Finite Group Databasebeta

← C2×#10594962 #11903157

Subgroups — C2×#10594962 #11903157

Order 1152.

2713 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63905C211yesmaximal, characteristic, complemented
9#10594962C2116yesmaximal, direct product factor
10C2×#63885C211yesmaximal, characteristic, complemented
11C2×#63884C211yesmaximal, characteristic, complemented
12C2×#63879C211yesmaximal, characteristic, complemented
13C2×#63877C211yesmaximal, characteristic, complemented
14C2×#63859C211yesmaximal, characteristic, complemented
15C2×#63858C211yesmaximal, characteristic, complemented
16C2×#63847C211yesmaximal, characteristic, complemented
17C2×#5601—31nomaximal
18C2×#5540—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2218yescomplemented
36C2×C3×#217C2211yescharacteristic
37C3×#930C2218yescomplemented
38C3×C4×#67C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45#63980C2218yescomplemented
46#63980C2218yescomplemented
47#67⋊Dic3C2218yescomplemented
48#67⋊Dic3C2218yescomplemented
49C2×#3724C2211yescharacteristic
50C2×#3724C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63905C2218yescomplemented
62#63885C2218yescomplemented
63#63884C2218yescomplemented
64#63879C2218yescomplemented
65#63877C2218yescomplemented
66#63859C2218yescomplemented
67#63858C2218yescomplemented
68#63847C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#935—31no—
77C2×D4×Dic3—31no—
78C2×D4×Dic3—31no—
79C2×#930D311yescharacteristic, complemented
80C2×#929—31no—
81C2×C4×#67—31no—
82C2×C4×#67D311yescharacteristic, complemented
83C22×Dic3⋊C4—31no—
84C22×Dic3⋊C4—31no—
85C22×Dic3⋊C4—61no—
86#5601—316no—
87#5540—316no—
88C2×#898—31no—
89C2×#894—31no—
90C2×#889—31no—
91C2×#889—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#67⋊C4—31no—
95C2×#67⋊C4—31no—
96C2×#67⋊C4—31no—
97C2×#879—31no—
98C2×#879—31no—
99C2×#877—31no—
100C2×#876—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4—42no—
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2314yes—
110C22×C3⋊Dic3—24no—
111C22×C3⋊Dic3—42no—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2314yes—
116C22×C3⋊Dic3C2314yes—
117C22×C3⋊Dic3C2311yescharacteristic
118C2×C3×#67—24no—
119C2×C3×#67—24no—
120C2×C3×#67—24no—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×D12—42no—
130C2×C3×D12C2314yes—
131C2×C3×C4×D3—42no—
132C2×C3×C4×D3C2314yes—
133C2×#625—24no—
134C2×#625—42no—
135C2×#625C2314yes—
136C2×#625C2314yes—
137C2×D3×Dic3—24no—
138C2×D3×Dic3—42no—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141#3750C2314yes—
142#3750C2314yes—
143#3750C2314yes—
144#3750C2314yes—
145C3×#217C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×C4⋊Dic3C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×C4×Dic3C2314yes—
152#3724C2314yes—
153#3724C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162Dic32C2314yes—
163Dic32C2314yes—
164C2×#553—91noSylow
165C22×C3×D4—31no—
166C22×C3×D4—31no—
167C22×C3×D4—31no—
168C22×C3×D4—31no—
169C23×C3×C4—21no—
170C23×C3×C4—31no—
171C23×C3×C4C2×D311yescharacteristic
172C23×C3×C4C2×D311yescharacteristic
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67C2×D311yescharacteristic
178C22×#67C2×D311yescharacteristic
179C22×#67C2×D311yescharacteristic
180C23×Dic3—31no—
181C23×Dic3—31no—
182C23×Dic3—31no—
183C23×Dic3—31no—
184C23×Dic3—31no—
185C23×Dic3—31no—
186C23×Dic3—61no—
187C23×Dic3—61no—
188C22×D12C2×D311yescharacteristic
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3C2×D311yescharacteristic
192C3×#121—38no—
193C3×C4×D4—38no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C42—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217C2×D311yescharacteristic
208#939—38no—
209#939—38no—
210#939—38no—
