C4—34no—
815C4⋊C4—34no—
816C4⋊C4—94no—
817C4⋊C4—94no—
818C4⋊C4—94no—
819C4⋊C4—94no—
820C22⋊C4—34no—
821C22⋊C4—34no—
822C22⋊C4—34no—
823C22⋊C4—34no—
824C22⋊C4—94no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—94no—
830C22⋊C4—94no—
831C22⋊C4—94no—
832C42—94no—
833C22×C3—24no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—21no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—48no—
856C22×C3—44no—
857C22×C3—44no—
858C22×C3—44no—
859C22×C3—44no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—84no—
867C22×C3—124no—
868C22×C3—124no—
869C22×C3#100412yes—
870C22×C3#100412yes—
871C22×C3#100412yes—
872C22×C3#100412yes—
873C22×C3#100912yes—
874C22×C3#100912yes—
875C22×C3C24×D311yescharacteristic
876C22×C3C24×D311yescharacteristic
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—44no—
884C2×D3—44no—
885C2×D3—64no—
886C2×D3—64no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—122no—
900C2×D3—122no—
901C2×D3—122no—
902C2×D3—122no—
903C2×D3—128no—
904C2×D3—128no—
905C2×D3—1232no—
906C2×D3—1216no—
907C2×D3—1216no—
908C2×D3—124no—
909C2×D3—124no—
910C2×D3—124no—
911C2×D3—124no—
912C3×C4—22no—
913C3×C4—22no—
914C3×C4—42no—
915C3×C4—62no—
916C3×C4—62no—
917C3×C4—62no—
918C3×C4—62no—
919C3×C4—62no—
920C3×C4—62no—
921Dic3—22no—
922Dic3—22no—
923Dic3—22no—
924Dic3—22no—
925Dic3—22no—
926Dic3—22no—
927Dic3—62no—
928Dic3—62no—
929Dic3—62no—
930Dic3—62no—
931Dic3—122no—
932Dic3—122no—
933C32C2×#56011yescharacteristic, complemented, Sylow
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—32no—
941C23—32no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—92no—
949C23—92no—
950C23—182no—
951C23—182no—
952C23—182no—
953C23—182no—
954C23—182no—
955C23—182no—
956C23—364no—
957C23—364no—
958C23—364no—
959C23—3616no—
960C23C22×D3212yes—
961C23C22×D3212yes—
962C23C22×D3211yescharacteristic
963D4—44no—
964D4—124no—
965D4—124no—
966D4—124no—
967D4—124no—
968D4—364no—
969D4—364no—
970D4—364no—
971D4—364no—
972D4—364no—
973D4—364no—
974D4—364no—
975C2×C4—22no—
976C2×C4—32no—
977C2×C4—32no—
978C2×C4—32no—
979C2×C4—32no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—92no—
989C2×C4—92no—
990C2×C4—124no—
991C2×C4—124no—
992C2×C4—182no—
993C2×C4—182no—
994C2×C4—364no—
995C2×C4C22×D3212yes—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—24no—
1000C2×C3—44no—
1001C2×C3—42no—
1002C2×C3—42no—
1003C2×C3—42no—
1004C2×C3—42no—
1005C2×C3—82no—
1006C2×C3—122no—
1007C2×C3—122no—
1008C2×C3#562014yescomplemented
1009C2×C3#562014yescomplemented
1010C2×C3C2×#100411yescharacteristic
1011C2×C3C2×#100411yescharacteristic
1012C2×C3C2×#100411yescharacteristic
1013C2×C3C2×#100411yescharacteristic
1014C2×C3C2×#100911yescharacteristic
1015C2×C3C2×#100911yescharacteristic
1016D3—42no—
1017D3—42no—
1018D3—124no—
1019D3—124no—
1020D3—122no—
1021D3—122no—
1022D3—122no—
1023D3—122no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—22no—
1028C22—22no—
1029C22—22no—
1030C22—44no—
1031C22—44no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—62no—
1038C22—124no—
1039C22—124no—
1040C22—182no—
1041C22—182no—
1042C22—182no—
1043C22—182no—
1044C22—182no—
1045C22—182no—
1046C22—3616no—
1047C22—364no—
1048C22—364no—
