Finite Group Databasebeta

← C2×#10595135 #11902431

Subgroups — C2×#10595135 #11902431

Order 1152.

4131 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#626C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×C3×#937C211yesmaximal, characteristic, complemented
5C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
6C2×#63978C211yesmaximal, characteristic, complemented
7C2×#63974C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C2×D3×#217C211yesmaximal, characteristic, complemented
10C2×#63964C211yesmaximal, characteristic, complemented
11C2×#63958C211yesmaximal, characteristic, complemented
12#10595135C2116yesmaximal, direct product factor
13C2×#63890C211yesmaximal, characteristic, complemented
14C2×#63880C211yesmaximal, characteristic, complemented
15C2×#63854C211yesmaximal, characteristic, complemented
16C2×#63852C211yesmaximal, characteristic, complemented
17C2×#5591—31nomaximal
18C2×#5550—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C22×#638C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic, complemented
26C23×C3×Dic3C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic, complemented
28C22×#627C2211yescharacteristic, complemented
29C22×#626—28no—
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2218yescomplemented
35C22×#624C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic
42#64146C2218yescomplemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic
46C2×C3×#217C2211yescharacteristic
47C2×C3×#217C2211yescharacteristic, complemented
48C3×#937C2218yescomplemented
49C3×D4×Dic3C2218yescomplemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
53C2×C3×C4×Dic3C2211yescharacteristic, complemented
54#63978C2218yescomplemented
55#63974C2218yescomplemented
56#63971C2218yescomplemented
57D3×#217C2218yescomplemented
58C2×#3724C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60C2×Dic3⋊Dic3C2211yescharacteristic, complemented
61#63964C2218yescomplemented
62C2×#3722C2211yescharacteristic, complemented
63C2×#3722C2211yescharacteristic, complemented
64C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
65C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
66#63958C2218yescomplemented
67#63890C2218yescomplemented
68#63880C2218yescomplemented
69#63854C2218yescomplemented
70#63852C2218yescomplemented
71C23×#67—31no—
72C22×#237—31no—
73C22×#235—31no—
74C23×D12—31no—
75C2×C3×#120—31no—
76C2×C3×C4×D4—31no—
77C22×#217—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#938—31no—
81C2×#937—31no—
82C2×#937—31no—
83C2×#937—61no—
84C2×#937D311yescharacteristic, complemented
85C2×D4×Dic3D311yescharacteristic, complemented
86C2×#930—31no—
87C2×#924—31no—
88#5591—316no—
89#5550—316no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#886—31no—
93C2×#885—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#883—31no—
97C2×#67⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×#878—31no—
102C2×#875—31no—
103C2×C4×D12—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3—24no—
107C23×C3⋊D3—24no—
108C23×C3⋊D3—42no—
109C23×C3⋊D3C2311yescharacteristic
110C23×C3⋊D3C2314yes—
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3—24no—
113C23×C3×D3—24no—
114C23×C3×D3—42no—
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2314yes—
117C23×C3×D3C2311yescharacteristic
118C2×C32×D4—24no—
119C2×C32×D4C2314yes—
120C22×C32×C4C2311yescharacteristic
121C2×#638—24no—
122C2×#638—42no—
123C2×#638C2314yescomplemented
124C2×#638C2314yescomplemented
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C2×C3×#67—24no—
128C2×C3×#67—42no—
129C2×C3×#67C2314yescomplemented
130C2×C3×#67C2314yescomplemented
131C22×C3×Dic3—24no—
132C22×C3×Dic3—24no—
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2314yes—
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2314yescomplemented
