Finite Group Databasebeta

← C2×#10595185 #11901309

Subgroups — C2×#10595185 #11901309

Order 1152.

2885 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
1C2×#64147C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic, complemented
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×#63978C211yesmaximal, characteristic, complemented
5C2×#63977C211yesmaximal, characteristic, complemented
6C2×Dic3×#67C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×D3×#217C211yesmaximal, characteristic, complemented
9C2×#63959C211yesmaximal, characteristic, complemented
10C2×#63956C211yesmaximal, characteristic, complemented
11C2×#63953C211yesmaximal, characteristic, complemented
12#10595185C2116yesmaximal, direct product factor
13C2×#63893C211yesmaximal, characteristic, complemented
14C2×#63881C211yesmaximal, characteristic, complemented
15C2×#63861C211yesmaximal, characteristic, complemented
16C2×#63853C211yesmaximal, characteristic, complemented
17C2×#5657—31nomaximal
18C2×#5593—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic, complemented
27C22×#627C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic, complemented
34#64147C2218yescomplemented
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic, complemented
40C3×#937C2218yescomplemented
41C3×#935C2218yescomplemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46#63978C2218yescomplemented
47#63977C2218yescomplemented
48Dic3×#67C2218yescomplemented
49#63971C2218yescomplemented
50D3×#217C2218yescomplemented
51C2×#3724C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×#3722C2211yescharacteristic, complemented
55C2×#3722C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60#63959C2218yescomplemented
61#63956C2218yescomplemented
62C2×Dic32C2211yescharacteristic, complemented
63C2×Dic32C2211yescharacteristic, complemented
64#63953C2218yescomplemented
65#63893C2218yescomplemented
66#63881C2218yescomplemented
67#63861C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#120—31no—
71C2×#953—31no—
72C22×#217—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#938—31no—
76C2×#938—31no—
77C2×#938—61no—
78C2×#937D311yescharacteristic, complemented
79C2×#936—31no—
80C2×#935D311yescharacteristic, complemented
81C2×D4×Dic3—31no—
82C2×#930—31no—
83C2×C4×#67—31no—
84#5657—316no—
85#5593—316no—
86C2×#898—31no—
87C2×#897—31no—
88C2×#894—31no—
89C2×#893—31no—
90C2×#885—31no—
91C2×#885—31no—
92C2×#885—31no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#67⋊C4—31no—
97C2×D3×C22⋊C4—31no—
98C2×#879—31no—
99C2×#879—31no—
100C2×#879—31no—
101C2×#878—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3—24no—
106C23×C3×D3—42no—
107C23×C3×D3—42no—
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2314yes—
111C2×C32×D4—42no—
112C2×C32×D4C2314yes—
113C22×C32×C4C2311yescharacteristic
114C2×#638—42no—
115C2×#638—42no—
116C2×#638C2314yes—
117C2×#638C2314yescomplemented
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121C2×C4×C3⋊D3—42no—
122C2×C4×C3⋊D3C2314yescomplemented
123C2×C3×#67—24no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C22×C3×Dic3—42no—
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2314yescomplemented
135C2×#627—42no—
136C2×#627C2314yescomplemented
137C2×#626—24no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×D3×Dic3—42no—
142C2×D3×Dic3—42no—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yes—
145#3757C2314yes—
146#3757C2314yescomplemented
147C4⋊(C3⋊Dic3)C2314yescomplemented
148C3×#217C2314yes—
149C3×#217C2314yes—
150C3×#217C2314yes—
151C3×#217C2314yescomplemented
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×Dic3⋊C4C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156#3724C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yescomplemented
