Finite Group Databasebeta

← C2×#10594141 #11903267

Subgroups — C2×#10594141 #11903267

Order 1152.

2613 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C2×C3×#878C211yesmaximal, characteristic, complemented
3C2×C3×#878C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×#63952C211yesmaximal, characteristic
7C2×#63952C211yesmaximal, characteristic
8C2×#63895C211yesmaximal, characteristic, complemented
9C2×#63888C211yesmaximal, characteristic, complemented
10C2×#63883C211yesmaximal, characteristic, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×#63870C211yesmaximal, characteristic, complemented
13C2×#63847C211yesmaximal, characteristic, complemented
14C2×#63843C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10594141C2116yesmaximal, direct product factor
17C2×#5636—31nomaximal
18C2×#5635—31nomaximal
19C22×#638C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C22×#624C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64090C2218yes—
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C3×#878C2218yescomplemented
43C3×#878C2218yescomplemented
44#63982C2218yescomplemented
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2218yescomplemented
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×Dic32C2211yescharacteristic
58C2×Dic32C2211yescharacteristic
59#63952C2218yes—
60#63952C2218yes—
61#63895C2218yescomplemented
62#63888C2218yescomplemented
63#63883C2218yescomplemented
64#63871C2218yescomplemented
65#63870C2218yescomplemented
66#63847C2218yescomplemented
67#63843C2218yescomplemented
68#63839C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×Q8×Dic3—31no—
74C2×#944—31no—
75C2×C4×#67—31no—
76C2×C4×#67—31no—
77C22×C4⋊Dic3—31no—
78C22×Dic3⋊C4—31no—
79#5636—316no—
80#5635—316no—
81C2×#897—31no—
82C2×#897—31no—
83C2×#896—31no—
84C2×#896—31no—
85C2×D3×C4⋊C4—31no—
86C2×D3×C4⋊C4—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#889—31no—
91C2×#888—31no—
92C2×#887—31no—
93C2×#67⋊C4—31no—
94C2×#67⋊C4—31no—
95C2×#67⋊C4—31no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4—61no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878D311yescharacteristic, complemented
101C2×#878D311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C2×#638Q818yescomplemented
107C2×#638C2314yes—
108C22×C3⋊Dic3—42no—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2314yes—
112C22×C3⋊Dic3C2311yescharacteristic
113C2×C4×C3⋊D3—42no—
114C2×C4×C3⋊D3C2314yes—
115C22×C3×Dic3—24no—
116C22×C3×Dic3—42no—
117C22×C3×Dic3C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2314yes—
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×Dic6—24no—
128C2×C3×Dic6—42no—
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2314yes—
131C2×#627—42no—
132C2×#627C2314yes—
133C2×#624—24no—
134C2×#624—42no—
135C2×#624C2314yes—
136C2×#624C2314yes—
137C32×C22⋊C4C2314yes—
138#3752C2314yes—
139#3750C2314yes—
140C4×C3⋊Dic3C2314yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×C4⋊Dic3C2314yes—
144C3×C4⋊Dic3C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149#3724C2314yes—
150#3724C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160Dic32C2314yes—
161Dic32C2314yes—
162C2×#554—91noSylow
163C22×C3×Q8—31no—
164C22×C3×Q8—31no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—61no—
170C23×Dic3—31no—
171C23×Dic3—31no—
172C23×Dic3—61no—
173C23×Dic3C2×D311yescharacteristic
174C23×Dic3C2×D311yescharacteristic
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—61no—
182C22×Dic6—31no—
183C22×Dic6—31no—
184C22×Dic6C2×D311yescharacteristic
185C22×Dic6C2×D311yescharacteristic
186C3×C22⋊Q8—38no—
187C3×C22⋊Q8—38no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C22⋊C4—21no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C22⋊C4C2×D311yescharacteristic
199C2×#217C2×D311yescharacteristic
200C2×#217C2×D311yescharacteristic
201#946—38no—
202#946—38no—
