Finite Group Databasebeta

← C2×#10595196 #11903154

Subgroups — C2×#10595196 #11903154

Order 1152.

2717 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64148C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63978C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63975C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63969C211yesmaximal, characteristic, complemented
9C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10C2×#63955C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595196C2116yesmaximal, direct product factor
13C2×#63880C211yesmaximal, characteristic, complemented
14C2×#63867C211yesmaximal, characteristic, complemented
15C2×#63858C211yesmaximal, characteristic, complemented
16C2×#63848C211yesmaximal, characteristic, complemented
17C2×#5601—31nomaximal
18C2×#5565—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#624C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32#64148C2218yescomplemented
33C2×#3752C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C3×#939C2218yescomplemented
39C3×D4×Dic3C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44#63978C2218yescomplemented
45#63978C2218yescomplemented
46#63975C2218yescomplemented
47#67⋊Dic3C2218yescomplemented
48#63969C2218yescomplemented
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2218yescomplemented
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61#63955C2218yescomplemented
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64#63952C2218yescomplemented
65#63880C2218yescomplemented
66#63867C2218yescomplemented
67#63858C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—61no—
76C2×#939D311yescharacteristic, complemented
77C2×#935—31no—
78C2×D4×Dic3—31no—
79C2×D4×Dic3D311yescharacteristic, complemented
80C2×#930—31no—
81C2×#930—31no—
82C2×C4×#67—31no—
83C2×#926—31no—
84C22×C4⋊Dic3—31no—
85C22×Dic3⋊C4—31no—
86#5601—316no—
87#5565—316no—
88C2×#898—31no—
89C2×#898—31no—
90C2×#898—31no—
91C2×#889—31no—
92C2×#883—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#67⋊C4—31no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4—31no—
98C2×#879—31no—
99C2×#877—31no—
100C2×C4×D12—31no—
101C2×#870—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C2×C32×D4—24no—
107C2×C32×D4C2314yes—
108C22×C32×C4C2311yescharacteristic
109C2×#638—24no—
110C2×#638—42no—
111C2×#638C2314yes—
112C2×#638C2314yes—
113C22×C3⋊Dic3—42no—
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2314yes—
118C2×C3×#67—24no—
119C2×C3×#67—42no—
120C2×C3×#67C2314yes—
121C2×C3×#67C2314yes—
122C22×C3×Dic3—24no—
123C22×C3×Dic3—24no—
124C22×C3×Dic3—42no—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2314yes—
132C22×C3×Dic3C2314yes—
133C22×C3×Dic3C2314yes—
134C22×C3×Dic3C2311yescharacteristic
135C2×#626—24no—
136C2×#626C2314yes—
137C2×#624—42no—
138C2×#624C2314yes—
139C2×D3×Dic3—42no—
140C2×D3×Dic3C2314yes—
141#3757C2314yes—
142#3752C2314yes—
143#3750C2314yes—
144C3×#217C2314yes—
145C3×#217C2314yes—
146C3×#217C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×C4⋊Dic3C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×C4×Dic3C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162Dic32C2314yes—
163Dic32C2314yes—
164C2×#553—91noSylow
165C22×C3×D4—21no—
166C22×C3×D4—31no—
167C22×C3×D4—31no—
168C22×C3×D4C2×D311yescharacteristic
169C22×C3×D4C2×D311yescharacteristic
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C23×C3×C4—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—61no—
179C22×#67—61no—
180C22×#67C2×D311yescharacteristic
181C22×#67C2×D311yescharacteristic
182C23×Dic3—31no—
183C23×Dic3—31no—
184C23×Dic3—31no—
185C23×Dic3—61no—
186C23×Dic3C2×D311yescharacteristic
187C23×Dic3C2×D311yescharacteristic
188C23×Dic3C2×D311yescharacteristic
189C22×D12—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C3×#121—38no—
194C3×C4×D4—38no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C42—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—61no—
207C2×#217C2×D311yescharacteristic
208C2×#217C2×D311yescharacteristic
209C2×#217C2×D311yescharacteristic
210#939—38no—
211#939—38no—
212#939—38no—
213#939—38no—