211#939—38no—
212#939—38no—
213#935—38no—
214D4×Dic3—38no—
215D4×Dic3—38no—
216#930C2×D318yescomplemented
217#929—38no—
218C4×#67—38no—
219C4×#67C2×D318yescomplemented
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4C2×D311yescharacteristic
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229C2×C4⋊Dic3—31no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3C2×D311yescharacteristic
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—38no—
241C2×Dic3⋊C4—38no—
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—61no—
249C2×Dic3⋊C4—61no—
250C2×Dic3⋊C4—61no—
251C2×Dic3⋊C4—61no—
252C2×Dic3⋊C4—68no—
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#894—38no—
261#889—38no—
262#889—38no—
263#884—38no—
264#883—38no—
265#67⋊C4—38no—
266#67⋊C4—38no—
267#67⋊C4—38no—
268#879—38no—
269#879—38no—
270#877—38no—
271#876—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32#4114yes—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3C2412yes—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×C32×C4—22no—
291C2×C32×C4—22no—
292C2×C32×C4—44no—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—28no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—44no—
300C2×C3⋊Dic3#4114yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
304C2×C3⋊Dic3C2412yes—
305C3×#67—28no—
306C3×#67—28no—
307C3×#67—28no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C3×D12—44no—
319C3×C4×D3—44no—
320#625—28no—
321#625—44no—
322D3×Dic3—28no—
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—31no—
342C24×C3—31no—
343C24×C3—31no—
344C24×C3C22×D311yescharacteristic
345C24×C3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C2×C3×D4—34no—
350C2×C3×D4—34no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—64no—
354C2×C3×D4—64no—
355C2×C3×D4—64no—
356C2×C3×D4—122no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—24no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—34no—
366C22×C3×C4—42no—
367C22×C3×C4—42no—
368C22×C3×C4—44no—
369C22×C3×C4—122no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D314yes—
375C22×C3×C4C22×D314yes—
376C2×#67—24no—
377C2×#67—24no—
378C2×#67—24no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67—122no—
386C2×#67—122no—
387C2×#67C22×D314yes—
388C2×#67C22×D314yes—
389C2×#67C22×D314yes—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—34no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—34no—
400C22×Dic3—34no—
401C22×Dic3—34no—
402C22×Dic3—34no—
403C22×Dic3—34no—
404C22×Dic3—61no—
405C22×Dic3—64no—
406C22×Dic3—61no—
407C22×Dic3—61no—
408C22×Dic3—61no—
409C22×Dic3—64no—
410C22×Dic3—64no—
411C22×Dic3—64no—
412C22×Dic3—64no—
413C22×Dic3—68no—
414C22×Dic3—122no—
415C22×Dic3—122no—
416C22×Dic3—122no—
417C22×Dic3—124no—
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C2×D12—42no—
424C2×D12C22×D314yes—
425C2×C4×D3—34no—
426C2×C4×D3—34no—
427C2×C4×D3—42no—
428C2×C4×D3—64no—
429C2×C4×D3—122no—
430C2×C4×D3C22×D314yes—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C42—34no—
438#217—34no—
439#217—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217C22×D314yes—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4C22×D314yes—
452(C2×D3)⋊C4C22×D314yes—
453(C2×D3)⋊C4C22×D314yes—
454C4⋊Dic3—34no—
455C4⋊Dic3—34no—
456C4⋊Dic3C22×D314yes—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—64no—
472Dic3⋊C4—64no—
473Dic3⋊C4—64no—
474Dic3⋊C4—64no—
475Dic3⋊C4C22×D314yes—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3C22×D314yes—
481C22×C32—28no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32C2×#4114yes—
485C22×C32C2×#4112yes—
486C22×C32C2×#4112yes—
487C22×C32H(5,𝔽2)12yes—
488C22×C32C2511yescharacteristic
