Finite Group Databasebeta

← C2×#10595267 #11901327

Subgroups — C2×#10595267 #11901327

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C2×#63976C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63970C211yesmaximal, characteristic, complemented
8C2×#63964C211yesmaximal, characteristic, complemented
9C2×#63962C211yesmaximal, characteristic, complemented
10C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
11C2×#63959C211yesmaximal, characteristic, complemented
12#10595267C2116yesmaximal, direct product factor
13C2×#63915C211yesmaximal, characteristic, complemented
14C2×#63891C211yesmaximal, characteristic, complemented
15C2×#63862C211yesmaximal, characteristic, complemented
16C2×#63861C211yesmaximal, characteristic, complemented
17C2×#5617—31nomaximal
18C2×#5593—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic, complemented
27C23×C3×Dic3C2211yescharacteristic
28C22×#627C2211yescharacteristic, complemented
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic, complemented
34D4×C3⋊Dic3C2218yescomplemented
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic, complemented
39C3×#939C2218yescomplemented
40C3×#937C2218yescomplemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45#63980C2218yescomplemented
46#63976C2218yescomplemented
47#67⋊Dic3C2218yescomplemented
48#63970C2218yescomplemented
49C2×#3724C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53#63964C2218yescomplemented
54#63962C2218yescomplemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2218yescomplemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63959C2218yescomplemented
64C2×Dic32C2211yescharacteristic, complemented
65#63915C2218yescomplemented
66#63891C2218yescomplemented
67#63862C2218yescomplemented
68#63861C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×#120—31no—
71C2×#953—31no—
72C22×#217—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#939D311yescharacteristic, complemented
77C2×#938—31no—
78C2×#937—31no—
79C2×#937D311yescharacteristic, complemented
80C2×#936—31no—
81C2×#935—31no—
82C2×D4×Dic3—31no—
83C2×D4×Dic3—31no—
84C2×D4×Dic3—31no—
85C2×D4×Dic3—61no—
86C22×(C2×D3)⋊C4—31no—
87C2×#924—31no—
88#5617—316no—
89#5593—316no—
90C2×#898—31no—
91C2×#898—31no—
92C2×#886—31no—
93C2×#886—31no—
94C2×#885—31no—
95C2×#885—31no—
96C2×#885—31no—
97C2×#883—31no—
98C2×#67⋊C4—31no—
99C2×#879—31no—
100C2×#879—31no—
101C2×#878—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3—24no—
105C23×C3×D3—42no—
106C23×C3×D3—42no—
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2314yes—
111C2×C32×D4—24no—
112C2×C32×D4C2314yes—
113C22×C32×C4C2311yescharacteristic
114C22×C3⋊Dic3—42no—
115C22×C3⋊Dic3—42no—
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2314yes—
121C22×C3⋊Dic3C2314yescomplemented
122C2×C3×#67—24no—
123C2×C3×#67—42no—
124C2×C3×#67—42no—
125C2×C3×#67—42no—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yescomplemented
130C22×C3×Dic3—42no—
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2314yes—
137C2×#627—42no—
138C2×#627C2314yescomplemented
139C2×#625—42no—
140C2×#625—42no—
141C2×#625C2314yes—
142C2×#625C2314yes—
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yescomplemented
145#3757C2314yes—
146#3757C2314yescomplemented
147C4⋊(C3⋊Dic3)C2314yescomplemented
148C4×C3⋊Dic3C2314yescomplemented
149C3×#217C2314yes—
150C3×#217C2314yescomplemented
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155#3724C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C25×C3—31no—
169C24×D3C2×D311yescharacteristic
170C22×C3×D4—21no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4C2×D311yescharacteristic
176C22×C3×D4C2×D311yescharacteristic