141C2×#627—24no—
142C2×#627C2314yescomplemented
143C2×#626—24no—
144C2×#626—24no—
145C2×#626—24no—
146C2×#626—232no—
147C2×#626D418yescomplemented
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#624—24no—
153C2×#624—42no—
154C2×#624C2314yescomplemented
155C2×#624C2314yescomplemented
156#3804—232no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3—42no—
159C2×D3×Dic3C2314yescomplemented
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yes—
162#3752C2314yescomplemented
163#3752C2314yescomplemented
164C3×#217C2314yes—
165C3×#217C2314yes—
166C3×#217C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×C4⋊Dic3C2314yescomplemented
170C3×C4×Dic3C2314yescomplemented
171#3724C2314yescomplemented
172Dic3⋊Dic3C2314yescomplemented
173Dic3⋊Dic3C2314yescomplemented
174#3722C2314yescomplemented
175#3722C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—61no—
183C24×D3C2×D311yescharacteristic
184C22×C3×D4—21no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4C2×D311yescharacteristic
188C22×C3×D4C2×D311yescharacteristic
189C23×C3×C4—31no—
190C23×C3×C4—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—38no—
200C22×#67—61no—
201C22×#67—61no—
202C22×#67—68no—
203C22×#67C2×D311yescharacteristic, complemented
204C22×#67C2×D311yescharacteristic, complemented
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3C2×D311yescharacteristic
208C23×Dic3C2×D311yescharacteristic, complemented
209C2×#237—38no—
210C2×#237—68no—
211C2×#235—38no—
212C2×#235—68no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—38no—
218C22×D12—68no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×#120—38no—
228C3×C4×D4—38no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C42—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—38no—
241C2×#217—61no—
242C2×#217C2×D311yescharacteristic
243C2×#217C2×D311yescharacteristic
244C2×#217C2×D311yescharacteristic, complemented
245#939—38no—
246#939—38no—
247#938—38no—
248#937—38no—
249#937—38no—
250#937—68no—
251#937C2×D318yescomplemented
252D4×Dic3C2×D318yescomplemented
253#930—38no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—61no—
265C2×(C2×D3)⋊C4—61no—
266C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
267C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
268C2×C4⋊Dic3—31no—
269C2×C4⋊Dic3—31no—
270C2×C4⋊Dic3C2×D311yescharacteristic, complemented
271#924—38no—
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×C4×Dic3C2×D311yescharacteristic, complemented
277#894—38no—
278#894—38no—
279#886—38no—
280#885—38no—
281#884—38no—
282#884—38no—
283#883—38no—
284#67⋊C4—38no—
285D3×C22⋊C4—38no—
286D3×C22⋊C4—38no—
287D3×C22⋊C4—38no—
288#878—38no—
289#875—38no—
290C4×D12—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32#4114yescomplemented
297C23×C32C2412yes—
298C23×C32C2412yes—
299C23×C32C2411yescharacteristic
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—22no—
304C22×C3⋊D3—22no—
305C22×C3⋊D3—28no—
306C22×C3⋊D3—28no—
307C22×C3⋊D3—44no—
308C22×C3⋊D3—416no—
309C22×C3⋊D3C2×D414yes—
310C22×C3⋊D3C2412yes—
311C22×C3⋊D3C2412yes—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3—28no—
317C22×C3×D3—22no—
318C22×C3×D3—28no—
319C22×C3×D3—44no—
320C22×C3×D3—416no—
321C22×C3×D3C2×D414yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324C32×D4—28no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327#638—28no—
328#638—44no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3C2412yes—
332C2×C3⋊Dic3C2412yes—
333C3×#67—28no—
334C3×#67—44no—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—22no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—28no—
341C2×C3×Dic3—28no—
342C2×C3×Dic3C2×D414yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349#627—28no—
350#626—28no—
351#626—28no—
352#626—28no—
353#626C2×D4116yescomplemented
