Finite Group Databasebeta

← C2×#10594573 #11901418

Subgroups — C2×#10594573 #11901418

Order 1152.

2497 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#896C211yesmaximal, characteristic, complemented
4C2×#63912C211yesmaximal, characteristic
5C2×#63905C211yesmaximal, characteristic, complemented
6C2×C4×#626C211yesmaximal, characteristic, complemented
7C2×#63891C211yesmaximal, characteristic, complemented
8C2×#63887C211yesmaximal, characteristic, complemented
9C2×#63881C211yesmaximal, characteristic, complemented
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63867C211yesmaximal, characteristic, complemented
12C2×#63858C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic, complemented
14C2×#63853C211yesmaximal, characteristic, complemented
15C2×#63845C211yesmaximal, characteristic, complemented
16#10594573C2116yesmaximal, direct product factor
17C2×#5707—31nomaximal
18C2×#5638—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C4⋊C4×C3⋊D3C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#898C2218yescomplemented
44C3×#896C2218yescomplemented
45C2×#3724C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63912C2218yes—
58#63905C2218yescomplemented
59C4×#626C2218yescomplemented
60#63891C2218yescomplemented
61#63887C2218yescomplemented
62#63881C2218yescomplemented
63#63871C2218yescomplemented
64#63867C2218yescomplemented
65#63858C2218yescomplemented
66#63853C2218yescomplemented
67#63853C2218yescomplemented
68#63845C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#929—31no—
74C2×C4×#67—31no—
75#5707—316no—
76#5638—316no—
77C2×#898—31no—
78C2×#898D311yescharacteristic, complemented
79C2×#897—31no—
80C2×#896D311yescharacteristic, complemented
81C2×#894—31no—
82C2×#894—31no—
83C2×#893—31no—
84C2×D3×C4⋊C4—31no—
85C2×D3×C4⋊C4—31no—
86C2×D3×C4⋊C4—61no—
87C2×#890—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#886—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#883—31no—
96C2×#883—31no—
97C2×#67⋊C4—31no—
98C2×#879—31no—
99C2×#878—31no—
100C2×C4×D12—31no—
101C2×#870—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
110C22×C3⋊Dic3C2311yescharacteristic
111C2×C4×C3⋊D3—24no—
112C2×C4×C3⋊D3—42no—
113C2×C4×C3⋊D3—42no—
114C2×C4×C3⋊D3C2314yes—
115C2×C4×C3⋊D3C2314yes—
116C2×C4×C3⋊D3C2314yes—
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×C4×D3—42no—
124C2×C3×C4×D3C2314yes—
125C2×C3×Dic6—42no—
126C2×C3×Dic6C2314yes—
127C2×#626—24no—
128C2×#626—24no—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#625—42no—
132C2×#625C2314yes—
133C2×D3×Dic3—42no—
134C2×D3×Dic3C2314yes—
135C32×C4⋊C4C2314yes—
136C4⋊(C3⋊Dic3)C2314yes—
137#3750C2314yes—
138#3750C2314yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×C4⋊Dic3C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×C4×Dic3C2314yes—
149#3724C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160Dic32C2314yes—
161C2×#539—91noSylow
162C22×C3×Q8—31no—
163C23×C3×C4—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C23×Dic3—31no—
169C22×D12—31no—
170C22×D12—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—61no—
179C22×C4×D3—61no—
180C22×C4×D3—61no—
181C22×C4×D3C2×D311yescharacteristic
182C22×Dic6C2×D311yescharacteristic
183C3×#126—38no—
184C3×C22⋊Q8—38no—
185C2×C3×C4⋊C4—21no—
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×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C42—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201#946—38no—
202#946—38no—
203#929—38no—
204C4×#67—38no—
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)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3—61no—