203Q8×Dic3—38no—
204#944—38no—
205C4×#67—38no—
206C4×#67—38no—
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—61no—
214C2×C4⋊Dic3—38no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3C2×D311yescharacteristic
222C2×C4⋊Dic3C2×D311yescharacteristic
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—38no—
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—31no—
238C2×Dic3⋊C4—61no—
239C2×Dic3⋊C4C2×D311yescharacteristic
240C2×Dic3⋊C4C2×D311yescharacteristic
241C2×Dic3⋊C4C2×D311yescharacteristic
242C2×Dic3⋊C4C2×D311yescharacteristic
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—61no—
250#897—38no—
251#897—38no—
252#896—38no—
253#896—38no—
254D3×C4⋊C4—38no—
255D3×C4⋊C4—38no—
256#889—38no—
257#889—38no—
258#889—38no—
259#889—38no—
260#888—38no—
261#887—38no—
262#67⋊C4—38no—
263#67⋊C4—38no—
264#67⋊C4—38no—
265#67⋊C4—38no—
266#67⋊C4—68no—
267#878—38no—
268#878—38no—
269#878C2×D318yescomplemented
270#878C2×D318yescomplemented
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2×Q814yes—
274C23×C32C2412yes—
275C23×C32C2411yescharacteristic
276C22×C3⋊D3—22no—
277C22×C3⋊D3—22no—
278C22×C3⋊D3C2×Q814yes—
279C22×C3⋊D3C2412yes—
280C2×C32×C4—22no—
281C2×C32×C4—22no—
282C2×C32×C4C2412yes—
283C2×C32×C4C2412yes—
284#638C2×Q8116yescomplemented
285C2×C3⋊Dic3—22no—
286C2×C3⋊Dic3—22no—
287C2×C3⋊Dic3—44no—
288C2×C3⋊Dic3C2×Q814yes—
289C2×C3⋊Dic3C2412yes—
290C2×C3⋊Dic3C2412yes—
291C2×C3⋊Dic3C2412yes—
292C4×C3⋊D3—44no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—28no—
301C2×C3×Dic3—44no—
302C2×C3×Dic3#4114yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C3×Dic6—28no—
312C3×Dic6—44no—
313#627—44no—
314#624—28no—
315#624—44no—
316#554—916no—
317C2×C4⋊Q8—91no—
318C2×#125—91no—
319C2×#125—91no—
320C2×C22⋊Q8—31no—
321C2×C22⋊Q8—31no—
322C2×C22⋊Q8—91no—
323C2×C22⋊Q8—91no—
324C2×C22⋊Q8—91no—
325C2×C22⋊Q8—91no—
326C2×C4×Q8—91no—
327C2×C4×D4—91no—
328C2×C4×D4—91no—
329C2×C4×D4—91no—
330C22×C4⋊C4—91no—
331C22×C4⋊C4—91no—
332C24×C3—21no—
333C24×C3C22×D311yescharacteristic
334C24×C3C22×D311yescharacteristic
335C23×D3—31no—
336C23×D3—31no—
337C23×D3—61no—
338C2×C3×Q8—34no—
339C2×C3×Q8—34no—
340C2×C3×Q8—64no—
341C2×C3×Q8—122no—
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—31no—
351C22×C3×C4—31no—
352C22×C3×C4—34no—
353C22×C3×C4—34no—
354C22×C3×C4—64no—
355C22×C3×C4—122no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C2×#67—38no—
361C2×#67—38no—
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—64no—
365C2×#67—68no—
366C22×Dic3—24no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—34no—
374C22×Dic3—34no—
375C22×Dic3—42no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—64no—
379C22×Dic3—61no—
380C22×Dic3—122no—
381C22×Dic3—122no—
382C22×Dic3—124no—
383C22×Dic3C22×D314yes—
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D314yes—
392C22×Dic3C22×D311yescharacteristic
393C2×C4×D3—34no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—34no—
397C2×C4×D3—34no—
398C2×C4×D3—34no—
399C2×C4×D3—64no—
400C2×C4×D3—64no—
401C2×C4×D3—64no—
402C2×C4×D3—122no—
403C2×C4×D3—122no—
404C2×C4×D3—122no—
405C2×C4×D3—122no—
406C2×C4×D3—124no—
407C2×Dic6—24no—
408C2×Dic6—34no—
409C2×Dic6—34no—
410C2×Dic6—42no—
411C2×Dic6—122no—
412C2×Dic6—122no—
413C2×Dic6C22×D314yes—
414C2×Dic6C22×D314yes—
415C3×C4⋊C4—34no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—34no—
421C3×C22⋊C4—24no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4—34no—
424C3×C22⋊C4C22×D314yes—
425C3×C22⋊C4C22×D314yes—
426#217C22×D314yes—
427#217C22×D314yes—
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—64no—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3C22×D314yes—
442C4⋊Dic3C22×D314yes—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
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—64no—
