Finite Group Databasebeta

← C2×#10595507 #11901332

Subgroups — C2×#10595507 #11901332

Order 1152.

3003 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64162C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic, complemented
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C2×#63978C211yesmaximal, characteristic, complemented
5#10595507C2116yesmaximal, direct product factor
6C2×#63975C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C2×#63969C211yesmaximal, characteristic, complemented
10C2×#63964C211yesmaximal, characteristic, complemented
11C2×#63959C211yesmaximal, characteristic, complemented
12C2×#63958C211yesmaximal, characteristic, complemented
13C2×#63956C211yesmaximal, characteristic, complemented
14C2×#63956C211yesmaximal, characteristic, complemented
15C2×#63953C211yesmaximal, characteristic, complemented
16C2×#63952C211yesmaximal, characteristic, complemented
17C2×#5593—31nomaximal
18C2×#5494—31nomaximal
19C25×C32C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C22×#627C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic, complemented
30C22×#624C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32#64162C2218yescomplemented
33C2×#3757C2211yescharacteristic
34C2×#3757C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36C3×#953C2218yescomplemented
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic
42C2×C3×#217C2211yescharacteristic
43C2×C3×#217C2211yescharacteristic
44C2×C3×#217C2218yescomplemented
45#63978C2218yescomplemented
46#63975C2218yescomplemented
47Dic3×#67C2218yescomplemented
48#63971C2218yescomplemented
49#63969C2218yescomplemented
50C2×#3724C2211yescharacteristic, complemented
51C2×#3724C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×Dic3⋊Dic3C2211yescharacteristic, complemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56#63964C2218yescomplemented
57C2×#3722C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63959C2218yescomplemented
62#63958C2218yescomplemented
63#63956C2218yescomplemented
64#63956C2218yescomplemented
65C2×Dic32C2211yescharacteristic, complemented
66C2×Dic32C2211yescharacteristic, complemented
67#63953C2218yescomplemented
68#63952C2218yescomplemented
69C2×C3×#120—31no—
70C22×C3×C22⋊C4—31no—
71C2×#953—31no—
72C2×#953—31no—
73C2×#953—61no—
74C2×#953D311yescharacteristic, complemented
75C22×#217D311yescharacteristic, complemented
76C2×#939—31no—
77C2×#939—31no—
78C2×#938—31no—
79C2×#936—31no—
80C2×#935—31no—
81C2×D4×Dic3—31no—
82C2×#930—31no—
83C2×C4×#67—31no—
84C2×C4×#67—31no—
85C2×#924—31no—
86#5593—316no—
87#5494—316no—
88C2×#885—31no—
89C2×#885—31no—
90C2×#885—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#883—31no—
96C2×#67⋊C4—31no—
97C2×#879—31no—
98C2×#879—31no—
99C2×#879—31no—
100C2×#879—31no—
101C2×#878—31no—
102C24×C32—24no—
103C24×C32—42no—
104C24×C32—42no—
105C24×C32C2311yescharacteristic
106C24×C32C2311yescharacteristic
107C24×C32C2311yescharacteristic
108C24×C32C2314yes—
109C23×C3⋊D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C2×#638—24no—
112C2×#638—42no—
113C2×#638—42no—
114C2×#638C2314yes—
115C2×#638C2314yes—
116C2×#638C2314yes—
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2311yescharacteristic
120C2×C3×#67—24no—
121C2×C3×#67—42no—
