Finite Group Databasebeta

← C2×#10594413 #11903195

Subgroups — C2×#10594413 #11903195

Order 1152.

2617 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64098C211yesmaximal, characteristic, complemented
2C2×C3×#894C211yesmaximal, characteristic, complemented
3C2×C3×#893C211yesmaximal, characteristic, complemented
4C2×#63908C211yesmaximal, characteristic, complemented
5C2×#63905C211yesmaximal, characteristic, complemented
6C2×#63902C211yesmaximal, characteristic, complemented
7C2×C4×#625C211yesmaximal, characteristic, complemented
8C2×#63885C211yesmaximal, characteristic, complemented
9C2×#63885C211yesmaximal, characteristic, complemented
10C2×#63885C211yesmaximal, characteristic, complemented
11C2×#63879C211yesmaximal, characteristic, complemented
12C2×#63877C211yesmaximal, characteristic, complemented
13C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14C2×#63861C211yesmaximal, characteristic, complemented
15C2×#63859C211yesmaximal, characteristic, complemented
16#10594413C2116yesmaximal, direct product factor
17C2×#5661—31nomaximal
18C2×#5540—31nomaximal
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38#64098C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C3×#894C2218yescomplemented
47C3×#893C2218yescomplemented
48C2×#3724C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63908C2218yescomplemented
58#63905C2218yescomplemented
59#63902C2218yescomplemented
60C4×#625C2218yescomplemented
61#63885C2218yescomplemented
62#63885C2218yescomplemented
63#63885C2218yescomplemented
64#63879C2218yescomplemented
65#63877C2218yescomplemented
66D3×Dic3⋊C4C2218yescomplemented
67#63861C2218yescomplemented
68#63859C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#938—31no—
75C2×#930—31no—
76C2×#929—31no—
77C2×C4×#67—31no—
78C2×C4×#67—31no—
79C2×C4×#67—31no—
80C22×Dic3⋊C4—31no—
81#5661—316no—
82#5540—316no—
83C2×#898—31no—
84C2×#894D311yescharacteristic, complemented
85C2×#893D311yescharacteristic, complemented
86C2×D3×C4⋊C4—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#889—61no—
90C2×#884—31no—
91C2×#884—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—
102C23×C3×D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×D12—24no—
118C2×C3×D12—42no—
119C2×C3×D12C2314yes—
120C2×C3×D12C2314yes—
121C2×C3×C4×D3—42no—
122C2×C3×C4×D3—42no—
123C2×C3×C4×D3—42no—
124C2×C3×C4×D3C2314yes—
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2314yes—
127C2×#625—24no—
128C2×#625—24no—
129C2×#625—24no—
130C2×#625—42no—
131C2×#625C2314yes—
132C2×#625C2314yes—
133C2×#625C2314yes—
134C2×#625C2314yes—
135C2×D3×Dic3—24no—
136C2×D3×Dic3—24no—
137C2×D3×Dic3—42no—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141C32×C4⋊C4C2314yes—
142C4⋊(C3⋊Dic3)C2314yes—
143#3750C2314yes—
144#3750C2314yes—
145#3750C2314yes—
146#3750C2314yes—
147C4×C3⋊Dic3C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×C4×Dic3C2314yes—
155#3724C2314yes—
156#3724C2314yes—
157Dic3⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164C2×#553—91noSylow
165C22×C3×D4—31no—
166C22×C3×D4—31no—
167C23×C3×C4—31no—
168C23×C3×C4—31no—
169C23×C3×C4—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C23×Dic3—31no—
179C23×Dic3—31no—
180C23×Dic3—31no—
181C22×D12C2×D311yescharacteristic
182C22×D12C2×D311yescharacteristic
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3C2×D311yescharacteristic
187C22×C4×D3C2×D311yescharacteristic
188C22×C4×D3C2×D311yescharacteristic
189C3×#123—38no—
190C3×C4×D4—38no—
191C2×C3×C4⋊C4—21no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4C2×D311yescharacteristic
194C2×C3×C4⋊C4C2×D311yescharacteristic
195C2×C3×C22⋊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—
206#939—38no—
207#939—38no—
208#939—38no—
209#938—38no—
210#930—38no—
211#929—38no—
212C4×#67—38no—
213C4×#67—38no—
214C4×#67—38no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4C2×D311yescharacteristic
