Finite Group Databasebeta

← C2×#10594588 #11910261

Subgroups — C2×#10594588 #11910261

Order 1152.

2475 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64103C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×#896C211yesmaximal, characteristic, complemented
4C2×#63912C211yesmaximal, characteristic, complemented
5C2×#63910C211yesmaximal, characteristic, complemented
6C2×#63909C211yesmaximal, characteristic, complemented
7C2×#63907C211yesmaximal, characteristic, complemented
8C2×#63907C211yesmaximal, characteristic, complemented
9C2×#63906C211yesmaximal, characteristic, complemented
10C2×#63905C211yesmaximal, characteristic, complemented
11C2×#63888C211yesmaximal, characteristic, complemented
12C2×#63871C211yesmaximal, characteristic, complemented
13C2×#63854C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63847C211yesmaximal, characteristic, complemented
16#10594588C2116yesmaximal, direct product factor
17C2×#5647—31nomaximal
18C2×#5647—31nomaximal
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36#64103C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C3×#897C2218yescomplemented
46C3×#896C2218yescomplemented
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63912C2218yescomplemented
58#63910C2218yescomplemented
59#63909C2218yescomplemented
60#63907C2218yescomplemented
61#63907C2218yescomplemented
62#63906C2218yescomplemented
63#63905C2218yescomplemented
64#63888C2218yescomplemented
65#63871C2218yescomplemented
66#63854C2218yescomplemented
67#63850C2218yescomplemented
68#63847C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#947—31no—
72C2×#947—31no—
73C2×#946—31no—
74C2×#946—31no—
75C2×#930—31no—
76C2×#930—31no—
77C2×#929—31no—
78C2×#929—31no—
79#5647—316no—
80#5647—316no—
81C2×#897—31no—
82C2×#897D311yescharacteristic, complemented
83C2×#896—31no—
84C2×#896D311yescharacteristic, complemented
85C2×#895—31no—
86C2×#895—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#894—31no—
90C2×#894—31no—
91C2×#894—61no—
92C2×#889—31no—
93C2×#889—31no—
94C2×#885—31no—
95C2×#885—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#884—31no—
99C2×#884—31no—
100C2×#883—31no—
101C2×#883—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
111C2×C4⋊(C3⋊D3)—42no—
112C2×C4⋊(C3⋊D3)C2314yes—
113C2×C4×C3⋊D3—42no—
114C2×C4×C3⋊D3C2314yes—
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×C4×D3—42no—
122C2×C3×C4×D3—42no—
123C2×C3×C4×D3C2314yes—
124C2×C3×C4×D3C2314yes—
125C2×C3×Dic6—42no—
126C2×C3×Dic6—42no—
127C2×C3×Dic6C2314yes—
128C2×C3×Dic6C2314yes—
129C2×#626—42no—
130C2×#626—42no—
131C2×#626—42no—
132C2×#626—42no—
133C2×#626C2314yes—
134C2×#626C2314yes—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×#625—42no—
138C2×#625C2314yes—
139C2×#624—42no—
140C2×#624C2314yes—
141C32×C4⋊C4C2314yes—
142#3752C2314yes—
143#3752C2314yes—
144#3752C2314yes—
145#3750C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×C4⋊Dic3C2314yes—
151C3×C4⋊Dic3C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154#3724C2314yes—
155#3724C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160#3722C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164C2×#562—91noSylow
165C22×C3×Q8—31no—
166C22×C3×Q8—31no—
167C23×C3×C4—31no—
168C23×C3×C4—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×D12—31no—
176C22×D12—31no—
177C22×D12—31no—
178C22×D12—31no—
179C22×D12—31no—
180C22×D12—31no—
181C22×D12—61no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—61no—
187C22×C4×D3C2×D311yescharacteristic
188C22×C4×D3C2×D311yescharacteristic
189C22×Dic6C2×D311yescharacteristic
190C22×Dic6C2×D311yescharacteristic
191C3×C22⋊Q8—38no—
192C3×C22⋊Q8—38no—
193C2×C3×C4⋊C4—21no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C4⋊C4—31no—
198C2×C3×C4⋊C4C2×D311yescharacteristic
199C2×C3×C4⋊C4C2×D311yescharacteristic
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×#217—31no—
205C2×#217—31no—