225C2×C4⋊Dic3C2×D311yescharacteristic
226C2×Dic3⋊C4—31no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
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—61no—
238C2×Dic3⋊C4—61no—
239C2×Dic3⋊C4C2×D311yescharacteristic
240C2×Dic3⋊C4C2×D311yescharacteristic
241C2×Dic3⋊C4C2×D311yescharacteristic
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3C2×D311yescharacteristic
245#898—38no—
246#898C2×D318yescomplemented
247#897—38no—
248#896C2×D318yescomplemented
249#894—38no—
250#894—38no—
251#893—38no—
252D3×C4⋊C4—38no—
253D3×C4⋊C4—38no—
254D3×C4⋊C4—68no—
255#890—38no—
256#889—38no—
257#889—38no—
258#886—38no—
259#884—38no—
260#884—38no—
261#883—38no—
262#883—38no—
263#883—38no—
264#883—38no—
265#67⋊C4—38no—
266#879—38no—
267#878—38no—
268C4×D12—38no—
269#870—38no—
270C23×C32C2411yescharacteristic
271C22×C3⋊D3—22no—
272C22×C3⋊D3—22no—
273C22×C3⋊D3#4114yes—
274C22×C3⋊D3C2412yes—
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×D3C2412yes—
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⋊Dic3—22no—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C4×C3⋊D3—28no—
296C4×C3⋊D3—44no—
297C4×C3⋊D3—44no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C3×C4×D3—44no—
311C3×Dic6—44no—
312#626—28no—
313#626—28no—
314#625—44no—
315D3×Dic3—44no—
316#539—916no—
317C2×#126—31no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#125—91no—
321C2×#123—91no—
322C2×#123—91no—
323C2×#123—91no—
324C2×#123—91no—
325C2×C22⋊Q8—31no—
326C2×C22⋊Q8—91no—
327C2×C22⋊Q8—91no—
328C2×#121—91no—
329C2×C4×D4—91no—
330C2×C4×D4—91no—
331C22×C4⋊C4—91no—
332C24×C3—31no—
333C24×C3—31no—
334C23×D3—31no—
335C23×D3—31no—
336C23×D3—61no—
337C23×D3C22×D311yescharacteristic
338C23×D3C22×D311yescharacteristic
339C2×C3×Q8—34no—
340C2×C3×Q8—122no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—34no—
351C22×C3×C4—122no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—64no—
363C2×#67—64no—
364C2×#67—122no—
365C2×#67—122no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—34no—
373C22×Dic3—61no—
374C22×Dic3—61no—
375C22×Dic3—61no—
376C22×Dic3—122no—
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C2×D12—34no—
384C2×D12—34no—
385C2×D12—64no—
386C2×D12—64no—
387C2×C4×D3—34no—
388C2×C4×D3—34no—
389C2×C4×D3—34no—
390C2×C4×D3—34no—
391C2×C4×D3—34no—
392C2×C4×D3—34no—
393C2×C4×D3—34no—
394C2×C4×D3—42no—
395C2×C4×D3—64no—
396C2×C4×D3—64no—
397C2×C4×D3—64no—
398C2×C4×D3—64no—
399C2×C4×D3—64no—
400C2×C4×D3—68no—
401C2×C4×D3—122no—
402C2×C4×D3—122no—
403C2×C4×D3—122no—
404C2×C4×D3—122no—
405C2×C4×D3—122no—
406C2×C4×D3—124no—
407C2×C4×D3—124no—
408C2×C4×D3C22×D314yes—
409C2×Dic6—42no—
410C2×Dic6C22×D314yes—
411C3×C4⋊C4—24no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4—34no—
416C3×C4⋊C4C22×D314yes—
417C3×C4⋊C4C22×D314yes—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—34no—
422C3×C22⋊C4—34no—
423C3×C42—34no—
424#217—34no—
425#217—34no—
426#217—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)⋊C4C22×D314yes—
435(C2×D3)⋊C4C22×D314yes—
436(C2×D3)⋊C4C22×D314yes—
437(C2×D3)⋊C4C22×D314yes—
438(C2×D3)⋊C4C22×D314yes—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444C4⋊Dic3—34no—
445C4⋊Dic3—34no—
446C4⋊Dic3—64no—
447C4⋊Dic3C22×D314yes—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—64no—
460Dic3⋊C4—64no—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463Dic3⋊C4C22×D314yes—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3C22×D314yes—
467C22×C32C2×#4112yes—
468C22×C32H(5,𝔽2)12yes—
469C22×C322−1+412yes—
470C22×C32C2511yescharacteristic