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—44no—
499C2×C3×D3—44no—
500C2×C3×D3—44no—
501C32×C4—22no—
502C32×C4—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3⋊Dic3C2×#4114yes—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C22×D4—31no—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—31no—
516C22×D4—91no—
517C22×D4—91no—
518C23×C4—31no—
519C23×C4—91no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523C23×C4D3211yescharacteristic
524#126—98no—
525#126—98no—
526#125—98no—
527#123—98no—
528#123—98no—
529#121—38no—
530#121—98no—
531#121—98no—
532#121—98no—
533C4×D4—38no—
534C4×D4—98no—
535C4×D4—98no—
536C4×D4—98no—
537#117—98no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4—91no—
548C2×C4⋊C4—98no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C42—31no—
560C2×C42—91no—
561C2×C42—91no—
562C23×C3—24no—
563C23×C3—24no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—21no—
570C23×C3—24no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—32no—
574C23×C3—62no—
575C23×C3—62no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—62no—
583C23×C3#23514yes—
584C23×C3#23714yes—
585C23×C3C23×D312yes—
586C23×C3C23×D312yes—
587C23×C3C23×D311yescharacteristic
588C23×C3C23×D311yescharacteristic
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3C23×D312yes—
599C22×D3C23×D312yes—
600C22×D3C23×D312yes—
601C3×D4—68no—
602C3×D4—68no—
603C3×D4—68no—
604C3×D4—124no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—42no—
617C2×C3×C4—42no—
618C2×C3×C4—44no—
619C2×C3×C4—44no—
620C2×C3×C4—48no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—124no—
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631#67—28no—
632#67—28no—
633#67—28no—
634#67—68no—
635#67—68no—
636#67—124no—
637#67—124no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—34no—
644C2×Dic3—34no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—64no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—68no—
659C2×Dic3—68no—
660C2×Dic3—68no—
661C2×Dic3—616no—
662C2×Dic3—64no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—122no—
670C2×Dic3—122no—
671C2×Dic3—124no—
672C2×Dic3—124no—
673C2×Dic3—124no—
674C2×Dic3—128no—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D312yes—
680D12—44no—
681C4×D3—44no—
682C4×D3—68no—
683C4×D3—124no—
684C2×C32—24no—
685C2×C32#55314yescomplemented
686C2×C32C22×#4111yescharacteristic
687C2×C32C22×#4111yescharacteristic
688C2×C32C2×H(5,𝔽2)11yescharacteristic
689C3×D3—42no—
690C3×D3—42no—
691C3×D3—42no—
692C24—31no—
693C24—31no—
694C24—31no—
695C24C2×D3211yescharacteristic
696C2×D4—34no—
697C2×D4—34no—
698C2×D4—34no—
699C2×D4—34no—
700C2×D4—64no—
701C2×D4—64no—
702C2×D4—64no—
703C2×D4—94no—
704C2×D4—94no—
705C2×D4—122no—
706C2×D4—184no—
707C2×D4—362no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—34no—
714C22×C4—42no—
715C22×C4—94no—
716C22×C4—94no—
717C22×C4—91no—
718C22×C4—94no—
719C22×C4—91no—
720C22×C4—91no—
721C22×C4—91no—
722C22×C4—94no—
723C22×C4—122no—
724C22×C4—184no—
725C22×C4—184no—
726C22×C4—362no—
727C22×C4—362no—
728C22×C4C2×D3211yescharacteristic
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3214yes—
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C42—34no—
752C42—94no—
753C42—94no—
754C22×C3—24no—
755C22×C3—24no—
756C22×C3—216no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—28no—
762C22×C3—28no—
763C22×C3—24no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—21no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—124no—
778C22×C3—124no—
779C22×C3—124no—
780C22×C3C2×#23514yes—
781C22×C3C2×#23512yes—
782C22×C3C2×#23714yes—
783C22×C3C2×#23712yes—
784C22×C3#100412yes—
785C22×C3#100412yes—
786C22×C3D3×#4112yes—
787C22×C3D3×#4112yes—