1049C22#6431412yes—
1050C22#6431412yes—
1051C22#6433012yes—
1052C22C23×D3211yescharacteristic
1053C4—22no—
1054C4—62no—
1055C4—62no—
1056C4—62no—
1057C4—62no—
1058C4—62no—
1059C4—62no—
1060C4—182no—
1061C4—182no—
1062C3—21no—
1063C3C2×#562011yescharacteristic, complemented
1064C3C2×#562011yescharacteristic, complemented
1065C2—42no—
1066C2—42no—
1067C2—122no—
1068C2—122no—
1069C2—362no—
1070C2—362no—
1071C2#1059526414yesdirect product factor
1072C2C2×#6431411yescharacteristic
1073C2C2×#6431411yescharacteristic
1074C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64146C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#938C2semidirect
4. C2×#63981C2semidirect
5. C2×#63981C2semidirect
6. C2×#63979C2semidirect
7. C2×#63978C2semidirect
8. C2×#63971C2semidirect
9. C2×#63970C2semidirect
10. C2×#63966C2semidirect
11. C2×#63956C2semidirect
12. #10595264C2direct (N × H)
13. C2×#63906C2semidirect
14. C2×#63890C2semidirect
15. C2×#63850C2semidirect
16. C2×#63848C2semidirect
25. C22×C3×#67C22semidirect
26. C22×C3×#67C22semidirect
27. C23×C3×Dic3C22semidirect
28. C22×C3×C4×D3C22semidirect
33. C22×#625C22semidirect
34. C22×D3×Dic3C22semidirect
36. #64146C22semidirect
41. C2×C3×#217C22semidirect
42. C3×#939C22semidirect
43. C3×#938C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×C4⋊Dic3C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. #63981C22semidirect
48. #63981C22semidirect
49. #63979C22semidirect
50. #63978C22semidirect
51. #63971C22semidirect
52. #63970C22semidirect
53. C2×#3724C22semidirect
54. #63966C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63956C22semidirect
64. C2×Dic32C22semidirect
65. #63906C22semidirect
66. #63890C22semidirect
67. #63850C22semidirect
68. #63848C22semidirect
76. C2×#939D3semidirect
78. C2×#938D3semidirect
127. C2×C3×#67C23semidirect
128. C2×C3×#67C23semidirect
136. C22×C3×Dic3C23semidirect
138. C2×C3×C4×D3C23semidirect
148. C2×#625C23semidirect
150. C2×D3×Dic3C23semidirect
156. C3×#217C23semidirect
157. C3×(C2×D3)⋊C4C23semidirect
158. C3×C4⋊Dic3C23semidirect
159. C3×Dic3⋊C4C23semidirect
160. #3724C23semidirect
161. Dic3⋊Dic3C23semidirect
162. Dic3⋊Dic3C23semidirect
163. Dic3⋊Dic3C23semidirect
168. (C2×D3)⋊Dic3C23semidirect
169. Dic32C23semidirect
197. C22×#67C2×D3semidirect
198. C22×#67C2×D3semidirect
200. C23×Dic3C2×D3semidirect
206. C22×C4×D3C2×D3semidirect
221. C2×#217C2×D3semidirect
227. #939C2×D3semidirect
229. #938C2×D3semidirect
254. C2×(C2×D3)⋊C4C2×D3semidirect
258. C2×C4⋊Dic3C2×D3semidirect
264. C2×Dic3⋊C4C2×D3semidirect
442. C2×#67C22×D3semidirect
443. C2×#67C22×D3semidirect
459. C22×Dic3C22×D3semidirect
471. C2×C4×D3C22×D3semidirect
484. #217C22×D3semidirect
500. (C2×D3)⋊C4C22×D3semidirect
504. C4⋊Dic3C22×D3semidirect
510. Dic3⋊C4C22×D3semidirect
757. C2×C32#560semidirect
933. C32C2×#560semidirect
1008. C2×C3#5620semidirect
1009. C2×C3#5620semidirect
1063. C3C2×#5620semidirect
1064. C3C2×#5620semidirect
1071. C2#10595264direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641462
C2×C3×#9392
C2×C3×#9382
C2×#639812
C2×#639792
C2×#639782
C2×#639712
C2×#639702
C2×#639662
C2×#639562
#105952642
C2×#639062
C2×#638902
C2×#638502
C2×#638482
C2×#56203