471C2×C3⋊D3—28no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3C2×#4114yes—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—44no—
482C2×C3×D3—44no—
483C32×C4—22no—
484C32×C4—22no—
485C32×C4—22no—
486C3⋊Dic3—22no—
487C3⋊Dic3—22no—
488C3⋊Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C22×Q8—31no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—91no—
499C23×C4—31no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4—91no—
503C23×C4—91no—
504#126—38no—
505#126—98no—
506#125—98no—
507#125—98no—
508#123—98no—
509#123—98no—
510#123—98no—
511#123—98no—
512C22⋊Q8—38no—
513C22⋊Q8—98no—
514C22⋊Q8—98no—
515#121—98no—
516C4×D4—98no—
517C4×D4—98no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—98no—
532C2×C4⋊C4D3211yescharacteristic
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C42—31no—
544C2×C42—91no—
545C23×C3—21no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—62no—
552C23×C3—62no—
553C23×C3—62no—
554C23×C3C23×D311yescharacteristic
555C23×C3C23×D311yescharacteristic
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—34no—
563C22×D3—34no—
564C22×D3—32no—
565C22×D3—32no—
566C22×D3—64no—
567C22×D3—62no—
568C22×D3—64no—
569C22×D3—64no—
570C22×D3—62no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—62no—
574C22×D3C23×D312yes—
575C22×D3C23×D312yes—
576C3×Q8—124no—
577C2×C3×C4—24no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
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—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—42no—
594C2×C3×C4—42no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—62no—
598C2×C3×C4—62no—
599C2×C3×C4—62no—
600C2×C3×C4—62no—
601C2×C3×C4—124no—
602C2×C3×C4C23×D312yes—
603C2×C3×C4C23×D312yes—
604C2×C3×C4C23×D312yes—
605C2×C3×C4C23×D312yes—
606C2×C3×C4C23×D312yes—
607C2×C3×C4C23×D312yes—
608#67—68no—
609#67—68no—
610#67—124no—
611#67—124no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—64no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—122no—
635C2×Dic3—122no—
636C2×Dic3—124no—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642C2×Dic3C23×D312yes—
643D12—68no—
644D12—68no—
645C4×D3—44no—
646C4×D3—68no—
647C4×D3—68no—
648C4×D3—616no—
649C4×D3—124no—
650C4×D3—124no—
651C4×D3—124no—
652C4×D3—124no—
653C4×D3—124no—
654C4×D3—128no—
655C4×D3—128no—
656Dic6—44no—
657C2×C32#53914yescomplemented
658C2×C32C22×#4111yescharacteristic
659C2×C32C2×H(5,𝔽2)11yescharacteristic
660C2×C32C2×2−1+411yescharacteristic
661C3⋊D3—24no—
662C3×D3—42no—
663C3×D3—42no—
664C24—31no—
665C24—31no—
666C24—91no—
667C2×Q8—34no—
668C2×Q8—122no—
669C2×D4—94no—
670C2×D4—94no—
671C2×D4—94no—
672C2×D4—184no—
673C2×D4—184no—
674C2×D4—362no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—34no—
682C22×C4—94no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—94no—
687C22×C4—94no—
688C22×C4—94no—
689C22×C4—122no—
690C22×C4—184no—
691C22×C4—362no—
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—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C4⋊C4—94no—
710C4⋊C4C2×D3214yes—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—34no—
715C22⋊C4—34no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C22⋊C4—94no—
720C22⋊C4—94no—
721C42—34no—
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—62no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—124no—
734C22×C3—124no—
735C22×C3#100412yes—
736C22×C3#100712yes—
737C22×C3D3×#4112yes—
738C22×C3D3×#4112yes—
739C22×C3#100912yes—
740C22×C3#101012yes—
741C22×C3C24×D311yescharacteristic
742C22×C3C24×D311yescharacteristic
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—34no—
750C2×D3—34no—
751C2×D3—44no—
752C2×D3—44no—
753C2×D3—64no—