458Dic3⋊C4C22×D314yes—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461Dic3⋊C4C22×D314yes—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3—34no—
468C4×Dic3—64no—
469C22×C32—28no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32C22×Q814yes—
473C22×C32C22×Q812yes—
474C22×C32C2×#4112yes—
475C22×C32H(5,𝔽2)12yes—
476C22×C32C2511yescharacteristic
477C2×C3⋊D3—28no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3C22×Q814yes—
481C32×C4—22no—
482C32×C4—22no—
483C3⋊Dic3—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3C22×Q814yes—
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—
498C23×C4—31no—
499C23×C4—31no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4—91no—
503C23×C4—91no—
504C4⋊Q8—98no—
505#125—98no—
506#125—98no—
507C22⋊Q8—38no—
508C22⋊Q8—38no—
509C22⋊Q8—98no—
510C22⋊Q8—98no—
511C22⋊Q8—98no—
512C22⋊Q8—98no—
513C4×Q8—98no—
514C4×D4—98no—
515C4×D4—98no—
516C4×D4—98no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—98no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—98no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532C2×C4⋊C4—91no—
533C2×C4⋊C4—91no—
534C2×C4⋊C4—91no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4D3211yescharacteristic
541C2×C42—91no—
542C2×C42—91no—
543C2×C42—91no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—21no—
550C23×C3—24no—
551C23×C3—42no—
552C23×C3—42no—
553C23×C3D3×Q814yes—
554C23×C3D3×Q814yes—
555C23×C3C23×D312yes—
556C23×C3C23×D312yes—
557C23×C3C23×D311yescharacteristic
558C23×C3C23×D311yescharacteristic
559C22×D3—34no—
560C22×D3—34no—
561C22×D3—32no—
562C22×D3—32no—
563C22×D3—64no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—62no—
568C22×D3—62no—
569C22×D3—122no—
570C22×D3—122no—
571C3×Q8—68no—
572C3×Q8—124no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—34no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—42no—
589C2×C3×C4—42no—
590C2×C3×C4—68no—
591C2×C3×C4—62no—
592C2×C3×C4—62no—
593C2×C3×C4—62no—
594C2×C3×C4—62no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—62no—
598C2×C3×C4—124no—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601C2×C3×C4C23×D312yes—
602C2×C3×C4C23×D312yes—
603#67—316no—
604#67—316no—
605#67—616no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—28no—
614C2×Dic3—34no—
615C2×Dic3—34no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—44no—
623C2×Dic3—64no—
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—122no—
633C2×Dic3—124no—
634C2×Dic3—124no—
635C2×Dic3—128no—
636C2×Dic3#23714yes—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C4×D3—68no—
646C4×D3—68no—
647C4×D3—124no—
648C4×D3—124no—
649C4×D3—124no—
650C4×D3—124no—
651C4×D3—128no—
652Dic6—28no—
653Dic6—44no—
654Dic6—124no—
655Dic6—124no—
656C2×C32—24no—
657C2×C32#55414yescomplemented
658C2×C32C23×Q811yescharacteristic
659C2×C32C22×#4111yescharacteristic
660C2×C32C2×H(5,𝔽2)11yescharacteristic
661C3⋊D3—24no—
662C24—91no—
663C24C2×D3211yescharacteristic
664C2×Q8—34no—
665C2×Q8—34no—
666C2×Q8—64no—
667C2×Q8—94no—
668C2×Q8—122no—
669C2×Q8—362no—
670C2×D4—94no—
671C2×D4—98no—
672C22×C4—31no—
673C22×C4—34no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—34no—
682C22×C4—64no—
683C22×C4—94no—
684C22×C4—94no—
685C22×C4—91no—
686C22×C4—91no—
687C22×C4—91no—
688C22×C4—94no—
689C22×C4—94no—
690C22×C4—122no—
691C22×C4—184no—
692C22×C4—362no—
693C22×C4—362no—
694C22×C4—362no—
695C22×C4C2×D3211yescharacteristic
696C22×C4C2×D3211yescharacteristic
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—34no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C4⋊C4—94no—
710C4⋊C4—94no—
711C4⋊C4—94no—
712C4⋊C4—94no—
713C22⋊C4—34no—
714C22⋊C4—34no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4C2×D3214yes—
719C42—94no—
720C42—94no—
721C42—94no—
722C22×C3—28no—
723C22×C3—28no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—24no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—21no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—48no—