122C2×C3×#67—42no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C2×C3×#67C2314yes—
126C22×C3×Dic3—42no—
127C22×C3×Dic3—42no—
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2314yes—
136C22×C3×Dic3C2314yes—
137C2×#627—42no—
138C2×#627C2314yescomplemented
139C2×#626—42no—
140C2×#626C2314yescomplemented
141C2×#624—42no—
142C2×#624C2314yescomplemented
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yescomplemented
145#3757C2314yes—
146#3757C2314yes—
147#3757C2314yes—
148C3×#217C2314yes—
149C3×#217C2314yes—
150C3×#217C2314yes—
151C3×#217C2314yes—
152C3×#217C2314yes—
153C3×#217C2314yes—
154C3×#217C2314yes—
155#3724C2314yescomplemented
156#3724C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159Dic3⋊Dic3C2314yescomplemented
160Dic3⋊Dic3C2314yescomplemented
161#3722C2314yescomplemented
162#3722C2314yescomplemented
163(C2×D3)⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yescomplemented
165Dic32C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C25×C3—21no—
169C25×C3C2×D311yescharacteristic
170C25×C3C2×D311yescharacteristic
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C23×C3×C4—31no—
175C23×C3×C4—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—61no—
184C22×#67—61no—
185C22×#67—61no—
186C22×#67C2×D311yescharacteristic
187C22×#67C2×D311yescharacteristic
188C22×#67C2×D311yescharacteristic
189C23×Dic3—31no—
190C23×Dic3C2×D311yescharacteristic
191C23×Dic3C2×D311yescharacteristic
192C22×D12—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×Dic6—31no—
197C22×Dic6—31no—
198C3×#120—38no—
199C2×C3×C22⋊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—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—38no—
207#953—38no—
208#953—38no—
209#953—68no—
210#953C2×D318yescomplemented
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217—31no—
218C2×#217—31no—
219C2×#217—61no—
220C2×#217—61no—
221C2×#217—61no—
222C2×#217C2×D311yescharacteristic
223C2×#217C2×D311yescharacteristic
224C2×#217C2×D311yescharacteristic
225C2×#217C2×D311yescharacteristic
226C2×#217C2×D311yescharacteristic
227C2×#217C2×D311yescharacteristic
228C2×#217C2×D311yescharacteristic
229C2×#217C2×D318yescomplemented
230#939—38no—
231#939—38no—
232#938—38no—
233#936—38no—
234#935—38no—
235D4×Dic3—38no—
236#930—38no—
237C4×#67—38no—
238C4×#67—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×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—31no—
248C2×C4⋊Dic3—31no—
249#924—38no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×C4×Dic3—31no—
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3—31no—
262#885—38no—
263#885—38no—
264#885—38no—
265#884—38no—
266#884—38no—
267#883—38no—
268#883—38no—
269#883—38no—
270#67⋊C4—38no—
271#879—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—28no—
281C23×C32—22no—
282C23×C32—22no—
283C23×C32—22no—
284C23×C32—22no—
285C23×C32—44no—
286C23×C32—44no—
287C23×C32—416no—
288C23×C32#4114yes—
289C23×C32C2412yes—
290C23×C32C2412yes—
291C23×C32C2412yes—
292C23×C32C2411yescharacteristic
293C22×C3⋊D3—22no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3—22no—
296C22×C3⋊D3C2412yes—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3C2412yes—
301#638—28no—
302#638—44no—
303#638—44no—
304C2×C3⋊Dic3—22no—