754C2×D3—64no—
755C2×D3—616no—
756C2×D3—64no—
757C2×D3—68no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—68no—
762C2×D3—62no—
763C3×C4—24no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4—62no—
776C3×C4—62no—
777C3×C4—62no—
778Dic3—22no—
779Dic3—22no—
780Dic3—22no—
781Dic3—22no—
782Dic3—22no—
783Dic3—22no—
784Dic3—64no—
785Dic3—62no—
786Dic3—62no—
787Dic3—62no—
788Dic3—62no—
789Dic3—62no—
790Dic3—62no—
791Dic3—122no—
792Dic3—122no—
793C32C2×#53911yescharacteristic, complemented, Sylow
794C23—32no—
795C23—32no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—94no—
803C23—92no—
804C23—182no—
805C23—182no—
806C23C22×D3211yescharacteristic
807Q8—124no—
808D4—188no—
809D4—188no—
810D4—364no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—32no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—92no—
827C2×C4—92no—
828C2×C4—92no—
829C2×C4—124no—
830C2×C4—188no—
831C2×C4—182no—
832C2×C4—182no—
833C2×C4—182no—
834C2×C4—364no—
835C2×C4—364no—
836C2×C4—364no—
837C2×C4C22×D3212yes—
838C2×C4C22×D3212yes—
839C2×C4C22×D3212yes—
840C2×C3—24no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—122no—
845C2×C3—122no—
846C2×C3#563814yescomplemented
847C2×C3#570714yescomplemented
848C2×C3C2×#100411yescharacteristic
849C2×C3C2×#100711yescharacteristic
850C2×C3C2×D3×#4111yescharacteristic
851C2×C3C2×D3×#4111yescharacteristic
852C2×C3C2×#100911yescharacteristic
853C2×C3C2×#101011yescharacteristic
854D3—42no—
855D3—42no—
856D3—68no—
857D3—64no—
858D3—64no—
859C22—62no—
860C22—62no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—62no—
865C22—94no—
866C22—124no—
867C22—124no—
868C22—188no—
869C22—182no—
870C22—182no—
871C22#6430612yes—
872C22#6431412yes—
873C22#6431512yes—
874C22C23×D3211yescharacteristic
875C4—22no—
876C4—22no—
877C4—22no—
878C4—62no—
879C4—62no—
880C4—62no—
881C4—62no—
882C4—62no—
883C4—62no—
884C4—182no—
885C4—182no—
886C4—182no—
887C3—21no—
888C3C2×#563811yescharacteristic, complemented
889C3C2×#570711yescharacteristic, complemented
890C2—122no—
891C2—122no—
892C2—184no—
893C2#1059457314yesdirect product factor
894C2C2×#6430611yescharacteristic
895C2C2×#6431411yescharacteristic
896C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63912C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#539
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×C4⋊C4×C3⋊D3C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#896C2semidirect
5. C2×#63905C2semidirect
6. C2×C4×#626C2semidirect
7. C2×#63891C2semidirect
8. C2×#63887C2semidirect
9. C2×#63881C2semidirect
10. C2×#63871C2semidirect
11. C2×#63867C2semidirect
12. C2×#63858C2semidirect
13. C2×#63853C2semidirect
14. C2×#63853C2semidirect
15. C2×#63845C2semidirect
16. #10594573C2direct (N × H)
32. C4⋊C4×C3⋊D3C22semidirect
43. C3×#898C22semidirect
44. C3×#896C22semidirect
58. #63905C22semidirect
59. C4×#626C22semidirect
60. #63891C22semidirect
61. #63887C22semidirect
62. #63881C22semidirect
63. #63871C22semidirect
64. #63867C22semidirect
65. #63858C22semidirect
66. #63853C22semidirect
67. #63853C22semidirect
68. #63845C22semidirect
78. C2×#898D3semidirect
80. C2×#896D3semidirect
246. #898C2×D3semidirect
248. #896C2×D3semidirect
657. C2×C32#539semidirect
793. C32C2×#539semidirect
846. C2×C3#5638semidirect
847. C2×C3#5707semidirect
888. C3C2×#5638semidirect
889. C3C2×#5707semidirect
893. C2#10594573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C3×#8982
C2×C3×#8962
C2×#639122
C2×#639052
C2×C4×#6262
C2×#638912
C2×#638872
C2×#638812
C2×#638712
C2×#638672
C2×#638582
C2×#638532
C2×#638452
#105945732
C2×#57073
C2×#56383