736C22×C3C2×#23712yes—
737C22×C3#100412yes—
738C22×C3C2×D3×Q814yes—
739C22×C3C2×D3×Q814yes—
740C22×C3C2×D3×Q812yes—
741C22×C3C2×D3×Q812yes—
742C22×C3D3×#4112yes—
743C22×C3#100912yes—
744C22×C3C24×D311yescharacteristic
745C22×C3C24×D311yescharacteristic
746C2×D3—34no—
747C2×D3—34no—
748C2×D3—64no—
749C2×D3—68no—
750C2×D3—68no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—128no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—34no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4—62no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—62no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—62no—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—22no—
779Dic3—34no—
780Dic3—34no—
781Dic3—64no—
782Dic3—64no—
783Dic3—62no—
784Dic3—62no—
785Dic3—62no—
786Dic3—62no—
787Dic3—122no—
788Dic3C2×#23714yes—
789C32C2×#55411yescharacteristic, complemented, Sylow
790C23—22no—
791C23—22no—
792C23—94no—
793C23—92no—
794C23—182no—
795C23—182no—
796C23#379714yes—
797C23C22×D3212yes—
798C23C22×D3211yescharacteristic
799Q8—68no—
800Q8—124no—
801Q8—364no—
802D4—916no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—34no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—68no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—94no—
823C2×C4—92no—
824C2×C4—92no—
825C2×C4—92no—
826C2×C4—124no—
827C2×C4—188no—
828C2×C4—182no—
829C2×C4—182no—
830C2×C4—364no—
831C2×C4—364no—
832C2×C4—364no—
833C2×C4C22×D3212yes—
834C2×C4C22×D3212yes—
835C2×C3—24no—
836C2×C3—24no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—24no—
841C2×C3—44no—
842C2×C3#563514yescomplemented
843C2×C3#563614yescomplemented
844C2×C3C22×#23711yescharacteristic
845C2×C3C2×#100411yescharacteristic
846C2×C3C22×D3×Q811yescharacteristic
847C2×C3C22×D3×Q811yescharacteristic
848C2×C3C2×D3×#4111yescharacteristic
849C2×C3C2×#100911yescharacteristic
850D3—64no—
851D3—64no—
852D3—124no—
853C22—22no—
854C22—22no—
855C22—28no—
856C22—94no—
857C22—182no—
858C22—182no—
859C22—188no—
860C22C2×#379714yes—
861C22C2×#379712yes—
862C22D3×#23712yes—
863C22#6431412yes—
864C22C23×D3211yescharacteristic
865C4—22no—
866C4—22no—
867C4—34no—
868C4—62no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—62no—
873C4—62no—
874C4—62no—
875C4—94no—
876C4—182no—
877C4—182no—
878C3—21no—
879C3C2×#563511yescharacteristic, complemented
880C3C2×#563611yescharacteristic, complemented
881C2—24no—
882C2—184no—
883C2#1059414114yesdirect product factor
884C2C22×#379711yescharacteristic
885C2C2×D3×#23711yescharacteristic
886C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#878C2semidirect
3. C2×C3×#878C2semidirect
4. C2×#63982C2semidirect
5. C22×Dic3⋊Dic3C2semidirect
8. C2×#63895C2semidirect
9. C2×#63888C2semidirect
10. C2×#63883C2semidirect
11. C2×#63871C2semidirect
12. C2×#63870C2semidirect
13. C2×#63847C2semidirect
14. C2×#63843C2semidirect
15. C2×#63839C2semidirect
16. #10594141C2direct (N × H)
42. C3×#878C22semidirect
43. C3×#878C22semidirect
44. #63982C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
61. #63895C22semidirect
62. #63888C22semidirect
63. #63883C22semidirect
64. #63871C22semidirect
65. #63870C22semidirect
66. #63847C22semidirect
67. #63843C22semidirect
68. #63839C22semidirect
100. C2×#878D3semidirect
101. C2×#878D3semidirect
106. C2×#638Q8semidirect
269. #878C2×D3semidirect
270. #878C2×D3semidirect
284. #638C2×Q8semidirect
657. C2×C32#554semidirect
789. C32C2×#554semidirect
842. C2×C3#5635semidirect
843. C2×C3#5636semidirect
879. C3C2×#5635semidirect
880. C3C2×#5636semidirect
883. C2#10594141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640902
C2×C3×#8782
C2×#639822
C22×Dic3⋊Dic32
C2×#639522
C2×#638952
C2×#638882
C2×#638832
C2×#638712
C2×#638702
C2×#638472
C2×#638432
C2×#638392
#105941412
C2×#56363
C2×#56353