214#939—68no—
215#939C2×D318yescomplemented
216#935—38no—
217D4×Dic3—38no—
218D4×Dic3C2×D318yescomplemented
219#930—38no—
220#930—38no—
221C4×#67—38no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—61no—
231C2×(C2×D3)⋊C4C2×D311yescharacteristic
232#926—38no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3—31no—
239C2×C4⋊Dic3—38no—
240C2×C4⋊Dic3C2×D311yescharacteristic
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—38no—
252C2×Dic3⋊C4—61no—
253C2×Dic3⋊C4C2×D311yescharacteristic
254C2×C4×Dic3—31no—
255C2×C4×Dic3—31no—
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3C2×D311yescharacteristic
259#898—38no—
260#898—38no—
261#898—38no—
262#889—38no—
263#883—38no—
264#883—38no—
265#883—38no—
266#67⋊C4—38no—
267#67⋊C4—38no—
268#67⋊C4—38no—
269#879—38no—
270#877—38no—
271C4×D12—38no—
272#870—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32#4114yes—
279C23×C32C2412yes—
280C23×C32C2412yes—
281C23×C32C2411yescharacteristic
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3C2412yes—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3C2412yes—
290C32×D4—28no—
291C2×C32×C4—22no—
292C2×C32×C4C2412yes—
293#638—28no—
294#638—44no—
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—44no—
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C3×#67—28no—
303C3×#67—44no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—28no—
311C2×C3×Dic3—28no—
312C2×C3×Dic3—44no—
313C2×C3×Dic3#4114yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321#626—28no—
322#624—44no—
323D3×Dic3—44no—
324#553—916no—
325C2×#126—91no—
326C2×#126—91no—
327C2×#125—91no—
328C2×#123—91no—
329C2×#123—91no—
330C2×#121—31no—
331C2×#121—91no—
332C2×#121—91no—
333C2×#121—91no—
334C2×C4×D4—31no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338C2×#117—91no—
339C22×C4⋊C4—91no—
340C24×C3—21no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C24×C3C22×D311yescharacteristic
346C24×C3C22×D311yescharacteristic
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3C22×D311yescharacteristic
351C2×C3×D4—24no—
352C2×C3×D4—24no—
353C2×C3×D4—24no—
354C2×C3×D4—34no—
355C2×C3×D4—34no—
356C2×C3×D4—44no—
357C2×C3×D4—64no—
358C2×C3×D4—122no—
359C2×C3×D4C22×D314yes—
360C2×C3×D4C22×D314yes—
361C22×C3×C4—21no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—34no—
370C22×C3×C4—34no—
371C22×C3×C4—34no—
372C22×C3×C4—64no—
373C22×C3×C4—64no—
374C22×C3×C4—122no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—24no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—42no—
384C2×#67—64no—
385C2×#67—64no—
386C2×#67—64no—
387C2×#67—64no—
388C2×#67—64no—
389C2×#67—124no—
390C2×#67—122no—
391C2×#67—122no—
392C2×#67—124no—
393C2×#67C22×D314yes—
394C2×#67C22×D314yes—
395C22×Dic3—24no—
396C22×Dic3—24no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—34no—
404C22×Dic3—34no—
405C22×Dic3—34no—
406C22×Dic3—42no—
407C22×Dic3—61no—
408C22×Dic3—61no—
409C22×Dic3—61no—
410C22×Dic3—64no—
411C22×Dic3—122no—
412C22×Dic3—122no—
413C22×Dic3—122no—
414C22×Dic3—124no—
415C22×Dic3C22×D314yes—
416C22×Dic3C22×D311yescharacteristic
417C22×Dic3C22×D311yescharacteristic
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D314yes—
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D314yes—
424C22×Dic3C22×D311yescharacteristic
425C2×D12—34no—
426C2×D12—64no—
427C2×C4×D3—34no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—122no—
431C2×C4×D3—122no—
432C2×C4×D3—122no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C42—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—64no—
445#217C22×D314yes—
446#217C22×D314yes—
447#217C22×D314yes—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—64no—
457(C2×D3)⋊C4C22×D314yes—
458C4⋊Dic3—34no—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3C22×D314yes—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—64no—
476Dic3⋊C4C22×D314yes—
477C4×Dic3—34no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3—34no—
481C4×Dic3C22×D314yes—
482C22×C32—28no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—22no—
488C22×C32—44no—
489C22×C32C2×#4114yes—
490C22×C32C2×#4112yes—
491C22×C32C2×#4112yes—