206#947—38no—
207#947—38no—
208#946—38no—
209#946—38no—
210#930—38no—
211#930—38no—
212#929—38no—
213#929—38no—
214C2×(C2×D3)⋊C4—31no—
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)⋊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)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—61no—
229C2×(C2×D3)⋊C4—61no—
230C2×(C2×D3)⋊C4—61no—
231C2×(C2×D3)⋊C4C2×D311yescharacteristic
232C2×(C2×D3)⋊C4C2×D311yescharacteristic
233C2×(C2×D3)⋊C4C2×D311yescharacteristic
234C2×(C2×D3)⋊C4C2×D311yescharacteristic
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3C2×D311yescharacteristic
238C2×C4⋊Dic3C2×D311yescharacteristic
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
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—61no—
248C2×Dic3⋊C4C2×D311yescharacteristic
249C2×Dic3⋊C4C2×D311yescharacteristic
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252#897—38no—
253#897C2×D318yescomplemented
254#896—38no—
255#896C2×D318yescomplemented
256#895—38no—
257#895—38no—
258#894—38no—
259#894—38no—
260#894—38no—
261#894—38no—
262#894—68no—
263#889—38no—
264#889—38no—
265#885—38no—
266#885—38no—
267#884—38no—
268#884—38no—
269#884—38no—
270#884—38no—
271#883—38no—
272#883—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⋊D3C2412yes—
281C22×C3⋊D3C2412yes—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
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⋊Dic3C2412yes—
299C2×C3⋊Dic3C2412yes—
300C4⋊(C3⋊D3)—44no—
301C4×C3⋊D3—44no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
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—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C3×C4×D3—44no—
315C3×C4×D3—44no—
316C3×Dic6—44no—
317C3×Dic6—44no—
318#626—44no—
319#626—44no—
320#626—44no—
321#626—44no—
322#625—44no—
323#624—44no—
324#562—916no—
325C2×#125—91no—
326C2×#124—91no—
327C2×#124—91no—
328C2×#123—91no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—31no—
333C2×C22⋊Q8—31no—
334C2×C22⋊Q8—91no—
335C2×C22⋊Q8—91no—
336C2×#121—91no—
337C2×#121—91no—
338C2×#121—91no—
339C2×#121—91no—
340C24×C3—31no—
341C24×C3—31no—
342C23×D3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—31no—
346C23×D3—61no—
347C23×D3—61no—
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C2×C3×Q8—34no—
351C2×C3×Q8—34no—
352C2×C3×Q8—122no—
353C2×C3×Q8—122no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—34no—
364C22×C3×C4—34no—
365C22×C3×C4—122no—
366C22×C3×C4—122no—
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—122no—
380C2×#67—122no—
381C2×#67—122no—
382C2×#67—122no—
383C2×#67—122no—
384C2×#67—122no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C2×D12—34no—
398C2×D12—34no—
399C2×D12—34no—
400C2×D12—34no—
401C2×D12—34no—
402C2×D12—34no—
403C2×D12—64no—
404C2×D12—122no—
405C2×D12—122no—
406C2×D12—124no—
407C2×D12—122no—
408C2×D12—122no—
409C2×D12—122no—
410C2×D12—122no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—42no—
416C2×C4×D3—42no—
417C2×C4×D3—64no—
418C2×C4×D3—122no—
419C2×C4×D3—122no—
420C2×C4×D3—122no—
421C2×C4×D3—122no—
422C2×C4×D3—124no—
423C2×C4×D3C22×D314yes—
424C2×C4×D3C22×D314yes—
425C2×Dic6—42no—
426C2×Dic6—42no—
427C2×Dic6C22×D314yes—
428C2×Dic6C22×D314yes—
429C3×C4⋊C4—24no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4C22×D314yes—
435C3×C4⋊C4C22×D314yes—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4—34no—
440#217—34no—
441#217—34no—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—34no—
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)⋊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)⋊C4—64no—
458(C2×D3)⋊C4—64no—
459(C2×D3)⋊C4C22×D314yes—
460(C2×D3)⋊C4C22×D314yes—
461(C2×D3)⋊C4C22×D314yes—
462(C2×D3)⋊C4C22×D314yes—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3C22×D314yes—
466C4⋊Dic3C22×D314yes—
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—
