Finite Group Databasebeta

← C2×#10594466 #11901721

Subgroups — C2×#10594466 #11901721

Order 1152.

2435 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64103C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63910C211yesmaximal, characteristic
5C2×#63907C211yesmaximal, characteristic, complemented
6C2×#63895C211yesmaximal, characteristic, complemented
7C2×#63890C211yesmaximal, characteristic, complemented
8C2×#63887C211yesmaximal, characteristic, complemented
9C2×#63881C211yesmaximal, characteristic, complemented
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63864C211yesmaximal, characteristic, complemented
12C2×#63852C211yesmaximal, characteristic, complemented
13C2×#63848C211yesmaximal, characteristic, complemented
14C2×#63837C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594466C2116yesmaximal, direct product factor
17C2×#5733—31nomaximal
18C2×#5710—31nomaximal
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33#64103C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#898C2218yescomplemented
45C3×#888C2218yescomplemented
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63910C2218yes—
58#63907C2218yescomplemented
59#63895C2218yescomplemented
60#63890C2218yescomplemented
61#63887C2218yescomplemented
62#63881C2218yescomplemented
63#63871C2218yescomplemented
64#63864C2218yescomplemented
65#63852C2218yescomplemented
66#63848C2218yescomplemented
67#63837C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×C4⋊Q8—31no—
70C2×C3×#126—31no—
71C2×#947—31no—
72C2×#947—31no—
73C2×#946—31no—
74C2×#946—31no—
75#5733—316no—
76#5710—316no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#898D311yescharacteristic, complemented
80C2×#897—31no—
81C2×#897—31no—
82C2×#896—31no—
83C2×#895—31no—
84C2×#894—31no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#894—61no—
88C2×#893—31no—
89C2×#892—31no—
90C2×#888D311yescharacteristic, complemented
91C2×#887—31no—
92C2×#886—31no—
93C2×#885—31no—
94C2×#885—31no—
95C2×#884—31no—
96C2×#67⋊C4—31no—
97C2×#878—31no—
98C2×#875—31no—
99C2×#875—31no—
100C2×#872—31no—
101C2×C4×Dic6—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C4⋊(C3⋊D3)—42no—
111C2×C4⋊(C3⋊D3)C2314yes—
112C2×C4×C3⋊D3—42no—
113C2×C4×C3⋊D3C2314yes—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×Dic6—42no—
122C2×C3×Dic6—42no—
123C2×C3×Dic6C2314yes—
124C2×C3×Dic6C2314yes—
125C2×#627—24no—
126C2×#627C2314yes—
127C2×#626—24no—
128C2×#626—42no—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#624—24no—
132C2×#624C2314yes—
133C2×D3×Dic3—42no—
134C2×D3×Dic3C2314yes—
135C32×C4⋊C4C2314yes—
136#3752C2314yes—
137#3752C2314yes—
138#3752C2314yes—
139#3750C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×C4⋊Dic3C2314yes—
144C3×C4⋊Dic3C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×C4×Dic3C2314yes—
149C3×C4×Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153#3722C2314yes—
154#3722C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#542—91noSylow
162C22×C3×Q8—31no—
163C22×C3×Q8—31no—
164C22×#67—31no—
165C22×#67—31no—
166C23×Dic3—31no—
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—31no—
171C22×D12—61no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—61no—
178C22×Dic6—31no—
179C22×Dic6—31no—
180C22×Dic6C2×D311yescharacteristic
181C22×Dic6C2×D311yescharacteristic
182C3×C4⋊Q8—38no—
183C3×#126—38no—
184C2×C3×C4⋊C4—21no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C4⋊C4C2×D311yescharacteristic
191C2×C3×C4⋊C4C2×D311yescharacteristic
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C42—31no—
196C2×C3×C42—31no—
197C2×#217—31no—
198#947—38no—
199#947—38no—
200#946—38no—
201#946—38no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