354#624—28no—
355#624—44no—
356D3×Dic3—28no—
357D3×Dic3—44no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—31no—
369C2×#120—91no—
370C2×C4×D4—31no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—21no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—34no—
379C24×C3—64no—
380C24×C3—64no—
381C24×C3—122no—
382C24×C3C22×D311yescharacteristic
383C24×C3C22×D311yescharacteristic
384C24×C3C22×D311yescharacteristic
385C24×C3C22×D311yescharacteristic
386C23×D3—24no—
387C23×D3—24no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—31no—
391C23×D3—31no—
392C23×D3—34no—
393C23×D3—34no—
394C23×D3—42no—
395C23×D3—61no—
396C23×D3—61no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—64no—
402C23×D3—124no—
403C23×D3—124no—
404C23×D3—122no—
405C23×D3—122no—
406C23×D3—124no—
407C23×D3C22×D311yescharacteristic
408C23×D3C22×D314yes—
409C23×D3C22×D311yescharacteristic
410C2×C3×D4—24no—
411C2×C3×D4—24no—
412C2×C3×D4—24no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—44no—
416C2×C3×D4—64no—
417C2×C3×D4—122no—
418C2×C3×D4C22×D314yes—
419C2×C3×D4C22×D314yes—
420C22×C3×C4—21no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—34no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—34no—
429C22×C3×C4—64no—
430C22×C3×C4—64no—
431C22×C3×C4C22×D311yescharacteristic
432C22×C3×C4C22×D311yescharacteristic
433C2×#67—24no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—38no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—34no—
443C2×#67—42no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—632no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—64no—
452C2×#67—124no—
453C2×#67—122no—
454C2×#67—122no—
455C2×#67—124no—
456C2×#67C22×D314yescomplemented
457C2×#67C22×D314yescomplemented
458C22×Dic3—24no—
459C22×Dic3—24no—
460C22×Dic3—31no—
461C22×Dic3—31no—
462C22×Dic3—31no—
463C22×Dic3—31no—
464C22×Dic3—34no—
465C22×Dic3—34no—
466C22×Dic3—61no—
467C22×Dic3—61no—
468C22×Dic3—64no—
469C22×Dic3—122no—
470C22×Dic3C22×D314yes—
471C22×Dic3C22×D311yescharacteristic
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D314yescomplemented
478#237—632no—
479#235—632no—
480C2×D12—38no—
481C2×D12—34no—
482C2×D12—34no—
483C2×D12—34no—
484C2×D12—34no—
485C2×D12—632no—
486C2×D12—64no—
487C2×D12—64no—
488C2×D12—64no—
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—34no—
494C2×C4×D3—34no—
495C2×C4×D3—64no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3—122no—
499C2×C4×D3—122no—
500C2×C4×D3—122no—
501C2×Dic6—34no—
502C2×Dic6—34no—
503C2×Dic6—64no—
504C2×Dic6—64no—
505C3×C4⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C42—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—64no—
517#217C22×D314yes—
518#217C22×D314yes—
519#217C22×D314yescomplemented
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—64no—
531(C2×D3)⋊C4—64no—
532(C2×D3)⋊C4C22×D314yescomplemented
533(C2×D3)⋊C4C22×D314yescomplemented
534C4⋊Dic3—34no—
535C4⋊Dic3—34no—
536C4⋊Dic3C22×D314yescomplemented
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4—34no—
540Dic3⋊C4—34no—
541C4×Dic3C22×D314yescomplemented
542C22×C32—28no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32—44no—
549C22×C32C22×D412yes—
550C22×C32C2×#4112yes—
551C22×C32C2×#4114yescomplemented
552C22×C32H(5,𝔽2)12yes—
553C22×C32C2511yescharacteristic
554C2×C3⋊D3—22no—
555C2×C3⋊D3—28no—
556C2×C3⋊D3—22no—
557C2×C3⋊D3—22no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—22no—
560C2×C3⋊D3—416no—
561C2×C3⋊D3—44no—
562C2×C3⋊D3C22×D414yes—
563C2×C3×D3—28no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—416no—
570C2×C3×D3—44no—
571C2×C3×D3C22×D414yes—
572C32×C4—22no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3C22×D414yes—
581C25—31no—
582C25—91no—
583C2×#41—98no—
584C2×#41—188no—
