Finite Group Databasebeta

← C2×#10594394 #11903253

Subgroups — C2×#10594394 #11903253

Order 1152.

2609 conjugacy classes of subgroups.

The subgroup lattice has 882 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×#896C211yesmaximal, characteristic, complemented
3C2×C3×#889C211yesmaximal, characteristic, complemented
4C2×C4×#626C211yesmaximal, characteristic
5C2×#63899C211yesmaximal, characteristic, complemented
6C2×#63893C211yesmaximal, characteristic, complemented
7C2×#63881C211yesmaximal, characteristic
8C2×#63881C211yesmaximal, characteristic
9C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63865C211yesmaximal, characteristic, complemented
12C2×#63865C211yesmaximal, characteristic, complemented
13C2×#63845C211yesmaximal, characteristic, complemented
14C2×#63839C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594394C2116yesmaximal, direct product factor
17C2×#5690—31nomaximal
18C2×#5636—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#627C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C4⋊C4×C3⋊D3C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#896C2218yescomplemented
45C3×#889C2218yescomplemented
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57C4×#626C2218yes—
58#63899C2218yescomplemented
59#63893C2218yescomplemented
60#63881C2218yes—
61#63881C2218yes—
62D3×Dic3⋊C4C2218yescomplemented
63#63871C2218yescomplemented
64#63865C2218yescomplemented
65#63865C2218yescomplemented
66#63845C2218yescomplemented
67#63839C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#125—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#946—31no—
72C2×#944—31no—
73C2×C4×#67—31no—
74C22×Dic3⋊C4—31no—
75#5690—316no—
76#5636—316no—
77C2×#897—31no—
78C2×#897—31no—
79C2×#896—31no—
80C2×#896—31no—
81C2×#896—31no—
82C2×#896—31no—
83C2×#896—31no—
84C2×#896D311yescharacteristic, complemented
85C2×#893—31no—
86C2×#893—31no—
87C2×D3×C4⋊C4—31no—
88C2×D3×C4⋊C4—31no—
89C2×D3×C4⋊C4—31no—
90C2×D3×C4⋊C4—61no—
91C2×#890—31no—
92C2×#889—31no—
93C2×#889D311yescharacteristic, complemented
94C2×#888—31no—
95C2×#887—31no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×C4×D12—31no—
101C2×C4×Dic6—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C4×C3⋊D3—24no—
111C2×C4×C3⋊D3—42no—
112C2×C4×C3⋊D3—42no—
113C2×C4×C3⋊D3C2314yes—
114C2×C4×C3⋊D3C2314yes—
115C2×C4×C3⋊D3C2314yes—
116C22×C3×Dic3C2311yescharacteristic
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×#627—24no—
128C2×#627—42no—
129C2×#627C2314yes—
130C2×#627C2314yes—
131C2×#626Q818yescomplemented
132C2×#626C2314yes—
133C2×D3×Dic3—24no—
134C2×D3×Dic3—42no—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2314yes—
137C32×C4⋊C4C2314yes—
138C4⋊(C3⋊Dic3)C2314yes—
139#3750C2314yes—
140#3750C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×C4⋊Dic3C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×C4×Dic3C2314yes—
151#3724C2314yes—
152#3724C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158#3722C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160Dic32C2314yes—
161Dic32C2314yes—
162C2×#554—91noSylow
163C22×C3×Q8—31no—
164C23×C3×C4—31no—
165C22×#67—31no—
166C23×Dic3—31no—
167C23×Dic3—31no—
168C22×D12—31no—
169C22×C4×D3—31no—
170C22×C4×D3—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—61no—
178C22×C4×D3—61no—
179C22×C4×D3—61no—
180C22×C4×D3C2×D311yescharacteristic
181C22×Dic6—31no—
182C22×Dic6—31no—
183C22×Dic6—31no—
184C22×Dic6—31no—
185C22×Dic6C2×D311yescharacteristic
186C3×#125—38no—
187C3×C22⋊Q8—38no—
188C2×C3×C4⋊C4—21no—
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×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4C2×D311yescharacteristic
197C2×C3×C4⋊C4C2×D311yescharacteristic
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C42—31no—