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—61no—
220C2×(C2×D3)⋊C4—61no—
221C2×(C2×D3)⋊C4—61no—
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⋊Dic3C2×D311yescharacteristic
229C2×C4⋊Dic3C2×D311yescharacteristic
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—61no—
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×Dic3⋊C4C2×D311yescharacteristic
238C2×Dic3⋊C4C2×D311yescharacteristic
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3C2×D311yescharacteristic
244C2×C4×Dic3C2×D311yescharacteristic
245#898—38no—
246#898—38no—
247#898C2×D318yescomplemented
248#897—38no—
249#897—38no—
250#896—38no—
251#895—38no—
252#894—38no—
253#894—38no—
254#894—38no—
255#894—68no—
256#893—38no—
257#892—38no—
258#888C2×D318yescomplemented
259#887—38no—
260#886—38no—
261#885—38no—
262#885—38no—
263#884—38no—
264#67⋊C4—38no—
265#878—38no—
266#875—38no—
267#875—38no—
268#872—38no—
269C4×Dic6—38no—
270C23×C32C2411yescharacteristic
271C22×C3⋊D3—22no—
272C22×C3⋊D3—22no—
273C22×C3⋊D3—22no—
274C22×C3⋊D3—22no—
275C22×C3⋊D3—22no—
276C22×C3⋊D3—22no—
277C22×C3⋊D3C2412yes—
278C22×C3⋊D3C2412yes—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4—22no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C32×C4C2412yes—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3C2412yes—
292C2×C3⋊Dic3C2412yes—
293C4⋊(C3⋊D3)—44no—
294C4×C3⋊D3—44no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3#4114yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C3×Dic6—44no—
310C3×Dic6—44no—
311#627—28no—
312#626—28no—
313#626—44no—
314#624—28no—
315D3×Dic3—44no—
316#542—916no—
317C2×C4⋊Q8—31no—
318C2×#126—31no—
319C2×#126—91no—
320C2×#124—91no—
321C2×#124—91no—
322C2×#124—91no—
323C2×#123—91no—
324C2×#123—91no—
325C2×C22⋊Q8—91no—
326C2×C22⋊Q8—91no—
327C2×C22⋊Q8—91no—
328C2×#121—91no—
329C2×C4×Q8—91no—
330C2×C4×D4—91no—
331C2×#117—91no—
332C24×C3—31no—
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—31no—
336C23×D3—31no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3C22×D311yescharacteristic
340C2×C3×Q8—34no—
341C2×C3×Q8—34no—
342C2×C3×Q8—122no—
343C2×C3×Q8—122no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—64no—
363C2×#67—122no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—34no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—122no—
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C2×D12—34no—
380C2×D12—34no—
381C2×D12—34no—
382C2×D12—34no—
383C2×D12—64no—
384C2×D12—64no—
385C2×D12—122no—
386C2×D12—122no—
387C2×D12—124no—
388C2×D12—122no—
389C2×C4×D3—34no—
390C2×C4×D3—34no—
391C2×C4×D3—34no—
392C2×C4×D3—34no—
393C2×C4×D3—34no—
394C2×C4×D3—64no—
395C2×C4×D3—64no—
396C2×C4×D3—64no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C2×C4×D3—122no—
400C2×C4×D3—124no—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—42no—
404C2×Dic6—42no—
405C2×Dic6—64no—
406C2×Dic6—64no—
407C2×Dic6C22×D314yes—
408C2×Dic6C22×D314yes—
409C3×C4⋊C4—24no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4C22×D314yes—
416C3×C4⋊C4C22×D314yes—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C42—34no—
421C3×C42—34no—
422#217—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—64no—
441(C2×D3)⋊C4—64no—
442(C2×D3)⋊C4—64no—
443(C2×D3)⋊C4C22×D314yes—
444(C2×D3)⋊C4C22×D314yes—
445(C2×D3)⋊C4C22×D314yes—
446C4⋊Dic3—34no—
447C4⋊Dic3—34no—
448C4⋊Dic3—34no—
449C4⋊Dic3C22×D314yes—
450C4⋊Dic3C22×D314yes—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—64no—
457Dic3⋊C4C22×D314yes—
458Dic3⋊C4C22×D314yes—
459Dic3⋊C4C22×D314yes—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3C22×D314yes—
465C4×Dic3C22×D314yes—
466C22×C32C2×#4112yes—
467C22×C32H(5,𝔽2)12yes—
468C22×C322−1+412yes—