177C23×C3×C4—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67C2×D311yescharacteristic
183C22×#67C2×D311yescharacteristic
184C22×#67C2×D311yescharacteristic
185C22×#67C2×D311yescharacteristic, complemented
186C23×Dic3—31no—
187C23×Dic3—31no—
188C23×Dic3—31no—
189C23×Dic3—31no—
190C23×Dic3—31no—
191C23×Dic3—61no—
192C23×Dic3—61no—
193C23×Dic3C2×D311yescharacteristic
194C22×C4×D3—31no—
195C22×Dic6—31no—
196C22×Dic6—31no—
197C3×#121—38no—
198C3×#120—38no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205#953—38no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217—38no—
218C2×#217—61no—
219C2×#217—61no—
220C2×#217C2×D311yescharacteristic
221C2×#217C2×D311yescharacteristic, complemented
222#939—38no—
223#939—38no—
224#939—38no—
225#939C2×D318yescomplemented
226#938—38no—
227#937—38no—
228#937C2×D318yescomplemented
229#936—38no—
230#935—38no—
231D4×Dic3—38no—
232D4×Dic3—38no—
233D4×Dic3—38no—
234D4×Dic3—68no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—38no—
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244C2×(C2×D3)⋊C4C2×D311yescharacteristic
245C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—31no—
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3—31no—
250C2×C4⋊Dic3—31no—
251C2×C4⋊Dic3—61no—
252#924—38no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4C2×D311yescharacteristic, complemented
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3—31no—
262C2×C4×Dic3—31no—
263C2×C4×Dic3—61no—
264#898—38no—
265#898—38no—
266#886—38no—
267#886—38no—
268#885—38no—
269#885—38no—
270#885—38no—
271#883—38no—
272#67⋊C4—38no—
273#879—38no—
274#879—38no—
275#878—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32#4114yes—
282C23×C32C2412yes—
283C23×C32C2412yes—
284C23×C32C2411yescharacteristic
285C22×C3×D3—28no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
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—22no—
295C22×C3×D3—44no—
296C22×C3×D3—44no—
297C22×C3×D3—416no—
298C22×C3×D3C2412yes—
299C22×C3×D3C2412yes—
300C22×C3×D3C2412yes—
301C32×D4—28no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304C2×C3⋊Dic3—22no—
305C2×C3⋊Dic3—22no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—44no—
309C2×C3⋊Dic3—44no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C2×C3⋊Dic3C2412yes—
314C3×#67—28no—
315C3×#67—44no—
316C3×#67—44no—
317C3×#67—44no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—44no—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329#627—44no—
330#625—44no—
331#625—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—91no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—31no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—31no—
345C2×#120—91no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—21no—
350C24×C3—21no—
351C24×C3—31no—
352C24×C3—31no—
353C24×C3—31no—
354C24×C3—34no—
355C24×C3—64no—
356C24×C3—122no—
357C24×C3—122no—
358C24×C3C22×D311yescharacteristic
359C24×C3C22×D311yescharacteristic
360C24×C3C22×D311yescharacteristic
361C24×C3C22×D311yescharacteristic
362C23×D3—24no—
363C23×D3—42no—
364C23×D3—42no—
365C23×D3C22×D311yescharacteristic
366C23×D3C22×D311yescharacteristic
367C23×D3C22×D311yescharacteristic
368C23×D3C22×D314yes—
369C2×C3×D4—28no—
370C2×C3×D4—24no—
371C2×C3×D4—24no—
372C2×C3×D4—24no—
373C2×C3×D4—34no—
374C2×C3×D4—34no—
375C2×C3×D4—34no—
376C2×C3×D4—34no—
377C2×C3×D4—64no—
378C2×C3×D4—122no—
379C2×C3×D4—122no—
380C2×C3×D4—122no—
381C2×C3×D4C22×D314yes—
382C2×C3×D4C22×D314yes—
383C22×C3×C4—21no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—34no—
390C22×C3×C4—122no—