160#3722C2314yescomplemented
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165Dic32C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C25×C3—31no—
169C24×D3C2×D311yescharacteristic
170C22×C3×D4—21no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4C2×D311yescharacteristic
174C22×C3×D4C2×D311yescharacteristic
175C23×C3×C4—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—61no—
183C22×#67—61no—
184C22×#67C2×D311yescharacteristic
185C22×#67C2×D311yescharacteristic
186C23×Dic3—31no—
187C23×Dic3—31no—
188C23×Dic3C2×D311yescharacteristic, complemented
189C22×D12—31no—
190C22×D12—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—61no—
196C22×Dic6—31no—
197C22×Dic6—31no—
198C3×#123—38no—
199C3×#120—38no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208#953—38no—
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
222C2×#217C2×D311yescharacteristic
223C2×#217C2×D311yescharacteristic, complemented
224#939—38no—
225#939—38no—
226#938—38no—
227#938—38no—
228#938—68no—
229#937C2×D318yescomplemented
230#936—38no—
231#935C2×D318yescomplemented
232D4×Dic3—38no—
233#930—38no—
234C4×#67—38no—
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—31no—
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244C2×(C2×D3)⋊C4C2×D311yescharacteristic
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—31no—
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3—61no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4C2×D311yescharacteristic, complemented
255C2×Dic3⋊C4C2×D311yescharacteristic, complemented
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3—31no—
259C2×C4×Dic3—31no—
260#898—38no—
261#897—38no—
262#894—38no—
263#893—38no—
264#885—38no—
265#885—38no—
266#885—38no—
267#884—38no—
268#883—38no—
269#882—38no—
270#67⋊C4—38no—
271D3×C22⋊C4—38no—
272#879—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—22no—
282C23×C32C2412yes—
283C23×C32C2412yes—
284C23×C32C2411yescharacteristic
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3C2412yes—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—28no—
295C22×C3×D3—44no—
296C22×C3×D3—44no—
297C22×C3×D3—416no—
298C22×C3×D3#4114yes—
299C22×C3×D3C2412yes—
300C22×C3×D3C2412yes—
301C32×D4—44no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304#638—44no—
305#638—44no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3C2412yes—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C4×C3⋊D3—44no—
313C3×#67—28no—
314C3×#67—44no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—44no—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328#627—44no—
329#626—28no—
330#626—44no—
331D3×Dic3—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—31no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—91no—
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—34no—
354C24×C3—64no—
355C24×C3—122no—
356C24×C3—122no—
357C24×C3C22×D311yescharacteristic
358C24×C3C22×D311yescharacteristic
359C24×C3C22×D311yescharacteristic
360C24×C3C22×D311yescharacteristic
361C23×D3—24no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—42no—
365C23×D3—42no—
366C23×D3—61no—
367C23×D3C22×D311yescharacteristic
368C23×D3C22×D311yescharacteristic
369C23×D3C22×D314yes—
370C2×C3×D4—24no—
371C2×C3×D4—34no—
372C2×C3×D4—34no—
373C2×C3×D4—42no—
374C2×C3×D4—42no—
375C2×C3×D4—44no—
376C2×C3×D4—64no—
377C2×C3×D4—122no—
378C2×C3×D4C22×D314yes—
379C2×C3×D4C22×D314yes—
380C22×C3×C4—21no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—34no—
388C22×C3×C4—122no—
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C2×#67—24no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—42no—