585C22×Q8—91no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—98no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—188no—
596C22×D4D3211yescharacteristic
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—91no—
600C23×C4—91no—
601C23×C4—91no—
602C23×C4—91no—
603#124—98no—
604#123—98no—
605#123—98no—
606C22⋊Q8—98no—
607#121—98no—
608#121—98no—
609#121—98no—
610#120—38no—
611#120—98no—
612C4×D4—38no—
613C4×D4—98no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—91no—
616C2×C4⋊C4—91no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—98no—
624C2×C22⋊C4—98no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—91no—
631C2×C22⋊C4—91no—
632C2×C42—31no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—22no—
644C23×C3—22no—
645C23×C3—21no—
646C23×C3—24no—
647C23×C3—34no—
648C23×C3—32no—
649C23×C3—32no—
650C23×C3—42no—
651C23×C3—42no—
652C23×C3—42no—
653C23×C3—42no—
654C23×C3—42no—
655C23×C3—68no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—68no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3—124no—
663C23×C3—1216no—
664C23×C3#23514yescomplemented
665C23×C3#23714yescomplemented
666C23×C3C23×D312yes—
667C23×C3C23×D312yes—
668C23×C3C23×D312yes—
669C23×C3C23×D312yes—
670C23×C3C23×D311yescharacteristic
671C23×C3C23×D311yescharacteristic
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—22no—
675C22×D3—22no—
676C22×D3—28no—
677C22×D3—22no—
678C22×D3—28no—
679C22×D3—34no—
680C22×D3—34no—
681C22×D3—32no—
682C22×D3—32no—
683C22×D3—32no—
684C22×D3—32no—
685C22×D3—44no—
686C22×D3—416no—
687C22×D3—64no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—68no—
691C22×D3—68no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—64no—
697C22×D3—62no—
698C22×D3—68no—
699C22×D3—62no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—68no—
703C22×D3—62no—
704C22×D3—62no—
705C22×D3—128no—
706C22×D3—122no—
707C22×D3—122no—
708C22×D3—122no—
709C22×D3—122no—
710C22×D3—128no—
711C22×D3—124no—
712C22×D3—124no—
713C22×D3—1216no—
714C22×D3—1216no—
715C22×D3—128no—
716C22×D3—1232no—
717C22×D3D3×D414yes—
718C22×D3C23×D312yes—
719C22×D3C23×D312yes—
720C3×D4—28no—
721C3×D4—28no—
722C3×D4—48no—
723C3×D4—68no—
724C3×D4—124no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—22no—
728C2×C3×C4—34no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—32no—
732C2×C3×C4—32no—
733C2×C3×C4—32no—
734C2×C3×C4—32no—
735C2×C3×C4—42no—
736C2×C3×C4—68no—
737C2×C3×C4—68no—
738C2×C3×C4—62no—
739C2×C3×C4—62no—
740C2×C3×C4—62no—
741C2×C3×C4—62no—
742C2×C3×C4—62no—
743C2×C3×C4C23×D312yes—
744C2×C3×C4C23×D312yes—
745#67—28no—
746#67—316no—
747#67—44no—
748#67—68no—
749#67—68no—
750#67—68no—
751#67—68no—
752#67—68no—
753#67—128no—
754#67—124no—
755#67—124no—
756#67—128no—
757C2×Dic3—22no—
758C2×Dic3—22no—
759C2×Dic3—22no—
760C2×Dic3—22no—
761C2×Dic3—22no—
762C2×Dic3—28no—
763C2×Dic3—28no—
764C2×Dic3—32no—
765C2×Dic3—32no—
766C2×Dic3—32no—
767C2×Dic3—32no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—68no—
771C2×Dic3—62no—
772C2×Dic3—62no—
773C2×Dic3—62no—
774C2×Dic3—62no—
775C2×Dic3—122no—
776C2×Dic3—122no—
777C2×Dic3—124no—
778C2×Dic3D3×D414yes—
779C2×Dic3C23×D312yes—
780C2×Dic3C23×D312yes—
781C2×Dic3C23×D312yes—
782C2×Dic3C23×D312yes—
783C2×Dic3C23×D312yes—
784C2×Dic3C23×D312yes—
785D12—316no—
786D12—68no—
787D12—68no—
788D12—68no—
789C4×D3—68no—
790C4×D3—68no—
791C4×D3—68no—
792C4×D3—124no—
793C4×D3—124no—
794C4×D3—124no—
795Dic6—68no—
796Dic6—68no—
797C2×C32—24no—
798C2×C32—42no—
799C2×C32#54614yescomplemented
800C2×C32C23×D411yescharacteristic
801C2×C32C22×#4111yescharacteristic
802C2×C32C2×H(5,𝔽2)11yescharacteristic
803C3⋊D3—24no—
804C3⋊D3—42no—
805C3×D3—24no—
806C3×D3—42no—
807C24—31no—
808C24—31no—
809C24—34no—
810C24—64no—
811C24—64no—
812C24—91no—
813C24—91no—
814C24—94no—
815C24—122no—
816C24—184no—