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C2×#67—24no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—42no—
399C2×#67—42no—
400C2×#67—42no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—122no—
405C2×#67C22×D314yes—
406C2×#67C22×D314yes—
407C2×#67C22×D314yes—
408C2×#67C22×D314yescomplemented
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—31no—
417C22×Dic3—34no—
418C22×Dic3—34no—
419C22×Dic3—34no—
420C22×Dic3—34no—
421C22×Dic3—34no—
422C22×Dic3—42no—
423C22×Dic3—61no—
424C22×Dic3—61no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427C22×Dic3—64no—
428C22×Dic3—64no—
429C22×Dic3—122no—
430C22×Dic3—122no—
431C22×Dic3—122no—
432C22×Dic3—122no—
433C22×Dic3—122no—
434C22×Dic3—124no—
435C22×Dic3—124no—
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C22×Dic3C22×D311yescharacteristic
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441C22×Dic3C22×D314yes—
442C2×C4×D3—34no—
443C2×C4×D3—122no—
444C2×Dic6—34no—
445C2×Dic6—34no—
446C2×Dic6—122no—
447C2×Dic6—122no—
448C3×C4⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454#217—34no—
455#217—34no—
456#217—34no—
457#217—34no—
458#217—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—34no—
465#217—64no—
466#217—64no—
467#217C22×D314yes—
468#217C22×D314yescomplemented
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4C22×D314yes—
477(C2×D3)⋊C4C22×D314yes—
478(C2×D3)⋊C4C22×D314yescomplemented
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—64no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4C22×D314yescomplemented
491C4×Dic3—34no—
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3—34no—
495C4×Dic3—64no—
496C22×C32—22no—
497C22×C32—28no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—44no—
503C22×C32C2×#4114yes—
504C22×C32C2×#4112yes—
505C22×C32H(5,𝔽2)12yes—
506C22×C32H(5,𝔽2)12yes—
507C22×C32C2511yescharacteristic
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—416no—
518C2×C3×D3—44no—
519C2×C3×D3—44no—
520C2×C3×D3—44no—
521C32×C4—22no—
522C3⋊Dic3—22no—
523C3⋊Dic3—22no—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C25—31no—
532C22×Q8—91no—
533C22×D4—31no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—31no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4D3211yescharacteristic
540C23×C4—31no—
541C23×C4—91no—
542C23×C4—91no—
543C23×C4—91no—
544#126—98no—
545#126—98no—
546#124—98no—
547#124—98no—
548#123—98no—
549#123—98no—
550C22⋊Q8—98no—
551#121—38no—
552#121—98no—
553#121—98no—
554#120—38no—
555#120—98no—
556C4×D4—98no—
557C4×D4—98no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—98no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C42—91no—
580C2×C42—91no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—24no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—21no—
595C23×C3—24no—
596C23×C3—32no—
597C23×C3—32no—
598C23×C3—32no—
599C23×C3—42no—
600C23×C3—42no—
601C23×C3—42no—
602C23×C3—42no—
603C23×C3—62no—
604C23×C3—68no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—62no—
611C23×C3—62no—
612C23×C3—62no—
613C23×C3—124no—
614C23×C3—124no—
615C23×C3—1216no—
616C23×C3#23714yes—
617C23×C3#23714yes—
618C23×C3C23×D312yes—
619C23×C3C23×D312yes—
620C23×C3C23×D312yes—
621C23×C3C23×D312yes—
622C23×C3C23×D311yescharacteristic
623C23×C3C23×D311yescharacteristic
624C22×D3—22no—
625C22×D3—28no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—44no—
635C22×D3—44no—
636C22×D3—416no—
637C22×D3C23×D312yes—
638C22×D3C23×D312yes—
639C22×D3C23×D312yes—
640C3×D4—216no—
641C3×D4—28no—
642C3×D4—28no—
643C3×D4—68no—
644C3×D4—124no—
645C3×D4—124no—
646C3×D4—124no—
647C2×C3×C4—24no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—124no—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664#67—28no—