201C2×#217—31no—
202#946—38no—
203#944—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×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—61no—
220C2×C4⋊Dic3C2×D311yescharacteristic
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
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—38no—
233C2×Dic3⋊C4—61no—
234C2×Dic3⋊C4—61no—
235C2×Dic3⋊C4C2×D311yescharacteristic
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×Dic3⋊C4C2×D311yescharacteristic
238C2×Dic3⋊C4C2×D311yescharacteristic
239C2×Dic3⋊C4C2×D311yescharacteristic
240C2×Dic3⋊C4C2×D311yescharacteristic
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3C2×D311yescharacteristic
246#897—38no—
247#897—38no—
248#896—38no—
249#896—38no—
250#896—38no—
251#896—38no—
252#896—38no—
253#896C2×D318yescomplemented
254#893—38no—
255#893—38no—
256D3×C4⋊C4—38no—
257D3×C4⋊C4—38no—
258D3×C4⋊C4—38no—
259D3×C4⋊C4—68no—
260#890—38no—
261#889—38no—
262#889C2×D318yescomplemented
263#888—38no—
264#887—38no—
265#67⋊C4—38no—
266#67⋊C4—38no—
267#878—38no—
268#878—38no—
269C4×D12—38no—
270C4×Dic6—38no—
271C23×C32C2411yescharacteristic
272C22×C3⋊D3—22no—
273C22×C3⋊D3—22no—
274C22×C3⋊D3C2×Q814yes—
275C22×C3⋊D3C2412yes—
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×C4—22no—
283C2×C32×C4C2412yes—
284C2×C32×C4C2412yes—
285C2×C32×C4C2412yes—
286C2×C3⋊Dic3—22no—
287C2×C3⋊Dic3—22no—
288C2×C3⋊Dic3#4114yes—
289C2×C3⋊Dic3C2412yes—
290C2×C3⋊Dic3C2412yes—
291C2×C3⋊Dic3C2412yes—
292C4×C3⋊D3—28no—
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×Dic3C2×Q814yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C3×C4×D3—44no—
310C3×Dic6—44no—
311#627—28no—
312#627—44no—
313#626C2×Q8116yescomplemented
314D3×Dic3—28no—
315D3×Dic3—44no—
316#554—916no—
317C2×C4⋊Q8—91no—
318C2×#125—31no—
319C2×#125—91no—
320C2×C22⋊Q8—31no—
321C2×C22⋊Q8—91no—
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—31no—
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—61no—
336C23×D3C22×D311yescharacteristic
337C2×C3×Q8—34no—
338C2×C3×Q8—122no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—34no—
350C22×C3×C4—122no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C2×#67—38no—
358C2×#67—34no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—34no—
366C22×Dic3—34no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—64no—
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—38no—
380C2×D12—34no—
381C2×C4×D3—34no—
382C2×C4×D3—34no—
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—34no—
386C2×C4×D3—34no—
387C2×C4×D3—34no—
388C2×C4×D3—34no—
389C2×C4×D3—42no—
390C2×C4×D3—64no—
391C2×C4×D3—64no—
392C2×C4×D3—64no—
393C2×C4×D3—64no—
394C2×C4×D3—64no—
395C2×C4×D3—64no—
396C2×C4×D3—68no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C2×C4×D3—122no—
400C2×C4×D3—122no—
401C2×C4×D3—122no—
402C2×C4×D3—124no—
403C2×C4×D3—124no—
404C2×C4×D3C22×D314yes—
405C2×Dic6—34no—
406C2×Dic6—34no—
407C2×Dic6—34no—
408C2×Dic6—34no—
409C2×Dic6—42no—
410C2×Dic6—64no—
411C2×Dic6—64no—
412C2×Dic6—122no—
413C2×Dic6—122no—
414C2×Dic6C22×D314yes—
415C3×C4⋊C4—24no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—34no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4C22×D314yes—
424C3×C4⋊C4C22×D314yes—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C42—34no—
428#217—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)⋊C4C22×D314yes—
437(C2×D3)⋊C4C22×D314yes—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—64no—
444C4⋊Dic3C22×D314yes—
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—64no—
457Dic3⋊C4—64no—
458Dic3⋊C4C22×D314yes—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463Dic3⋊C4C22×D314yes—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3—34no—
468C4×Dic3C22×D314yes—