492C22×C32H(5,𝔽2)12yes—
493C22×C32C2511yescharacteristic
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—44no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—44no—
502C32×C4—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3C2×#4114yes—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4D3211yescharacteristic
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—31no—
522C23×C4—91no—
523C23×C4—91no—
524C23×C4—91no—
525#126—98no—
526#126—98no—
527#125—98no—
528#123—98no—
529#123—98no—
530#121—38no—
531#121—98no—
532#121—98no—
533#121—98no—
534C4×D4—38no—
535C4×D4—98no—
536C4×D4—98no—
537C4×D4—98no—
538#117—98no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—98no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4—91no—
548C2×C4⋊C4—91no—
549C2×C4⋊C4—91no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C42—31no—
561C2×C42—91no—
562C2×C42—91no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—21no—
576C23×C3—24no—
577C23×C3—32no—
578C23×C3—42no—
579C23×C3—42no—
580C23×C3—42no—
581C23×C3—42no—
582C23×C3—42no—
583C23×C3—62no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3#23514yes—
587C23×C3#23714yes—
588C23×C3C23×D312yes—
589C23×C3C23×D312yes—
590C23×C3C23×D312yes—
591C23×C3C23×D312yes—
592C23×C3C23×D311yescharacteristic
593C23×C3C23×D311yescharacteristic
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3C23×D312yes—
610C3×D4—28no—
611C3×D4—28no—
612C3×D4—48no—
613C3×D4—68no—
614C3×D4—124no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—34no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—32no—
625C2×C3×C4—32no—
626C2×C3×C4—42no—
627C2×C3×C4—68no—
628C2×C3×C4—68no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4—62no—
632C2×C3×C4—62no—
633C2×C3×C4—62no—
634C2×C3×C4—62no—
635C2×C3×C4—124no—
636C2×C3×C4C23×D312yes—
637C2×C3×C4C23×D312yes—
638#67—28no—
639#67—44no—
640#67—68no—
641#67—68no—
642#67—68no—
643#67—128no—
644#67—124no—
645#67—124no—
646#67—128no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—28no—
654C2×Dic3—28no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—44no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—64no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—62no—
672C2×Dic3—122no—
673C2×Dic3—122no—
674C2×Dic3—124no—
675C2×Dic3—124no—
676C2×Dic3—124no—
677C2×Dic3—128no—
678C2×Dic3#23714yes—
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D312yes—
686D12—68no—
687C4×D3—124no—
688C4×D3—124no—
689C4×D3—124no—
690C2×C32—24no—
691C2×C32—42no—
692C2×C32#55314yescomplemented
693C2×C32C22×#4111yescharacteristic
694C2×C32C22×#4111yescharacteristic
695C2×C32C2×H(5,𝔽2)11yescharacteristic
696C3⋊D3—42no—
697C3×D3—42no—
698C24—31no—
699C24—91no—
700C24C2×D3211yescharacteristic
701C24C2×D3211yescharacteristic
702C2×D4—24no—
703C2×D4—34no—
704C2×D4—34no—
705C2×D4—64no—
706C2×D4—94no—
707C2×D4—94no—
708C2×D4—94no—
709C2×D4—122no—
710C2×D4—184no—
711C2×D4—184no—
712C2×D4—362no—
713C2×D4C2×D3214yes—
714C22×C4—31no—
715C22×C4—34no—
716C22×C4—34no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—34no—
724C22×C4—64no—
725C22×C4—64no—
726C22×C4—94no—
727C22×C4—94no—
728C22×C4—91no—
729C22×C4—91no—
730C22×C4—91no—
731C22×C4—94no—
732C22×C4—122no—
733C22×C4—362no—
734C22×C4—362no—
735C22×C4—362no—
736C22×C4C2×D3211yescharacteristic
737C4⋊C4—34no—
738C4⋊C4—34no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—94no—
742C4⋊C4—94no—
743C4⋊C4—94no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—94no—
747C22⋊C4—34no—
748C22⋊C4—34no—
749C22⋊C4—34no—
750C22⋊C4—34no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C22⋊C4—94no—
756C22⋊C4—94no—
757C42—34no—
758C42—94no—
759C42—94no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—28no—
765C22×C3—28no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—24no—
776C22×C3—21no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—48no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—44no—
784C22×C3—44no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—84no—
789C22×C3—124no—
790C22×C3C2×#23514yes—
791C22×C3C2×#23512yes—
792C22×C3C2×#23712yes—
793C22×C3C2×#23714yes—