469C22×C32C2511yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—44no—
477C2×C3⋊D3—44no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—44no—
482C32×C4—22no—
483C32×C4—22no—
484C32×C4—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3C2×#4114yes—
494C22×Q8—31no—
495C22×Q8—31no—
496C22×Q8—91no—
497C22×D4—91no—
498C22×D4—91no—
499C22×D4—91no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4—91no—
503C4⋊Q8—38no—
504#126—38no—
505#126—98no—
506#124—98no—
507#124—98no—
508#124—98no—
509#123—98no—
510#123—98no—
511C22⋊Q8—98no—
512C22⋊Q8—98no—
513C22⋊Q8—98no—
514#121—98no—
515C4×Q8—98no—
516C4×D4—98no—
517#117—98no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4D3211yescharacteristic
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C42—31no—
541C2×C42—31no—
542C2×C42—91no—
543C2×C42—91no—
544C23×C3—21no—
545C23×C3—32no—
546C23×C3—62no—
547C23×C3—62no—
548C23×C3—62no—
549C23×C3C23×D311yescharacteristic
550C23×C3C23×D311yescharacteristic
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—32no—
555C22×D3—32no—
556C22×D3—32no—
557C22×D3—32no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—64no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—62no—
568C22×D3—62no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—122no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3—122no—
578C22×D3C23×D312yes—
579C3×Q8—124no—
580C3×Q8—124no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—34no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—42no—
599C2×C3×C4—42no—
600C2×C3×C4—42no—
601C2×C3×C4—62no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—62no—
605C2×C3×C4—62no—
606C2×C3×C4—62no—
607C2×C3×C4C23×D312yes—
608C2×C3×C4C23×D312yes—
609C2×C3×C4C23×D312yes—
610C2×C3×C4C23×D312yes—
611C2×C3×C4C23×D312yes—
612C2×C3×C4C23×D312yes—
613#67—68no—
614#67—124no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—32no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—122no—
632C2×Dic3—122no—
633C2×Dic3—124no—
634C2×Dic3#23914yes—
635C2×Dic3C23×D312yes—
636C2×Dic3C23×D312yes—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642D12—68no—
643D12—124no—
644D12—124no—
645D12—128no—
646D12—124no—
647C4×D3—68no—
648C4×D3—68no—
649C4×D3—124no—
650C4×D3—124no—
651C4×D3—124no—
652C4×D3—128no—
653Dic6—44no—
654Dic6—44no—
655Dic6—68no—
656Dic6—68no—
657C2×C32#54214yescomplemented
658C2×C32C22×#4111yescharacteristic
659C2×C32C2×H(5,𝔽2)11yescharacteristic
660C2×C32C2×2−1+411yescharacteristic
661C3⋊D3—42no—
662C3⋊D3—42no—
663C3×D3—42no—
664C24—31no—
665C24—91no—
666C24—91no—
667C2×Q8—34no—
668C2×Q8—34no—
669C2×Q8—94no—
670C2×Q8—122no—
671C2×Q8—122no—
672C2×Q8—184no—
673C2×D4—94no—
674C2×D4—94no—
675C2×D4—94no—
676C2×D4—184no—
677C2×D4—362no—
678C2×D4—362no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—94no—
687C22×C4—94no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—94no—
691C22×C4—184no—
692C22×C4—362no—
693C22×C4—362no—
694C22×C4C2×D3211yescharacteristic
695C22×C4C2×D3211yescharacteristic
696C22×C4C2×D3211yescharacteristic
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4C2×D3214yes—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—34no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C42—34no—
720C42—34no—
721C42—94no—
722C42—94no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—21no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—124no—
731C22×C3#100412yes—
732C22×C3C2×#23912yes—
733C22×C3#100712yes—
734C22×C3D3×#4112yes—
735C22×C3#100912yes—
736C22×C3#101012yes—
737C22×C3C24×D311yescharacteristic
738C22×C3C24×D311yescharacteristic
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—44no—
743C2×D3—64no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—122no—