305C2×C3⋊Dic3—22no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3C2412yes—
308C2×C3⋊Dic3C2412yes—
309C2×C3⋊Dic3C2412yes—
310C3×#67—28no—
311C3×#67—44no—
312C3×#67—44no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—44no—
321C2×C3×Dic3—44no—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329#627—44no—
330#626—44no—
331#624—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—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—31no—
345C2×#120—91no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C22×C22⋊C4—31no—
349C24×C3—24no—
350C24×C3—24no—
351C24×C3—21no—
352C24×C3—21no—
353C24×C3—21no—
354C24×C3—24no—
355C24×C3—31no—
356C24×C3—44no—
357C24×C3—42no—
358C24×C3—42no—
359C24×C3—42no—
360C24×C3—42no—
361C24×C3—44no—
362C24×C3—44no—
363C24×C3C22×D311yescharacteristic
364C24×C3C22×D311yescharacteristic
365C24×C3C22×D311yescharacteristic
366C24×C3C22×D311yescharacteristic
367C24×C3C22×D311yescharacteristic
368C24×C3C22×D311yescharacteristic
369C24×C3C22×D314yes—
370C24×C3C22×D314yes—
371C23×D3—31no—
372C23×D3—31no—
373C23×D3—61no—
374C23×D3C22×D311yescharacteristic
375C2×C3×D4—34no—
376C2×C3×D4—34no—
377C2×C3×D4—34no—
378C2×C3×D4—64no—
379C2×C3×D4—122no—
380C2×C3×D4—122no—
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—31no—
388C22×C3×C4—34no—
389C22×C3×C4—34no—
390C22×C3×C4—122no—
391C22×C3×C4—122no—
392C2×#67—24no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—34no—
399C2×#67—34no—
400C2×#67—42no—
401C2×#67—42no—
402C2×#67—64no—
403C2×#67—64no—
404C2×#67—64no—
405C2×#67—64no—
406C2×#67—64no—
407C2×#67—124no—
408C2×#67—122no—
409C2×#67—122no—
410C2×#67—122no—
411C2×#67—122no—
412C2×#67—122no—
413C2×#67—124no—
414C2×#67—124no—
415C2×#67C22×D314yes—
416C2×#67C22×D314yes—
417C2×#67C22×D314yes—
418C22×Dic3—31no—
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—31no—
424C22×Dic3—34no—
425C22×Dic3—42no—
426C22×Dic3—42no—
427C22×Dic3—61no—
428C22×Dic3—61no—
429C22×Dic3—61no—
430C22×Dic3—122no—
431C22×Dic3C22×D311yescharacteristic
432C22×Dic3C22×D311yescharacteristic
433C22×Dic3C22×D311yescharacteristic
434C22×Dic3C22×D311yescharacteristic
435C22×Dic3C22×D311yescharacteristic
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C22×Dic3C22×D314yes—
439C22×Dic3C22×D314yes—
440C2×D12—34no—
441C2×D12—122no—
442C2×C4×D3—34no—
443C2×C4×D3—34no—
444C2×C4×D3—34no—
445C2×C4×D3—122no—
446C2×C4×D3—122no—
447C2×C4×D3—122no—
448C2×Dic6—34no—
449C2×Dic6—34no—
450C2×Dic6—122no—
451C2×Dic6—122no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—34no—
465#217—34no—
466#217—34no—
467#217—64no—
468#217—64no—
469#217—64no—
470#217C22×D314yes—
471#217C22×D314yes—
472#217C22×D314yes—
473#217C22×D314yes—
474#217C22×D314yes—
475#217C22×D314yes—
476#217C22×D314yes—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486C4⋊Dic3—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495C4×Dic3—34no—
496C4×Dic3—34no—
497C4×Dic3—34no—
498C4×Dic3—34no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—28no—
502C22×C32—22no—
503C22×C32—22no—
504C22×C32—22no—
505C22×C32—22no—
506C22×C32—22no—
507C22×C32—22no—
508C22×C32—416no—
509C22×C32—44no—
510C22×C32—44no—
511C22×C32C2×#4114yes—
512C22×C32C2×#4112yes—
513C22×C32H(5,𝔽2)12yes—
514C22×C32H(5,𝔽2)12yes—
515C22×C32C2511yescharacteristic
516C2×C3⋊D3—22no—