469C22×C32C22×Q812yes—
470C22×C32C2×#4112yes—
471C22×C32H(5,𝔽2)12yes—
472C22×C32C2511yescharacteristic
473C2×C3⋊D3—28no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3C22×Q814yes—
477C2×C3×D3—28no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3C22×Q814yes—
481C32×C4—22no—
482C32×C4—22no—
483C32×C4—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3C2×#4114yes—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3C22×Q814yes—
494C22×Q8—31no—
495C22×Q8—91no—
496C22×Q8—91no—
497C22×D4—91no—
498C23×C4—31no—
499C23×C4—91no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4—91no—
503C23×C4—91no—
504C4⋊Q8—98no—
505#125—38no—
506#125—98no—
507C22⋊Q8—38no—
508C22⋊Q8—98no—
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—31no—
524C2×C4⋊C4—98no—
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—91no—
532C2×C4⋊C4—91no—
533C2×C4⋊C4—98no—
534C2×C4⋊C4D3211yescharacteristic
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C42—31no—
542C2×C42—91no—
543C2×C42—91no—
544C23×C3—21no—
545C23×C3—34no—
546C23×C3—32no—
547C23×C3—62no—
548C23×C3—62no—
549C23×C3C23×D311yescharacteristic
550C23×C3C23×D311yescharacteristic
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—34no—
554C22×D3—34no—
555C22×D3—32no—
556C22×D3—32no—
557C22×D3—64no—
558C22×D3—62no—
559C22×D3—64no—
560C22×D3—64no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3D3×Q814yes—
566C22×D3C23×D312yes—
567C3×Q8—124no—
568C2×C3×C4—24no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—34no—
579C2×C3×C4—32no—
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—42no—
587C2×C3×C4—42no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—62no—
593C2×C3×C4—62no—
594C2×C3×C4—124no—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601#67—316no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—34no—
609C2×Dic3—34no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—64no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—68no—
621C2×Dic3—62no—
622C2×Dic3—62no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—122no—
626C2×Dic3—122no—
627C2×Dic3—124no—
628C2×Dic3D3×Q814yes—
629C2×Dic3C23×D312yes—
630C2×Dic3C23×D312yes—
631C2×Dic3C23×D312yes—
632C2×Dic3C23×D312yes—
633C2×Dic3C23×D312yes—
634C2×Dic3C23×D312yes—
635C2×Dic3C23×D312yes—
636D12—316no—
637C4×D3—44no—
638C4×D3—68no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—616no—
642C4×D3—124no—
643C4×D3—124no—
644C4×D3—124no—
645C4×D3—124no—
646C4×D3—124no—
647C4×D3—128no—
648C4×D3—128no—
649Dic6—44no—
650Dic6—68no—
651Dic6—68no—
652Dic6—124no—
653Dic6—124no—
654C2×C32#55414yescomplemented
655C2×C32C23×Q811yescharacteristic
656C2×C32C22×#4111yescharacteristic
657C2×C32C2×H(5,𝔽2)11yescharacteristic
658C3⋊D3—24no—
659C3×D3—24no—
660C24—31no—
661C24—91no—
662C2×Q8—34no—
663C2×Q8—94no—
664C2×Q8—94no—
665C2×Q8—122no—
666C2×Q8—184no—
667C2×Q8—362no—
668C2×D4—94no—
669C2×D4—98no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—34no—
678C22×C4—94no—
679C22×C4—94no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—94no—
684C22×C4—94no—
685C22×C4—94no—
686C22×C4—122no—
687C22×C4—184no—
688C22×C4—184no—
689C22×C4—362no—
690C22×C4—362no—
691C22×C4—362no—
692C22×C4C2×D3211yescharacteristic
693C22×C4C2×D3211yescharacteristic
694C22×C4C2×D3211yescharacteristic
695C4⋊C4—34no—
696C4⋊C4—34no—
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⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C4⋊C4—94no—
710C4⋊C4C2×D3214yes—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C42—34no—
718C42—94no—
719C42—94no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—34no—
725C22×C3—68no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3#100412yes—
729C22×C3C2×D3×Q812yes—
730C22×C3C2×D3×Q812yes—