788C22×C3C24×D311yescharacteristic
789C22×C3C24×D311yescharacteristic
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—44no—
800C2×D3—44no—
801C2×D3—44no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—42no—
807C3×C4—42no—
808C3×C4—62no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—62no—
813Dic3—22no—
814Dic3—22no—
815Dic3—22no—
816Dic3—22no—
817Dic3—22no—
818Dic3—34no—
819Dic3—34no—
820Dic3—64no—
821Dic3—64no—
822Dic3—62no—
823Dic3—62no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—122no—
829Dic3—122no—
830C32C2×#55311yescharacteristic, complemented, Sylow
831C23—22no—
832C23—22no—
833C23—32no—
834C23—32no—
835C23—32no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23#379514yes—
846C23C22×D3212yes—
847C23C22×D3211yescharacteristic
848D4—68no—
849D4—68no—
850D4—68no—
851D4—124no—
852D4—188no—
853D4—364no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—44no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—94no—
868C2×C4—92no—
869C2×C4—92no—
870C2×C4—92no—
871C2×C4—92no—
872C2×C4—124no—
873C2×C4—188no—
874C2×C4—188no—
875C2×C4—182no—
876C2×C4—182no—
877C2×C4—182no—
878C2×C4—364no—
879C2×C4—364no—
880C2×C4C22×D3212yes—
881C2×C4C22×D3212yes—
882C2×C3—28no—
883C2×C3—24no—
884C2×C3—24no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—24no—
889C2×C3—122no—
890C2×C3—122no—
891C2×C3—122no—
892C2×C3#554014yescomplemented
893C2×C3#560114yescomplemented
894C2×C3C22×#23511yescharacteristic
895C2×C3C22×#23711yescharacteristic
896C2×C3C2×#100411yescharacteristic
897C2×C3C2×#100411yescharacteristic
898C2×C3C2×D3×#4111yescharacteristic
899C2×C3C2×D3×#4111yescharacteristic
900D3—42no—
901D3—42no—
902D3—42no—
903C22—22no—
904C22—22no—
905C22—28no—
906C22—62no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—124no—
916C22—124no—
917C22—124no—
918C22C2×#379514yes—
919C22C2×#379512yes—
920C22#6430612yes—
921C22#6433012yes—
922C22C23×D3211yescharacteristic
923C4—22no—
924C4—22no—
925C4—62no—
926C4—62no—
927C4—62no—
928C4—62no—
929C4—62no—
930C4—94no—
931C4—182no—
932C4—182no—
933C4—182no—
934C3—21no—
935C3C2×#554011yescharacteristic, complemented
936C3C2×#560111yescharacteristic, complemented
937C2—24no—
938C2—122no—
939C2—122no—
940C2—122no—
941C2#1059496214yesdirect product factor
942C2C22×#379511yescharacteristic
943C2C2×#6430611yescharacteristic
944C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3750C2semidirect
2. C2×C3×#930C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×#63980C2semidirect
5. C2×#63980C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×#63905C2semidirect
9. #10594962C2direct (N × H)
10. C2×#63885C2semidirect
11. C2×#63884C2semidirect
12. C2×#63879C2semidirect
13. C2×#63877C2semidirect
14. C2×#63859C2semidirect
15. C2×#63858C2semidirect
16. C2×#63847C2semidirect
35. C2×#3750C22semidirect
37. C3×#930C22semidirect
38. C3×C4×#67C22semidirect
45. #63980C22semidirect
46. #63980C22semidirect
47. #67⋊Dic3C22semidirect
48. #67⋊Dic3C22semidirect
61. #63905C22semidirect
62. #63885C22semidirect
63. #63884C22semidirect
64. #63879C22semidirect
65. #63877C22semidirect
66. #63859C22semidirect
67. #63858C22semidirect
68. #63847C22semidirect
79. C2×#930D3semidirect
82. C2×C4×#67D3semidirect
216. #930C2×D3semidirect
219. C4×#67C2×D3semidirect
685. C2×C32#553semidirect
830. C32C2×#553semidirect
892. C2×C3#5540semidirect
893. C2×C3#5601semidirect
935. C3C2×#5540semidirect
936. C3C2×#5601semidirect
941. C2#10594962direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C3×#9302
C2×C3×C4×#672
C2×#639802
C2×#67⋊Dic32
C2×#639052
#105949622
C2×#638852
C2×#638842
C2×#638792
C2×#638772
C2×#638592
C2×#638582
C2×#638472
C2×#56013
C2×#55403