517C2×C3⋊D3—22no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—44no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—44no—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3⋊Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—22no—
534C25D3211yescharacteristic
535C22×Q8—91no—
536C22×D4—31no—
537C22×D4—31no—
538C22×D4—31no—
539C22×D4—91no—
540C22×D4—91no—
541C22×D4—91no—
542C22×D4—91no—
543C23×C4—31no—
544C23×C4—31no—
545C23×C4—91no—
546C23×C4—91no—
547#126—98no—
548#126—98no—
549#124—98no—
550#124—98no—
551#123—98no—
552#123—98no—
553C22⋊Q8—98no—
554#121—98no—
555#121—98no—
556#121—98no—
557#120—38no—
558#120—98no—
559C4×D4—98no—
560C4×D4—98no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C4⋊C4—91no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—38no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C22⋊C4—91no—
580C2×C22⋊C4—91no—
581C2×C22⋊C4—91no—
582C2×C42—91no—
583C2×C42—91no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—24no—
589C23×C3—24no—
590C23×C3—28no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—28no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—21no—
608C23×C3—24no—
609C23×C3—32no—
610C23×C3—42no—
611C23×C3—42no—
612C23×C3—42no—
613C23×C3—42no—
614C23×C3—48no—
615C23×C3—42no—
616C23×C3—42no—
617C23×C3—44no—
618C23×C3—44no—
619C23×C3—44no—
620C23×C3—44no—
621C23×C3—48no—
622C23×C3—48no—
623C23×C3—416no—
624C23×C3—416no—
625C23×C3—432no—
626C23×C3—62no—
627C23×C3—62no—
628C23×C3—62no—
629C23×C3#23514yes—
630C23×C3#23714yes—
631C23×C3C23×D312yes—
632C23×C3C23×D312yes—
633C23×C3C23×D312yes—
634C23×C3C23×D312yes—
635C23×C3C23×D312yes—
636C23×C3C23×D312yes—
637C23×C3C23×D311yescharacteristic
638C23×C3C23×D311yescharacteristic
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—62no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—122no—
652C22×D3—122no—
653C22×D3—122no—
654C22×D3C23×D312yes—
655C3×D4—68no—
656C3×D4—124no—
657C3×D4—124no—
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—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—62no—
671C2×C3×C4—62no—
672C2×C3×C4—124no—
673C2×C3×C4—124no—
674#67—28no—
675#67—44no—
676#67—44no—
677#67—68no—
678#67—68no—
679#67—128no—
680#67—124no—
681#67—124no—
682#67—124no—
683#67—124no—
684#67—124no—
685#67—128no—
686#67—128no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—44no—
701C2×Dic3—44no—
702C2×Dic3—62no—
703C2×Dic3—62no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—62no—
708C2×Dic3—62no—
709C2×Dic3—62no—
710C2×Dic3—62no—
711C2×Dic3—122no—
712C2×Dic3—122no—
713C2×Dic3—122no—
714C2×Dic3—124no—
715C2×Dic3C23×D312yes—
716C2×Dic3C23×D312yes—
717C2×Dic3C23×D312yes—
718C2×Dic3C23×D312yes—
719C2×Dic3C23×D312yes—
720C2×Dic3C23×D312yes—
721C2×Dic3C23×D312yes—
722D12—124no—
723C4×D3—124no—
724C4×D3—124no—
725C4×D3—124no—
726Dic6—124no—
727Dic6—124no—
728C2×C32—24no—
729C2×C32—42no—
730C2×C32—42no—
731C2×C32#53814yescomplemented
732C2×C32C22×#4111yescharacteristic
733C2×C32C2×H(5,𝔽2)11yescharacteristic
734C2×C32C2×H(5,𝔽2)11yescharacteristic
735C3⋊D3—42no—
736C3×D3—42no—
737C24—24no—
738C24—31no—
739C24—42no—
740C24—42no—
741C24—91no—
742C24C2×D3211yescharacteristic
743C24C2×D3211yescharacteristic
744C24C2×D3211yescharacteristic
745C24C2×D3214yes—