221C2×(C2×D3)⋊C4C2×D311yescharacteristic
222C2×(C2×D3)⋊C4C2×D311yescharacteristic
223C2×(C2×D3)⋊C4C2×D311yescharacteristic
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×C4⋊Dic3—31no—
226C2×C4⋊Dic3—31no—
227C2×C4⋊Dic3—31no—
228C2×C4⋊Dic3—61no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
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—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—38no—
243C2×Dic3⋊C4—61no—
244C2×Dic3⋊C4—61no—
245C2×Dic3⋊C4—61no—
246C2×Dic3⋊C4—61no—
247C2×Dic3⋊C4C2×D311yescharacteristic
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3—61no—
253C2×C4×Dic3C2×D311yescharacteristic
254#898—38no—
255#894C2×D318yescomplemented
256#893C2×D318yescomplemented
257D3×C4⋊C4—38no—
258#889—38no—
259#889—38no—
260#889—68no—
261#884—38no—
262#884—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×C32C2411yescharacteristic
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
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#4114yes—
286C22×C3×D3C2412yes—
287C22×C3×D3C2412yes—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×C32×C4—22no—
291C2×C32×C4—22no—
292C2×C32×C4—22no—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295C2×C32×C4C2412yes—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3#4114yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C3×D12—28no—
313C3×D12—44no—
314C3×C4×D3—44no—
315C3×C4×D3—44no—
316C3×C4×D3—44no—
317#625—28no—
318#625—28no—
319#625—28no—
320#625—44no—
321D3×Dic3—28no—
322D3×Dic3—28no—
323D3×Dic3—44no—
324#553—916no—
325C2×#126—91no—
326C2×#126—91no—
327C2×#125—91no—
328C2×#123—31no—
329C2×#123—91no—
330C2×#121—91no—
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—31no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3—31no—
344C23×D3C22×D311yescharacteristic
345C23×D3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C2×C3×D4—34no—
349C2×C3×D4—34no—
350C2×C3×D4—64no—
351C2×C3×D4—122no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—34no—
360C22×C3×C4—34no—
361C22×C3×C4—34no—
362C22×C3×C4—122no—
363C22×C3×C4—122no—
364C22×C3×C4—122no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—64no—
380C2×#67—64no—
381C2×#67—64no—
382C2×#67—64no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67—122no—
386C2×#67—122no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—34no—
396C22×Dic3—34no—
397C22×Dic3—34no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402C22×Dic3—64no—
403C22×Dic3—64no—
404C22×Dic3—122no—
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C2×D12—24no—
410C2×D12—42no—
411C2×D12C22×D314yes—
412C2×D12C22×D314yes—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—42no—
417C2×C4×D3—42no—
418C2×C4×D3—42no—
419C2×C4×D3—64no—
420C2×C4×D3—64no—
421C2×C4×D3—122no—
422C2×C4×D3C22×D314yes—
423C2×C4×D3C22×D314yes—
424C2×C4×D3C22×D314yes—
425C3×C4⋊C4—24no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4C22×D314yes—
428C3×C4⋊C4C22×D314yes—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C42—34no—
435#217—34no—
436#217—34no—
437#217—34no—
438#217—34no—
439#217—34no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—34no—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4C22×D314yes—
446(C2×D3)⋊C4C22×D314yes—
447(C2×D3)⋊C4C22×D314yes—
448(C2×D3)⋊C4C22×D314yes—
449(C2×D3)⋊C4C22×D314yes—
450C4⋊Dic3—34no—
451C4⋊Dic3—34no—
452C4⋊Dic3—34no—
453C4⋊Dic3—64no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
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—64no—
468Dic3⋊C4—64no—
469Dic3⋊C4—64no—
470Dic3⋊C4—64no—
471Dic3⋊C4C22×D314yes—
472C4×Dic3—34no—
473C4×Dic3—34no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—64no—
477C4×Dic3C22×D314yes—
478C22×C32C2×#4112yes—
479C22×C32C2×#4112yes—
480C22×C32H(5,𝔽2)12yes—
481C22×C32C2511yescharacteristic
482C2×C3×D3—28no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—44no—