731C22×C3D3×#4112yes—
732C22×C3D3×#4112yes—
733C22×C3#100912yes—
734C22×C3C24×D311yescharacteristic
735C22×C3C24×D311yescharacteristic
736C2×D3—28no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—34no—
740C2×D3—34no—
741C2×D3—64no—
742C2×D3—64no—
743C2×D3—64no—
744C2×D3—616no—
745C2×D3—68no—
746C2×D3—68no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3C2×D3×Q814yes—
752C3×C4—24no—
753C3×C4—22no—
754C3×C4—22no—
755C3×C4—22no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—34no—
760C3×C4—42no—
761C3×C4—42no—
762C3×C4—62no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4—62no—
767C3×C4—62no—
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—22no—
773Dic3—22no—
774Dic3—34no—
775Dic3—34no—
776Dic3—64no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—122no—
782Dic3—122no—
783Dic3C2×D3×Q814yes—
784C32C2×#55411yescharacteristic, complemented, Sylow
785C23—34no—
786C23—32no—
787C23—62no—
788C23—62no—
789C23—94no—
790C23—92no—
791C23—182no—
792C23—182no—
793C23C22×D3211yescharacteristic
794Q8—124no—
795Q8—188no—
796Q8—364no—
797D4—916no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—34no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—94no—
816C2×C4—92no—
817C2×C4—92no—
818C2×C4—92no—
819C2×C4—124no—
820C2×C4—188no—
821C2×C4—188no—
822C2×C4—182no—
823C2×C4—182no—
824C2×C4—364no—
825C2×C4—364no—
826C2×C4—364no—
827C2×C4C22×D3212yes—
828C2×C4C22×D3212yes—
829C2×C4C22×D3212yes—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—24no—
834C2×C3—64no—
835C2×C3#563614yescomplemented
836C2×C3#569014yescomplemented
837C2×C3C2×#100411yescharacteristic
838C2×C3C22×D3×Q811yescharacteristic
839C2×C3C22×D3×Q811yescharacteristic
840C2×C3C2×D3×#4111yescharacteristic
841C2×C3C2×D3×#4111yescharacteristic
842C2×C3C2×#100911yescharacteristic
843D3—24no—
844D3—68no—
845D3—64no—
846D3—64no—
847C22—34no—
848C22—62no—
849C22—62no—
850C22—68no—
851C22—94no—
852C22—182no—
853C22—182no—
854C22—188no—
855C22#6430612yes—
856C22#6431412yes—
857C22D32×Q812yes—
858C22C23×D3211yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—34no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—62no—
867C4—62no—
868C4—62no—
869C4—94no—
870C4—182no—
871C4—182no—
872C3—21no—
873C3C2×#563611yescharacteristic, complemented
874C3C2×#569011yescharacteristic, complemented
875C2—64no—
876C2—184no—
877C2#1059439414yesdirect product factor
878C2C2×#6430611yescharacteristic
879C2C2×#6431411yescharacteristic
880C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#554
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×#896C2semidirect
3. C2×C3×#889C2semidirect
5. C2×#63899C2semidirect
6. C2×#63893C2semidirect
9. C2×D3×Dic3⋊C4C2semidirect
10. C2×#63871C2semidirect
11. C2×#63865C2semidirect
12. C2×#63865C2semidirect
13. C2×#63845C2semidirect
14. C2×#63839C2semidirect
15. C2×#63837C2semidirect
16. #10594394C2direct (N × H)
33. C4⋊C4×C3⋊D3C22semidirect
44. C3×#896C22semidirect
45. C3×#889C22semidirect
58. #63899C22semidirect
59. #63893C22semidirect
62. D3×Dic3⋊C4C22semidirect
63. #63871C22semidirect
64. #63865C22semidirect
65. #63865C22semidirect
66. #63845C22semidirect
67. #63839C22semidirect
68. #63837C22semidirect
84. C2×#896D3semidirect
93. C2×#889D3semidirect
131. C2×#626Q8semidirect
253. #896C2×D3semidirect
262. #889C2×D3semidirect
313. #626C2×Q8semidirect
654. C2×C32#554semidirect
784. C32C2×#554semidirect
835. C2×C3#5636semidirect
836. C2×C3#5690semidirect
873. C3C2×#5636semidirect
874. C3C2×#5690semidirect
877. C2#10594394direct (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×#8962
C2×C3×#8892
C2×C4×#6262
C2×#638992
C2×#638932
C2×#638812
C2×D3×Dic3⋊C42
C2×#638712
C2×#638652
C2×#638452
C2×#638392
C2×#638372
#105943942
C2×#56903
C2×#56363