794C22×C3C2×#23712yes—
795C22×C3#100412yes—
796C22×C3D3×#4112yes—
797C22×C3#100912yes—
798C22×C3C24×D311yescharacteristic
799C22×C3C24×D311yescharacteristic
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—44no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—122no—
811C2×D3—122no—
812C2×D3—122no—
813C2×D3—124no—
814C2×D3—124no—
815C2×D3—244no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—34no—
819C3×C4—42no—
820C3×C4—62no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—62no—
826Dic3—22no—
827Dic3—22no—
828Dic3—22no—
829Dic3—22no—
830Dic3—22no—
831Dic3—22no—
832Dic3—64no—
833Dic3—62no—
834Dic3—62no—
835Dic3—62no—
836Dic3—62no—
837Dic3—62no—
838Dic3—62no—
839Dic3—122no—
840Dic3—122no—
841Dic3C2×#23714yes—
842C32C2×#55311yescharacteristic, complemented, Sylow
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—32no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—92no—
853C23—182no—
854C23—182no—
855C23—182no—
856C23#380414yes—
857C23C22×D3212yes—
858C23C22×D3212yes—
859C23C22×D3211yescharacteristic
860D4—28no—
861D4—68no—
862D4—124no—
863D4—188no—
864D4—188no—
865D4—364no—
866C2×C4—22no—
867C2×C4—34no—
868C2×C4—32no—
869C2×C4—32no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—68no—
876C2×C4—68no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—92no—
884C2×C4—92no—
885C2×C4—92no—
886C2×C4—124no—
887C2×C4—182no—
888C2×C4—182no—
889C2×C4—182no—
890C2×C4—364no—
891C2×C4—364no—
892C2×C4—364no—
893C2×C4C22×D3212yes—
894C2×C3—24no—
895C2×C3—24no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—24no—
900C2×C3—44no—
901C2×C3—42no—
902C2×C3—42no—
903C2×C3—82no—
904C2×C3—122no—
905C2×C3#556514yescomplemented
906C2×C3#560114yescomplemented
907C2×C3C22×#23511yescharacteristic
908C2×C3C22×#23711yescharacteristic
909C2×C3C22×#23711yescharacteristic
910C2×C3C2×#100411yescharacteristic
911C2×C3C2×D3×#4111yescharacteristic
912C2×C3C2×#100911yescharacteristic
913D3—42no—
914D3—122no—
915D3—122no—
916D3—242no—
917C22—22no—
918C22—22no—
919C22—28no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—44no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—124no—
928C22—182no—
929C22—182no—
930C22—182no—
931C22—364no—
932C22D3×#23712yes—
933C22#6431412yes—
934C22C2×#380414yes—
935C22C2×#380412yes—
936C22C23×D3211yescharacteristic
937C4—22no—
938C4—34no—
939C4—62no—
940C4—62no—
941C4—62no—
942C4—62no—
943C4—62no—
944C4—62no—
945C4—182no—
946C4—182no—
947C4—182no—
948C3—21no—
949C3C2×#556511yescharacteristic, complemented
950C3C2×#560111yescharacteristic, complemented
951C2—24no—
952C2—42no—
953C2—122no—
954C2—362no—
955C2#1059519614yesdirect product factor
956C2C2×D3×#23711yescharacteristic
957C2C2×#6431411yescharacteristic
958C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64148C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63978C2semidirect
5. C2×#63978C2semidirect
6. C2×#63975C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×#63969C2semidirect
9. C22×Dic3⋊Dic3C2semidirect
10. C2×#63955C2semidirect
11. C2×#63952C2semidirect
12. #10595196C2direct (N × H)
13. C2×#63880C2semidirect
14. C2×#63867C2semidirect
15. C2×#63858C2semidirect
16. C2×#63848C2semidirect
32. #64148C22semidirect
38. C3×#939C22semidirect
39. C3×D4×Dic3C22semidirect
44. #63978C22semidirect
45. #63978C22semidirect
46. #63975C22semidirect
47. #67⋊Dic3C22semidirect
48. #63969C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
61. #63955C22semidirect
64. #63952C22semidirect
65. #63880C22semidirect
66. #63867C22semidirect
67. #63858C22semidirect
68. #63848C22semidirect
76. C2×#939D3semidirect
79. C2×D4×Dic3D3semidirect
215. #939C2×D3semidirect
218. D4×Dic3C2×D3semidirect
692. C2×C32#553semidirect
842. C32C2×#553semidirect
905. C2×C3#5565semidirect
906. C2×C3#5601semidirect
949. C3C2×#5565semidirect
950. C3C2×#5601semidirect
955. C2#10595196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641482
C2×C3×#9392
C2×C3×D4×Dic32
C2×#639782
C2×#639752
C2×#67⋊Dic32
C2×#639692
C22×Dic3⋊Dic32
C2×#639552
C2×#639522
#105951962
C2×#638802
C2×#638672
C2×#638582
C2×#638482
C2×#56013
C2×#55653