399C2×#67—64no—
400C2×#67—64no—
401C2×#67—64no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—122no—
405C2×#67—122no—
406C2×#67—122no—
407C2×#67—124no—
408C2×#67—124no—
409C2×#67C22×D314yes—
410C2×#67C22×D314yes—
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—42no—
420C22×Dic3—61no—
421C22×Dic3—61no—
422C22×Dic3—61no—
423C22×Dic3—122no—
424C22×Dic3—122no—
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D311yescharacteristic
428C22×Dic3C22×D311yescharacteristic
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D314yescomplemented
432C2×D12—34no—
433C2×D12—34no—
434C2×D12—64no—
435C2×D12—122no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—64no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—124no—
446C2×Dic6—34no—
447C2×Dic6—34no—
448C2×Dic6—122no—
449C2×Dic6—122no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458#217—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—34no—
465#217—34no—
466#217—64no—
467#217—64no—
468#217C22×D314yes—
469#217C22×D314yes—
470#217C22×D314yes—
471#217C22×D314yescomplemented
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4C22×D314yes—
481(C2×D3)⋊C4C22×D314yes—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486C4⋊Dic3—64no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4C22×D314yescomplemented
492Dic3⋊C4C22×D314yescomplemented
493C4×Dic3—34no—
494C4×Dic3—34no—
495C4×Dic3—34no—
496C4×Dic3—34no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—22no—
503C22×C32—44no—
504C22×C32—44no—
505C22×C32C2×#4112yes—
506C22×C32H(5,𝔽2)12yes—
507C22×C32H(5,𝔽2)12yes—
508C22×C32C2511yescharacteristic
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—22no—
512C2×C3⋊D3—44no—
513C2×C3×D3—28no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—416no—
520C2×C3×D3—44no—
521C2×C3×D3C2×#4114yes—
522C32×C4—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—
531C3×Dic3—22no—
532C25—31no—
533C22×Q8—91no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4D3211yescharacteristic
541C23×C4—31no—
542C23×C4—91no—
543C23×C4—91no—
544C23×C4—91no—
545#126—98no—
546#126—98no—
547#124—98no—
548#124—98no—
549#123—38no—
550#123—98no—
551C22⋊Q8—98no—
552#121—98no—
553#121—98no—
554#121—98no—
555#120—38no—
556#120—98no—
557C4×D4—98no—
558C4×D4—98no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—98no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C22⋊C4—91no—
580C2×C42—91no—
581C2×C42—91no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
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—22no—
595C23×C3—22no—
596C23×C3—21no—
597C23×C3—34no—
598C23×C3—32no—
599C23×C3—32no—
600C23×C3—42no—
601C23×C3—42no—
602C23×C3—42no—
603C23×C3—42no—
604C23×C3—42no—
605C23×C3—42no—
606C23×C3—68no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—62no—
611C23×C3—62no—
612C23×C3—124no—
613C23×C3—124no—
614C23×C3—1216no—
615C23×C3C23×D312yes—
616C23×C3C23×D312yes—
617C23×C3C23×D312yes—
618C23×C3C23×D312yes—
619C23×C3C23×D311yescharacteristic
620C23×C3C23×D311yescharacteristic
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—28no—
627C22×D3—32no—
628C22×D3—32no—
629C22×D3—44no—
630C22×D3—44no—
631C22×D3—416no—
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#23714yes—
643C22×D3C23×D312yes—
644C22×D3C23×D312yes—
645C3×D4—44no—
646C3×D4—44no—
647C3×D4—48no—
648C3×D4—68no—
649C3×D4—124no—
650C2×C3×C4—24no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4—62no—
666C2×C3×C4—124no—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669#67—28no—
670#67—44no—
671#67—68no—
672#67—124no—
673#67—124no—
674#67—124no—
675#67—124no—
676#67—124no—
677#67—128no—