746C2×Q8—94no—
747C2×Q8—362no—
748C2×D4—34no—
749C2×D4—34no—
750C2×D4—34no—
751C2×D4—64no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—94no—
755C2×D4—94no—
756C2×D4—122no—
757C2×D4—122no—
758C2×D4—184no—
759C2×D4—362no—
760C2×D4—362no—
761C2×D4—362no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—34no—
770C22×C4—34no—
771C22×C4—94no—
772C22×C4—94no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—122no—
777C22×C4—122no—
778C22×C4—362no—
779C22×C4—362no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C4⋊C4—94no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C22⋊C4—34no—
787C22⋊C4—34no—
788C22⋊C4—34no—
789C22⋊C4—34no—
790C22⋊C4—34no—
791C22⋊C4—34no—
792C22⋊C4—34no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—94no—
798C22⋊C4—94no—
799C22⋊C4—94no—
800C42—94no—
801C42—94no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—28no—
807C22×C3—28no—
808C22×C3—24no—
809C22×C3—24no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—24no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—21no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—48no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—416no—
835C22×C3—416no—
836C22×C3—48no—
837C22×C3—48no—
838C22×C3—432no—
839C22×C3—44no—
840C22×C3—44no—
841C22×C3—44no—
842C22×C3—44no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—124no—
847C22×C3C2×#23514yes—
848C22×C3C2×#23512yes—
849C22×C3C2×#23714yes—
850C22×C3C2×#23712yes—
851C22×C3#100412yes—
852C22×C3#100412yes—
853C22×C3#100412yes—
854C22×C3#100412yes—
855C22×C3C24×D311yescharacteristic
856C22×C3C24×D311yescharacteristic
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—44no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—122no—
868C2×D3—122no—
869C2×D3—122no—
870C2×D3—124no—
871C2×D3—124no—
872C2×D3—244no—
873C3×C4—62no—
874C3×C4—62no—
875C3×C4—62no—
876C3×C4—62no—
877C3×C4—62no—
878C3×C4—62no—
879C3×C4—62no—
880Dic3—22no—
881Dic3—22no—
882Dic3—22no—
883Dic3—22no—
884Dic3—22no—
885Dic3—22no—
886Dic3—22no—
887Dic3—62no—
888Dic3—62no—
889Dic3—62no—
890Dic3—62no—
891Dic3—62no—
892Dic3—62no—
893Dic3—122no—
894Dic3—122no—
895Dic3—122no—
896C32C2×#53811yescharacteristic, complemented, Sylow
897C23—22no—
898C23—22no—
899C23—28no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—32no—
907C23—44no—
908C23—44no—
909C23—416no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—92no—
914C23—182no—
915C23—182no—
916C23—182no—
917C23#380414yes—
918C23C22×D3212yes—
919C23C22×D3212yes—
920C23C22×D3212yes—
921C23C22×D3211yescharacteristic
922Q8—364no—
923D4—68no—
924D4—124no—
925D4—124no—
926D4—188no—
927D4—364no—
928D4—364no—
929D4—364no—
930C2×C4—32no—
931C2×C4—32no—
932C2×C4—32no—
933C2×C4—32no—
934C2×C4—32no—
935C2×C4—32no—
936C2×C4—32no—
937C2×C4—62no—
938C2×C4—62no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—92no—
945C2×C4—92no—
946C2×C4—92no—
947C2×C4—124no—
948C2×C4—124no—
949C2×C4—182no—
950C2×C4—182no—
951C2×C4—182no—
952C2×C4—364no—
953C2×C4—364no—
954C2×C3—24no—
955C2×C3—24no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—21no—
959C2×C3—24no—
960C2×C3—44no—
961C2×C3—44no—
962C2×C3—44no—
963C2×C3—42no—
964C2×C3—42no—
965C2×C3—42no—
966C2×C3—42no—
967C2×C3—122no—
968C2×C3#549414yescomplemented