665#67—44no—
666#67—44no—
667#67—44no—
668#67—124no—
669#67—124no—
670#67—124no—
671#67—124no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—44no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—64no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—122no—
700C2×Dic3—122no—
701C2×Dic3—122no—
702C2×Dic3—124no—
703C2×Dic3—124no—
704C2×Dic3—124no—
705C2×Dic3—124no—
706C2×Dic3—124no—
707C2×Dic3—128no—
708C2×Dic3—128no—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D312yes—
711C2×Dic3C23×D312yes—
712C2×Dic3C23×D312yes—
713C2×Dic3C23×D312yes—
714C4×D3—124no—
715Dic6—124no—
716Dic6—124no—
717C2×C32—24no—
718C2×C32—42no—
719C2×C32#53814yescomplemented
720C2×C32C22×#4111yescharacteristic
721C2×C32C2×H(5,𝔽2)11yescharacteristic
722C2×C32C2×H(5,𝔽2)11yescharacteristic
723C3×D3—42no—
724C3×D3—42no—
725C3×D3—42no—
726C24—31no—
727C24—31no—
728C24—31no—
729C24—34no—
730C24—64no—
731C24—122no—
732C24—122no—
733C24C2×D3211yescharacteristic
734C24C2×D3211yescharacteristic
735C2×Q8—94no—
736C2×Q8—362no—
737C2×D4—24no—
738C2×D4—34no—
739C2×D4—34no—
740C2×D4—34no—
741C2×D4—34no—
742C2×D4—64no—
743C2×D4—94no—
744C2×D4—94no—
745C2×D4—122no—
746C2×D4—122no—
747C2×D4—122no—
748C2×D4—362no—
749C2×D4—362no—
750C2×D4C2×D3214yes—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—34no—
757C22×C4—94no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—94no—
763C22×C4—94no—
764C22×C4—122no—
765C22×C4—362no—
766C22×C4—362no—
767C22×C4—362no—
768C22×C4C2×D3211yescharacteristic
769C4⋊C4—34no—
770C4⋊C4—94no—
771C4⋊C4—94no—
772C4⋊C4—94no—
773C4⋊C4—94no—
774C4⋊C4—94no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—34no—
779C22⋊C4—34no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C42—94no—
790C42—94no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—28no—
796C22×C3—28no—
797C22×C3—24no—
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—22no—
807C22×C3—24no—
808C22×C3—21no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—48no—
813C22×C3—42no—
814C22×C3—48no—
815C22×C3—44no—
816C22×C3—44no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—1216no—
827C22×C3—124no—
828C22×C3—124no—
829C22×C3—124no—
830C22×C3C2×#23714yes—
831C22×C3C2×#23714yes—
832C22×C3C2×#23712yes—
833C22×C3C2×#23712yes—
834C22×C3#100412yes—
835C22×C3#100412yes—
836C22×C3#100412yes—
837C22×C3#100912yes—
838C22×C3C24×D311yescharacteristic
839C22×C3C24×D311yescharacteristic
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—416no—
850C2×D3—44no—
851C2×D3—44no—
852C2×D3—44no—
853C3×C4—24no—
854C3×C4—22no—
855C3×C4—22no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—62no—
859C3×C4—62no—
860C3×C4—62no—
861Dic3—22no—
862Dic3—22no—
863Dic3—22no—
864Dic3—22no—
865Dic3—22no—
866Dic3—64no—
867Dic3—62no—
868Dic3—62no—
869Dic3—62no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—62no—
874Dic3—62no—
875Dic3—122no—
876Dic3—122no—
877Dic3—122no—
878C32C2×#53811yescharacteristic, complemented, Sylow
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—32no—
885C23—32no—
886C23—32no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—68no—
895C23—62no—
896C23—62no—
897C23—124no—
898C23—124no—
899C23—1216no—
900C23#380514yes—
901C23C22×D3212yes—
902C23C22×D3212yes—
903C23C22×D3211yescharacteristic
904Q8—364no—
905D4—28no—
906D4—68no—
907D4—124no—
908D4—124no—
909D4—124no—
910D4—364no—
911D4—364no—
912C2×C4—22no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—92no—
924C2×C4—92no—
925C2×C4—92no—
926C2×C4—92no—
927C2×C4—124no—
928C2×C4—182no—
929C2×C4—182no—
930C2×C4—182no—
931C2×C4—182no—
932C2×C4—364no—
933C2×C4—364no—
934C2×C4—364no—