678#67—128no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—32no—
691C2×Dic3—44no—
692C2×Dic3—62no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—122no—
702C2×Dic3—122no—
703C2×Dic3—122no—
704C2×Dic3—124no—
705C2×Dic3—124no—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D312yes—
711C2×Dic3C23×D312yes—
712D12—68no—
713D12—124no—
714C4×D3—124no—
715C4×D3—124no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—128no—
719Dic6—124no—
720Dic6—124no—
721C2×C32—42no—
722C2×C32—42no—
723C2×C32#53814yescomplemented
724C2×C32C22×#4111yescharacteristic
725C2×C32C2×H(5,𝔽2)11yescharacteristic
726C2×C32C2×H(5,𝔽2)11yescharacteristic
727C3⋊D3—42no—
728C3×D3—24no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—34no—
733C24—64no—
734C24—91no—
735C24—122no—
736C24—122no—
737C24C2×D3211yescharacteristic
738C24C2×D3211yescharacteristic
739C2×Q8—94no—
740C2×Q8—362no—
741C2×D4—34no—
742C2×D4—34no—
743C2×D4—42no—
744C2×D4—64no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—122no—
750C2×D4—184no—
751C2×D4—362no—
752C2×D4—362no—
753C2×D4—362no—
754C2×D4C2×D3214yes—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—34no—
762C22×C4—94no—
763C22×C4—94no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—94no—
768C22×C4—122no—
769C22×C4—362no—
770C22×C4—362no—
771C22×C4—362no—
772C22×C4C2×D3211yescharacteristic
773C4⋊C4—34no—
774C4⋊C4—34no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—34no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C42—94no—
794C42—94no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
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—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—21no—
811C22×C3—34no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—44no—
819C22×C3—44no—
820C22×C3—44no—
821C22×C3—44no—
822C22×C3—68no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—84no—
829C22×C3—84no—
830C22×C3—1216no—
831C22×C3—124no—
832C22×C3C2×#23712yes—
833C22×C3#100412yes—
834C22×C3#100412yes—
835C22×C3#100412yes—
836C22×C3D3×#4112yes—
837C22×C3#100912yes—
838C22×C3C24×D311yescharacteristic
839C22×C3C24×D311yescharacteristic
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—28no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—416no—
847C2×D3—44no—
848C2×D3—64no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—122no—
856C2×D3—122no—
857C2×D3—128no—
858C2×D3—124no—
859C2×D3—124no—
860C2×D3C2×#23714yes—
861C3×C4—24no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—62no—
865C3×C4—62no—
866C3×C4—62no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870Dic3—22no—
871Dic3—22no—
872Dic3—22no—
873Dic3—22no—
874Dic3—22no—
875Dic3—22no—
876Dic3—62no—
877Dic3—62no—
878Dic3—62no—
879Dic3—62no—
880Dic3—62no—
881Dic3—62no—
882Dic3—122no—
883Dic3—122no—
884Dic3—122no—
885C32C2×#53811yescharacteristic, complemented, Sylow
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—34no—
893C23—32no—
894C23—32no—
895C23—68no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—92no—
902C23—124no—
903C23—124no—
904C23—1216no—
905C23—182no—
906C23—182no—
907C23—182no—
908C23C22×D3212yes—
909C23C22×D3212yes—
910C23C22×D3211yescharacteristic
911Q8—364no—
912D4—44no—
913D4—68no—
914D4—124no—
915D4—188no—
916D4—364no—
917D4—364no—
918D4—364no—
919C2×C4—22no—
920C2×C4—32no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—62no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—62no—
930C2×C4—62no—
931C2×C4—62no—
932C2×C4—92no—
933C2×C4—92no—
934C2×C4—92no—
935C2×C4—124no—
936C2×C4—182no—
937C2×C4—182no—
938C2×C4—182no—
939C2×C4—364no—
940C2×C4—364no—
941C2×C4—364no—
942C2×C4C22×D3212yes—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—24no—