969C2×C3#559314yescomplemented
970C2×C3C22×#23511yescharacteristic
971C2×C3C22×#23711yescharacteristic
972C2×C3C2×#100411yescharacteristic
973C2×C3C2×#100411yescharacteristic
974C2×C3C2×#100411yescharacteristic
975C2×C3C2×#100411yescharacteristic
976D3—42no—
977D3—122no—
978D3—122no—
979D3—242no—
980C22—22no—
981C22—22no—
982C22—28no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—416no—
990C22—44no—
991C22—44no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—124no—
996C22—182no—
997C22—182no—
998C22—182no—
999C22—364no—
1000C22C2×#380414yes—
1001C22C2×#380412yes—
1002C22#6433012yes—
1003C22#6433012yes—
1004C22C23×D3211yescharacteristic
1005C4—62no—
1006C4—62no—
1007C4—62no—
1008C4—62no—
1009C4—62no—
1010C4—62no—
1011C4—62no—
1012C4—182no—
1013C4—182no—
1014C4—182no—
1015C3—21no—
1016C3C2×#549411yescharacteristic, complemented
1017C3C2×#559311yescharacteristic, complemented
1018C2—24no—
1019C2—42no—
1020C2—42no—
1021C2—122no—
1022C2—362no—
1023C2#1059550714yesdirect product factor
1024C2C22×#380411yescharacteristic
1025C2C2×#6433011yescharacteristic
1026C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
hypercenterC25D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C2×#64162C2semidirect
2. C2×C3×#953C2semidirect
3. C22×C3×#217C2semidirect
4. C2×#63978C2semidirect
5. #10595507C2direct (N × H)
6. C2×#63975C2semidirect
7. C2×Dic3×#67C2semidirect
8. C2×#63971C2semidirect
9. C2×#63969C2semidirect
10. C2×#63964C2semidirect
11. C2×#63959C2semidirect
12. C2×#63958C2semidirect
13. C2×#63956C2semidirect
14. C2×#63956C2semidirect
15. C2×#63953C2semidirect
16. C2×#63952C2semidirect
28. C22×#627C22semidirect
29. C22×#626C22semidirect
30. C22×#624C22semidirect
31. C22×D3×Dic3C22semidirect
32. #64162C22semidirect
36. C3×#953C22semidirect
44. C2×C3×#217C22semidirect
45. #63978C22semidirect
46. #63975C22semidirect
47. Dic3×#67C22semidirect
48. #63971C22semidirect
49. #63969C22semidirect
50. C2×#3724C22semidirect
51. C2×#3724C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. #63964C22semidirect
57. C2×#3722C22semidirect
58. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63959C22semidirect
62. #63958C22semidirect
63. #63956C22semidirect
64. #63956C22semidirect
65. C2×Dic32C22semidirect
66. C2×Dic32C22semidirect
67. #63953C22semidirect
68. #63952C22semidirect
74. C2×#953D3semidirect
75. C22×#217D3semidirect
138. C2×#627C23semidirect
140. C2×#626C23semidirect
142. C2×#624C23semidirect
144. C2×D3×Dic3C23semidirect
155. #3724C23semidirect
156. #3724C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
159. Dic3⋊Dic3C23semidirect
160. Dic3⋊Dic3C23semidirect
161. #3722C23semidirect
162. #3722C23semidirect
163. (C2×D3)⋊Dic3C23semidirect
164. (C2×D3)⋊Dic3C23semidirect
165. Dic32C23semidirect
166. Dic32C23semidirect
210. #953C2×D3semidirect
229. C2×#217C2×D3semidirect
731. C2×C32#538semidirect
896. C32C2×#538semidirect
968. C2×C3#5494semidirect
969. C2×C3#5593semidirect
1016. C3C2×#5494semidirect
1017. C3C2×#5593semidirect
1023. C2#10595507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641622
C2×C3×#9532
C22×C3×#2172
C2×#639782
#105955072
C2×#639752
C2×Dic3×#672
C2×#639712
C2×#639692
C2×#639642
C2×#639592
C2×#639582
C2×#639562
C2×#639532
C2×#639522
C2×#55933
C2×#54943