477Dic3⋊C4C22×D314yes—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C22×C32H(5,𝔽2)12yes—
481C22×C32H(5,𝔽2)12yes—
482C22×C322−1+412yes—
483C22×C32C2511yescharacteristic
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—44no—
491C2×C3⋊D3—44no—
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—
500C32×C4—22no—
501C32×C4—22no—
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—
511C22×Q8—31no—
512C22×Q8—31no—
513C22×D4—91no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4—91no—
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—91no—
522C23×C4—91no—
523#125—98no—
524#124—98no—
525#124—98no—
526#123—98no—
527#123—98no—
528#123—98no—
529#123—98no—
530C22⋊Q8—38no—
531C22⋊Q8—38no—
532C22⋊Q8—98no—
533C22⋊Q8—98no—
534#121—98no—
535#121—98no—
536#121—98no—
537#121—98no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4D3211yescharacteristic
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—91no—
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×C22⋊C4—91no—
560C2×C42—91no—
561C23×C3—21no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—62no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3—62no—
569C23×C3—62no—
570C23×C3C23×D311yescharacteristic
571C23×C3C23×D311yescharacteristic
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—32no—
579C22×D3—32no—
580C22×D3—32no—
581C22×D3—32no—
582C22×D3—62no—
583C22×D3—62no—
584C22×D3—64no—
585C22×D3—62no—
586C22×D3—62no—
587C22×D3—62no—
588C22×D3—62no—
589C22×D3—62no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—62no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—122no—
598C22×D3—122no—
599C22×D3—122no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3C23×D312yes—
603C22×D3C23×D312yes—
604C3×Q8—124no—
605C3×Q8—124no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—42no—
622C2×C3×C4—42no—
623C2×C3×C4—42no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—62no—
630C2×C3×C4—124no—
631C2×C3×C4—124no—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635C2×C3×C4C23×D312yes—
636C2×C3×C4C23×D312yes—
637C2×C3×C4C23×D312yes—
638#67—124no—
639#67—124no—
640#67—124no—
641#67—124no—
642#67—124no—
643#67—124no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
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×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668D12—124no—
669D12—124no—
670D12—128no—
671D12—124no—
672D12—124no—
673D12—124no—
674D12—124no—
675C4×D3—44no—
676C4×D3—44no—
677C4×D3—124no—
678C4×D3—124no—
679C4×D3—124no—
680C4×D3—124no—
681C4×D3—128no—
682Dic6—44no—
683Dic6—44no—
684C2×C32#56214yescomplemented
685C2×C32C2×H(5,𝔽2)11yescharacteristic
686C2×C32C2×H(5,𝔽2)11yescharacteristic
687C2×C32C2×2−1+411yescharacteristic
688C3⋊D3—42no—
689C3⋊D3—42no—
690C3×D3—42no—
691C3×D3—42no—
692C24—31no—
693C24—31no—
694C24—91no—
695C24—91no—
696C2×Q8—34no—
697C2×Q8—34no—
698C2×Q8—122no—
699C2×Q8—122no—
700C2×D4—94no—
701C2×D4—94no—
702C2×D4—94no—
703C2×D4—94no—
704C2×D4—94no—
705C2×D4—94no—
706C2×D4—362no—
707C2×D4—362no—
708C2×D4—362no—
709C2×D4—362no—
710C2×D4—362no—
711C2×D4—362no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—34no—
719C22×C4—34no—
720C22×C4—94no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—94no—
724C22×C4—122no—
725C22×C4—122no—
726C22×C4—362no—
727C22×C4—362no—
728C22×C4C2×D3211yescharacteristic
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—34no—
734C4⋊C4—34no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4C2×D3214yes—
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—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C42—94no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—21no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—124no—
765C22×C3—124no—
766C22×C3#100412yes—
767C22×C3#100412yes—
768C22×C3#100712yes—
769C22×C3#100712yes—
770C22×C3#100912yes—
771C22×C3#100912yes—
772C22×C3C24×D311yescharacteristic
773C22×C3C24×D311yescharacteristic