947C2×C3—42no—
948C2×C3—42no—
949C2×C3—42no—
950C2×C3—42no—
951C2×C3—64no—
952C2×C3—82no—
953C2×C3—82no—
954C2×C3—122no—
955C2×C3#559314yescomplemented
956C2×C3#565714yescomplemented
957C2×C3C22×#23711yescharacteristic
958C2×C3C2×#100411yescharacteristic
959C2×C3C2×#100411yescharacteristic
960C2×C3C2×#100411yescharacteristic
961C2×C3C2×D3×#4111yescharacteristic
962C2×C3C2×#100911yescharacteristic
963D3—24no—
964D3—42no—
965D3—124no—
966D3—122no—
967D3—122no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—34no—
975C22—44no—
976C22—44no—
977C22—62no—
978C22—62no—
979C22—68no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—1216no—
984C22—124no—
985C22—182no—
986C22—182no—
987C22—182no—
988C22—364no—
989C22D3×#23712yes—
990C22#6431412yes—
991C22#6433012yes—
992C22C23×D3211yescharacteristic
993C4—22no—
994C4—62no—
995C4—62no—
996C4—62no—
997C4—62no—
998C4—62no—
999C4—62no—
1000C4—182no—
1001C4—182no—
1002C4—182no—
1003C3—21no—
1004C3C2×#559311yescharacteristic, complemented
1005C3C2×#565711yescharacteristic, complemented
1006C2—42no—
1007C2—42no—
1008C2—64no—
1009C2—122no—
1010C2—362no—
1011C2#1059518514yesdirect product factor
1012C2C2×D3×#23711yescharacteristic
1013C2C2×#6431411yescharacteristic
1014C2C2×#6433011yescharacteristic
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×#64147C2semidirect
2. C2×C3×#937C2semidirect
3. C2×C3×#935C2semidirect
4. C2×#63978C2semidirect
5. C2×#63977C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×#63971C2semidirect
8. C2×D3×#217C2semidirect
9. C2×#63959C2semidirect
10. C2×#63956C2semidirect
11. C2×#63953C2semidirect
12. #10595185C2direct (N × H)
13. C2×#63893C2semidirect
14. C2×#63881C2semidirect
15. C2×#63861C2semidirect
16. C2×#63853C2semidirect
22. C22×#638C22semidirect
23. C22×C4×C3⋊D3C22semidirect
26. C23×C3×Dic3C22semidirect
27. C22×#627C22semidirect
33. C2×#3757C22semidirect
34. #64147C22semidirect
35. C2×C4⋊(C3⋊Dic3)C22semidirect
39. C2×C3×#217C22semidirect
40. C3×#937C22semidirect
41. C3×#935C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. #63978C22semidirect
47. #63977C22semidirect
48. Dic3×#67C22semidirect
49. #63971C22semidirect
50. D3×#217C22semidirect
51. C2×#3724C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. C2×#3722C22semidirect
55. C2×#3722C22semidirect
60. #63959C22semidirect
61. #63956C22semidirect
62. C2×Dic32C22semidirect
63. C2×Dic32C22semidirect
64. #63953C22semidirect
65. #63893C22semidirect
66. #63881C22semidirect
67. #63861C22semidirect
68. #63853C22semidirect
78. C2×#937D3semidirect
80. C2×#935D3semidirect
117. C2×#638C23semidirect
122. C2×C4×C3⋊D3C23semidirect
134. C22×C3×Dic3C23semidirect
136. C2×#627C23semidirect
146. #3757C23semidirect
147. C4⋊(C3⋊Dic3)C23semidirect
151. C3×#217C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. #3724C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
159. #3722C23semidirect
160. #3722C23semidirect
165. Dic32C23semidirect
166. Dic32C23semidirect
188. C23×Dic3C2×D3semidirect
223. C2×#217C2×D3semidirect
229. #937C2×D3semidirect
231. #935C2×D3semidirect
254. C2×Dic3⋊C4C2×D3semidirect
255. C2×Dic3⋊C4C2×D3semidirect
431. C22×Dic3C22×D3semidirect
471. #217C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
492. Dic3⋊C4C22×D3semidirect
723. C2×C32#538semidirect
885. C32C2×#538semidirect
955. C2×C3#5593semidirect
956. C2×C3#5657semidirect
1004. C3C2×#5593semidirect
1005. C3C2×#5657semidirect
1011. C2#10595185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C3×#9372
C2×C3×#9352
C2×#639782
C2×#639772
C2×Dic3×#672
C2×#639712
C2×D3×#2172
C2×#639592
C2×#639562
C2×#639532
#105951852
C2×#638932
C2×#638812
C2×#638612
C2×#638532
C2×#56573
C2×#55933