757C2×D3—122no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—128no—
762C2×D3—124no—
763C2×D3—124no—
764C2×D3—124no—
765C2×D3—124no—
766C2×D3—244no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—22no—
773C3×C4—34no—
774C3×C4—42no—
775C3×C4—42no—
776C3×C4—42no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—62no—
780C3×C4—62no—
781C3×C4—62no—
782C3×C4—62no—
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3—22no—
787Dic3—22no—
788Dic3—22no—
789Dic3—62no—
790Dic3—62no—
791Dic3—62no—
792Dic3—62no—
793Dic3—122no—
794Dic3—122no—
795Dic3C2×#23914yes—
796C32C2×#54211yescharacteristic, complemented, Sylow
797C23—32no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—92no—
802C23—92no—
803C23—182no—
804C23—182no—
805C23—182no—
806C23—182no—
807C23—182no—
808C23—182no—
809C23C22×D3211yescharacteristic
810Q8—124no—
811Q8—124no—
812Q8—188no—
813D4—188no—
814D4—364no—
815D4—364no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—34no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—92no—
834C2×C4—92no—
835C2×C4—188no—
836C2×C4—182no—
837C2×C4—182no—
838C2×C4—364no—
839C2×C4—364no—
840C2×C4C22×D3212yes—
841C2×C4C22×D3212yes—
842C2×C4C22×D3212yes—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—24no—
847C2×C3—122no—
848C2×C3#571014yescomplemented
849C2×C3#573314yescomplemented
850C2×C3C2×#100411yescharacteristic
851C2×C3C22×#23911yescharacteristic
852C2×C3C2×#100711yescharacteristic
853C2×C3C2×D3×#4111yescharacteristic
854C2×C3C2×#100911yescharacteristic
855C2×C3C2×#101011yescharacteristic
856D3—42no—
857D3—124no—
858D3—122no—
859D3—122no—
860D3—122no—
861D3—122no—
862D3—242no—
863C22—62no—
864C22—62no—
865C22—62no—
866C22—124no—
867C22—182no—
868C22—182no—
869C22—182no—
870C22—182no—
871C22—182no—
872C22—182no—
873C22—364no—
874C22—364no—
875C22#6429712yes—
876C22#6431412yes—
877C22D3×#23912yes—
878C22C23×D3211yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—34no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—182no—
890C4—182no—
891C3—21no—
892C3C2×#571011yescharacteristic, complemented
893C3C2×#573311yescharacteristic, complemented
894C2—122no—
895C2—362no—
896C2—362no—
897C2#1059446614yesdirect product factor
898C2C2×#6429711yescharacteristic
899C2C2×#6431411yescharacteristic
900C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63910C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#542
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×#898C2semidirect
3. C2×C3×#888C2semidirect
5. C2×#63907C2semidirect
6. C2×#63895C2semidirect
7. C2×#63890C2semidirect
8. C2×#63887C2semidirect
9. C2×#63881C2semidirect
10. C2×#63871C2semidirect
11. C2×#63864C2semidirect
12. C2×#63852C2semidirect
13. C2×#63848C2semidirect
14. C2×#63837C2semidirect
15. C2×#63836C2semidirect
16. #10594466C2direct (N × H)
33. #64103C22semidirect
44. C3×#898C22semidirect
45. C3×#888C22semidirect
58. #63907C22semidirect
59. #63895C22semidirect
60. #63890C22semidirect
61. #63887C22semidirect
62. #63881C22semidirect
63. #63871C22semidirect
64. #63864C22semidirect
65. #63852C22semidirect
66. #63848C22semidirect
67. #63837C22semidirect
68. #63836C22semidirect
79. C2×#898D3semidirect
90. C2×#888D3semidirect
247. #898C2×D3semidirect
258. #888C2×D3semidirect
657. C2×C32#542semidirect
796. C32C2×#542semidirect
848. C2×C3#5710semidirect
849. C2×C3#5733semidirect
892. C3C2×#5710semidirect
893. C3C2×#5733semidirect
897. C2#10594466direct (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×#8982
C2×C3×#8882
C2×#639102
C2×#639072
C2×#638952
C2×#638902
C2×#638872
C2×#638812
C2×#638712
C2×#638642
C2×#638522
C2×#638482
C2×#638372
C2×#638362
#105944662
C2×#57333
C2×#57103