495C2×C3×D3—44no—
496C2×C3×D3—44no—
497C2×C3×D3C2×#4114yes—
498C32×C4—22no—
499C32×C4—22no—
500C32×C4—22no—
501C3⋊Dic3—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3C2×#4114yes—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C22×D4—31no—
510C22×D4—31no—
511C22×D4—91no—
512C22×D4—91no—
513C22×D4—91no—
514C22×D4—91no—
515C23×C4—31no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—91no—
519C23×C4—91no—
520C23×C4—91no—
521#126—98no—
522#126—98no—
523#125—98no—
524#123—38no—
525#123—98no—
526#121—98no—
527#121—98no—
528#121—98no—
529#121—98no—
530C4×D4—38no—
531C4×D4—98no—
532C4×D4—98no—
533C4×D4—98no—
534#117—98no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—98no—
537C2×C4⋊C4—91no—
538C2×C4⋊C4—91no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4D3211yescharacteristic
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C42—31no—
557C2×C42—91no—
558C2×C42—91no—
559C23×C3—21no—
560C23×C3—34no—
561C23×C3—32no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3—62no—
569C23×C3—62no—
570C23×C3—62no—
571C23×C3—62no—
572C23×C3—62no—
573C23×C3—62no—
574C23×C3—62no—
575C23×C3—62no—
576C23×C3C23×D311yescharacteristic
577C23×C3C23×D311yescharacteristic
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3#23514yes—
590C22×D3C23×D312yes—
591C22×D3C23×D312yes—
592C22×D3C23×D312yes—
593C22×D3C23×D312yes—
594C3×D4—68no—
595C3×D4—124no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—32no—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
612C2×C3×C4—62no—
613C2×C3×C4—62no—
614C2×C3×C4—62no—
615C2×C3×C4—62no—
616C2×C3×C4—124no—
617C2×C3×C4—124no—
618C2×C3×C4—124no—
619C2×C3×C4C23×D312yes—
620C2×C3×C4C23×D312yes—
621C2×C3×C4C23×D312yes—
622C2×C3×C4C23×D312yes—
623C2×C3×C4C23×D312yes—
624C2×C3×C4C23×D312yes—
625#67—68no—
626#67—68no—
627#67—68no—
628#67—68no—
629#67—68no—
630#67—68no—
631#67—124no—
632#67—124no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—34no—
638C2×Dic3—34no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—64no—
648C2×Dic3—62no—
649C2×Dic3—62no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—68no—
653C2×Dic3—68no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—122no—
661C2×Dic3—122no—
662C2×Dic3—122no—
663C2×Dic3—124no—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668D12—28no—
669D12—44no—
670C4×D3—44no—
671C4×D3—44no—
672C4×D3—44no—
673C4×D3—68no—
674C4×D3—68no—
675C4×D3—124no—
676C2×C32#55314yescomplemented
677C2×C32C22×#4111yescharacteristic
678C2×C32C22×#4111yescharacteristic
679C2×C32C2×H(5,𝔽2)11yescharacteristic
680C3×D3—24no—
681C3×D3—42no—
682C3×D3—42no—
683C3×D3—42no—
684C24—31no—
685C24—31no—
686C24—31no—
687C24—31no—
688C2×D4—34no—
689C2×D4—34no—
690C2×D4—64no—
691C2×D4—94no—
692C2×D4—94no—
693C2×D4—94no—
694C2×D4—94no—
695C2×D4—122no—
696C2×D4—184no—
697C2×D4—184no—
698C2×D4—184no—
699C2×D4—362no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—34no—
705C22×C4—34no—
706C22×C4—34no—
707C22×C4—94no—
708C22×C4—94no—
709C22×C4—94no—
710C22×C4—91no—
711C22×C4—91no—
712C22×C4—91no—
713C22×C4—91no—
714C22×C4—122no—
715C22×C4—122no—
716C22×C4—122no—
717C22×C4—184no—
718C22×C4—184no—
719C22×C4—362no—
720C22×C4C2×D3211yescharacteristic
721C22×C4C2×D3211yescharacteristic
722C22×C4C2×D3211yescharacteristic
723C4⋊C4—34no—
724C4⋊C4—94no—
725C4⋊C4—94no—
726C4⋊C4—94no—
727C4⋊C4—94no—
728C4⋊C4—94no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4C2×D3214yes—
733C22⋊C4—34no—
734C22⋊C4—34no—
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—34no—
738C22⋊C4—94no—
739C22⋊C4—94no—
740C22⋊C4—94no—
741C22⋊C4—94no—
742C22⋊C4—94no—
743C42—34no—
744C42—94no—
745C42—94no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—34no—
751C22×C3—68no—
752C22×C3—62no—
753C22×C3—62no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—124no—
764C22×C3—124no—
765C22×C3—124no—
766C22×C3C2×#23512yes—