935C2×C4C22×D3212yes—
936C2×C3—24no—
937C2×C3—24no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—24no—
942C2×C3—44no—
943C2×C3—44no—
944C2×C3—42no—
945C2×C3—42no—
946C2×C3—122no—
947C2×C3—122no—
948C2×C3—122no—
949C2×C3#559314yescomplemented
950C2×C3#561714yescomplemented
951C2×C3C22×#23711yescharacteristic
952C2×C3C22×#23711yescharacteristic
953C2×C3C2×#100411yescharacteristic
954C2×C3C2×#100411yescharacteristic
955C2×C3C2×#100411yescharacteristic
956C2×C3C2×#100911yescharacteristic
957D3—42no—
958D3—42no—
959D3—42no—
960C22—22no—
961C22—22no—
962C22—28no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—44no—
967C22—62no—
968C22—62no—
969C22—62no—
970C22—62no—
971C22—62no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—1216no—
977C22—124no—
978C22—124no—
979C22—124no—
980C22#6431312yes—
981C22#6431412yes—
982C22C2×#380514yes—
983C22C2×#380512yes—
984C22C23×D3211yescharacteristic
985C4—22no—
986C4—62no—
987C4—62no—
988C4—62no—
989C4—62no—
990C4—62no—
991C4—182no—
992C4—182no—
993C4—182no—
994C4—182no—
995C3—21no—
996C3C2×#559311yescharacteristic, complemented
997C3C2×#561711yescharacteristic, complemented
998C2—24no—
999C2—42no—
1000C2—122no—
1001C2—122no—
1002C2—122no—
1003C2#1059526714yesdirect product factor
1004C2C2×#6431311yescharacteristic
1005C2C2×#6431411yescharacteristic
1006C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#937C2semidirect
4. C2×#63980C2semidirect
5. C2×#63976C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C2×#63970C2semidirect
8. C2×#63964C2semidirect
9. C2×#63962C2semidirect
10. C22×(C2×D3)⋊Dic3C2semidirect
11. C2×#63959C2semidirect
12. #10595267C2direct (N × H)
13. C2×#63915C2semidirect
14. C2×#63891C2semidirect
15. C2×#63862C2semidirect
16. C2×#63861C2semidirect
22. C23×C3⋊Dic3C22semidirect
26. C22×C3×#67C22semidirect
28. C22×#627C22semidirect
31. C22×D3×Dic3C22semidirect
33. C2×#3757C22semidirect
34. D4×C3⋊Dic3C22semidirect
35. C2×C4⋊(C3⋊Dic3)C22semidirect
36. C2×C4×C3⋊Dic3C22semidirect
38. C2×C3×#217C22semidirect
39. C3×#939C22semidirect
40. C3×#937C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. #63980C22semidirect
46. #63976C22semidirect
47. #67⋊Dic3C22semidirect
48. #63970C22semidirect
49. C2×#3724C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. #63964C22semidirect
54. #63962C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63959C22semidirect
64. C2×Dic32C22semidirect
65. #63915C22semidirect
66. #63891C22semidirect
67. #63862C22semidirect
68. #63861C22semidirect
76. C2×#939D3semidirect
79. C2×#937D3semidirect
121. C22×C3⋊Dic3C23semidirect
129. C2×C3×#67C23semidirect
138. C2×#627C23semidirect
144. C2×D3×Dic3C23semidirect
146. #3757C23semidirect
147. C4⋊(C3⋊Dic3)C23semidirect
148. C4×C3⋊Dic3C23semidirect
150. C3×#217C23semidirect
153. C3×(C2×D3)⋊C4C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. #3724C23semidirect
156. Dic3⋊Dic3C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
185. C22×#67C2×D3semidirect
221. C2×#217C2×D3semidirect
225. #939C2×D3semidirect
228. #937C2×D3semidirect
245. C2×(C2×D3)⋊C4C2×D3semidirect
258. C2×Dic3⋊C4C2×D3semidirect
408. C2×#67C22×D3semidirect
468. #217C22×D3semidirect
478. (C2×D3)⋊C4C22×D3semidirect
490. Dic3⋊C4C22×D3semidirect
719. C2×C32#538semidirect
878. C32C2×#538semidirect
949. C2×C3#5593semidirect
950. C2×C3#5617semidirect
996. C3C2×#5593semidirect
997. C3C2×#5617semidirect
1003. C2#10595267direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9392
C2×C3×#9372
C2×#639802
C2×#639762
C2×#67⋊Dic32
C2×#639702
C2×#639642
C2×#639622
C22×(C2×D3)⋊Dic32
C2×#639592
#105952672
C2×#639152
C2×#638912
C2×#638622
C2×#638612
C2×#56173
C2×#55933