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—44no—
781C2×D3—44no—
782C2×D3—64no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—62no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—122no—
796C2×D3—122no—
797C2×D3—122no—
798C2×D3—122no—
799C2×D3—122no—
800C2×D3—128no—
801C2×D3—124no—
802C2×D3—124no—
803C2×D3—124no—
804C2×D3—124no—
805C2×D3—244no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—42no—
813C3×C4—42no—
814C3×C4—42no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—62no—
820C3×C4—62no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—22no—
825Dic3—22no—
826Dic3—22no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—62no—
831Dic3—122no—
832Dic3—122no—
833C32C2×#56211yescharacteristic, complemented, Sylow
834C23—32no—
835C23—32no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—92no—
843C23—92no—
844C23—182no—
845C23—182no—
846C23—182no—
847C23—182no—
848C23—182no—
849C23—182no—
850C23C22×D3211yescharacteristic
851Q8—124no—
852Q8—124no—
853D4—364no—
854D4—364no—
855D4—364no—
856D4—364no—
857D4—364no—
858D4—364no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—92no—
875C2×C4—92no—
876C2×C4—124no—
877C2×C4—124no—
878C2×C4—182no—
879C2×C4—182no—
880C2×C4—364no—
881C2×C4—364no—
882C2×C4C22×D3212yes—
883C2×C4C22×D3212yes—
884C2×C4C22×D3212yes—
885C2×C3—24no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—122no—
890C2×C3—122no—
891C2×C3#564714yescomplemented
892C2×C3#564714yescomplemented
893C2×C3C2×#100411yescharacteristic
894C2×C3C2×#100411yescharacteristic
895C2×C3C2×#100711yescharacteristic
896C2×C3C2×#100711yescharacteristic
897C2×C3C2×#100911yescharacteristic
898C2×C3C2×#100911yescharacteristic
899D3—42no—
900D3—42no—
901D3—124no—
902D3—122no—
903D3—122no—
904D3—122no—
905D3—122no—
906D3—242no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—124no—
914C22—124no—
915C22—182no—
916C22—182no—
917C22—182no—
918C22—182no—
919C22—182no—
920C22—182no—
921C22—364no—
922C22—364no—
923C22#6430712yes—
924C22#6431412yes—
925C22#6431612yes—
926C22C23×D3211yescharacteristic
927C4—22no—
928C4—22no—
929C4—22no—
930C4—62no—
931C4—62no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—62no—
936C4—182no—
937C4—182no—
938C3—21no—
939C3C2×#564711yescharacteristic, complemented
940C3C2×#564711yescharacteristic, complemented
941C2—122no—
942C2—122no—
943C2—362no—
944C2—362no—
945C2#1059458814yesdirect product factor
946C2C2×#6430711yescharacteristic
947C2C2×#6431411yescharacteristic
948C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#562
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×#64103C2semidirect
2. C2×C3×#897C2semidirect
3. C2×C3×#896C2semidirect
4. C2×#63912C2semidirect
5. C2×#63910C2semidirect
6. C2×#63909C2semidirect
7. C2×#63907C2semidirect
8. C2×#63907C2semidirect
9. C2×#63906C2semidirect
10. C2×#63905C2semidirect
11. C2×#63888C2semidirect
12. C2×#63871C2semidirect
13. C2×#63854C2semidirect
14. C2×#63850C2semidirect
15. C2×#63847C2semidirect
16. #10594588C2direct (N × H)
36. #64103C22semidirect
45. C3×#897C22semidirect
46. C3×#896C22semidirect
57. #63912C22semidirect
58. #63910C22semidirect
59. #63909C22semidirect
60. #63907C22semidirect
61. #63907C22semidirect
62. #63906C22semidirect
63. #63905C22semidirect
64. #63888C22semidirect
65. #63871C22semidirect
66. #63854C22semidirect
67. #63850C22semidirect
68. #63847C22semidirect
82. C2×#897D3semidirect
84. C2×#896D3semidirect
253. #897C2×D3semidirect
255. #896C2×D3semidirect
684. C2×C32#562semidirect
833. C32C2×#562semidirect
891. C2×C3#5647semidirect
892. C2×C3#5647semidirect
939. C3C2×#5647semidirect
940. C3C2×#5647semidirect
945. C2#10594588direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641032
C2×C3×#8972
C2×C3×#8962
C2×#639122
C2×#639102
C2×#639092
C2×#639072
C2×#639062
C2×#639052
C2×#638882
C2×#638712
C2×#638542
C2×#638502
C2×#638472
#105945882
C2×#56473