767C22×C3#100412yes—
768C22×C3#100412yes—
769C22×C3D3×#4112yes—
770C22×C3D3×#4112yes—
771C22×C3D3×#4112yes—
772C22×C3C24×D311yescharacteristic
773C22×C3C24×D311yescharacteristic
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—28no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—44no—
787C2×D3—44no—
788C2×D3—44no—
789C2×D3C2×#23514yes—
790C3×C4—22no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—42no—
797C3×C4—42no—
798C3×C4—42no—
799C3×C4—62no—
800C3×C4—62no—
801C3×C4—62no—
802C3×C4—62no—
803Dic3—22no—
804Dic3—22no—
805Dic3—22no—
806Dic3—22no—
807Dic3—34no—
808Dic3—34no—
809Dic3—64no—
810Dic3—62no—
811Dic3—62no—
812Dic3—62no—
813Dic3—62no—
814Dic3—62no—
815Dic3—62no—
816Dic3—122no—
817Dic3—122no—
818Dic3—122no—
819C32C2×#55311yescharacteristic, complemented, Sylow
820C23—34no—
821C23—32no—
822C23—32no—
823C23—32no—
824C23—32no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23C22×D3211yescharacteristic
837D4—68no—
838D4—124no—
839D4—188no—
840D4—188no—
841D4—188no—
842D4—364no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—32no—
847C2×C4—32no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—94no—
855C2×C4—92no—
856C2×C4—92no—
857C2×C4—92no—
858C2×C4—92no—
859C2×C4—124no—
860C2×C4—124no—
861C2×C4—124no—
862C2×C4—188no—
863C2×C4—188no—
864C2×C4—182no—
865C2×C4—182no—
866C2×C4—182no—
867C2×C4—364no—
868C2×C4C22×D3212yes—
869C2×C4C22×D3212yes—
870C2×C4C22×D3212yes—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—24no—
875C2×C3—64no—
876C2×C3—122no—
877C2×C3—122no—
878C2×C3—122no—
879C2×C3#554014yescomplemented
880C2×C3#566114yescomplemented
881C2×C3C22×#23511yescharacteristic
882C2×C3C2×#100411yescharacteristic
883C2×C3C2×#100411yescharacteristic
884C2×C3C2×D3×#4111yescharacteristic
885C2×C3C2×D3×#4111yescharacteristic
886C2×C3C2×D3×#4111yescharacteristic
887D3—24no—
888D3—42no—
889D3—42no—
890D3—42no—
891C22—34no—
892C22—62no—
893C22—62no—
894C22—68no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—124no—
905C22—124no—
906C22—124no—
907C22D3×#23512yes—
908C22#6431312yes—
909C22#6431912yes—
910C22C23×D3211yescharacteristic
911C4—22no—
912C4—22no—
913C4—22no—
914C4—62no—
915C4—62no—
916C4—62no—
917C4—62no—
918C4—94no—
919C4—182no—
920C4—182no—
921C4—182no—
922C3—21no—
923C3C2×#554011yescharacteristic, complemented
924C3C2×#566111yescharacteristic, complemented
925C2—64no—
926C2—122no—
927C2—122no—
928C2—122no—
929C2#1059441314yesdirect product factor
930C2C2×D3×#23511yescharacteristic
931C2C2×#6431311yescharacteristic
932C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64098C2semidirect
2. C2×C3×#894C2semidirect
3. C2×C3×#893C2semidirect
4. C2×#63908C2semidirect
5. C2×#63905C2semidirect
6. C2×#63902C2semidirect
7. C2×C4×#625C2semidirect
8. C2×#63885C2semidirect
9. C2×#63885C2semidirect
10. C2×#63885C2semidirect
11. C2×#63879C2semidirect
12. C2×#63877C2semidirect
13. C2×D3×Dic3⋊C4C2semidirect
14. C2×#63861C2semidirect
15. C2×#63859C2semidirect
16. #10594413C2direct (N × H)
38. #64098C22semidirect
46. C3×#894C22semidirect
47. C3×#893C22semidirect
57. #63908C22semidirect
58. #63905C22semidirect
59. #63902C22semidirect
60. C4×#625C22semidirect
61. #63885C22semidirect
62. #63885C22semidirect
63. #63885C22semidirect
64. #63879C22semidirect
65. #63877C22semidirect
66. D3×Dic3⋊C4C22semidirect
67. #63861C22semidirect
68. #63859C22semidirect
84. C2×#894D3semidirect
85. C2×#893D3semidirect
255. #894C2×D3semidirect
256. #893C2×D3semidirect
676. C2×C32#553semidirect
819. C32C2×#553semidirect
879. C2×C3#5540semidirect
880. C2×C3#5661semidirect
923. C3C2×#5540semidirect
924. C3C2×#5661semidirect
929. C2#10594413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640982
C2×C3×#8942
C2×C3×#8932
C2×#639082
C2×#639052
C2×#639022
C2×C4×#6252
C2×#638852
C2×#638792
C2×#638772
C2×D3×Dic3⋊C42
C2×#638612
C2×#638592
#105944132
C2×#56613
C2×#55403