817C24—184no—
818C24—362no—
819C24C2×D3211yescharacteristic
820C24C2×D3211yescharacteristic
821#41—1832no—
822C2×Q8—94no—
823C2×Q8—184no—
824C2×D4—24no—
825C2×D4—34no—
826C2×D4—34no—
827C2×D4—64no—
828C2×D4—94no—
829C2×D4—98no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—94no—
833C2×D4—94no—
834C2×D4—94no—
835C2×D4—122no—
836C2×D4—184no—
837C2×D4—1832no—
838C2×D4—184no—
839C2×D4—184no—
840C2×D4—184no—
841C2×D4—362no—
842C2×D4C2×D3214yes—
843C22×C4—31no—
844C22×C4—34no—
845C22×C4—34no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—31no—
850C22×C4—31no—
851C22×C4—64no—
852C22×C4—64no—
853C22×C4—94no—
854C22×C4—94no—
855C22×C4—94no—
856C22×C4—94no—
857C22×C4—91no—
858C22×C4—91no—
859C22×C4—184no—
860C22×C4—184no—
861C22×C4—362no—
862C22×C4—362no—
863C22×C4C2×D3211yescharacteristic
864C4⋊C4—34no—
865C4⋊C4—94no—
866C4⋊C4—94no—
867C4⋊C4—94no—
868C22⋊C4—34no—
869C22⋊C4—34no—
870C22⋊C4—34no—
871C22⋊C4—34no—
872C22⋊C4—34no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C22⋊C4—94no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4—94no—
880C42—34no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—28no—
886C22×C3—28no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—22no—
890C22×C3—22no—
891C22×C3—22no—
892C22×C3—22no—
893C22×C3—22no—
894C22×C3—22no—
895C22×C3—22no—
896C22×C3—24no—
897C22×C3—21no—
898C22×C3—34no—
899C22×C3—48no—
900C22×C3—42no—
901C22×C3—42no—
902C22×C3—42no—
903C22×C3—42no—
904C22×C3—42no—
905C22×C3—44no—
906C22×C3—44no—
907C22×C3—62no—
908C22×C3—62no—
909C22×C3—68no—
910C22×C3—62no—
911C22×C3—62no—
912C22×C3—62no—
913C22×C3—84no—
914C22×C3—1216no—
915C22×C3—124no—
916C22×C3C2×#23512yes—
917C22×C3C2×#23514yescomplemented
918C22×C3C2×D3×D412yes—
919C22×C3C2×D3×D412yes—
920C22×C3C2×#23712yes—
921C22×C3C2×#23714yescomplemented
922C22×C3#100412yes—
923C22×C3#100912yes—
924C22×C3C24×D311yescharacteristic
925C22×C3C24×D311yescharacteristic
926C2×D3—22no—
927C2×D3—22no—
928C2×D3—28no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—22no—
932C2×D3—34no—
933C2×D3—34no—
934C2×D3—416no—
935C2×D3—44no—
936C2×D3—64no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—68no—
942C2×D3—68no—
943C2×D3—64no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—62no—
948C2×D3—62no—
949C2×D3—62no—
950C2×D3—128no—
951C2×D3—122no—
952C2×D3—122no—
953C2×D3—122no—
954C2×D3—122no—
955C2×D3—1216no—
956C2×D3—1216no—
957C2×D3—128no—
958C2×D3—1232no—
959C2×D3—124no—
960C2×D3—124no—
961C2×D3C2×D3×D414yes—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—34no—
965C3×C4—42no—
966C3×C4—62no—
967C3×C4—62no—
968C3×C4—62no—
969C3×C4—62no—
970C3×C4—62no—
971Dic3—22no—
972Dic3—22no—
973Dic3—22no—
974Dic3—22no—
975Dic3—22no—
976Dic3—62no—
977Dic3—62no—
978Dic3—62no—
979Dic3—62no—
980Dic3—122no—
981Dic3—122no—
982Dic3C2×D3×D414yes—
983C32C2×#54611yescharacteristic, complemented, Sylow
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—34no—
990C23—32no—
991C23—32no—
992C23—68no—
993C23—62no—
994C23—62no—
995C23—62no—
996C23—62no—
997C23—62no—
998C23—68no—
999C23—94no—
1000C23—92no—
1001C23—92no—
1002C23—124no—
1003C23—1216no—
1004C23—188no—
1005C23—182no—
1006C23—182no—
1007C23—182no—
1008C23—182no—
1009C23—182no—
1010C23—188no—
1011C23—364no—
1012C23—3616no—
1013C23#380414yescomplemented
1014C23C22×D3212yes—
1015C23C22×D3212yes—
1016C23C22×D3211yescharacteristic
1017Q8—188no—
1018D4—28no—
1019D4—68no—
1020D4—916no—
1021D4—124no—
1022D4—188no—
1023D4—188no—
1024D4—188no—
1025D4—188no—
1026D4—364no—
1027C2×C4—22no—
1028C2×C4—34no—
1029C2×C4—32no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—68no—
1036C2×C4—68no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—92no—
1043C2×C4—92no—
1044C2×C4—188no—
1045C2×C4—188no—
1046C2×C4—182no—
1047C2×C4—182no—
1048C2×C4—364no—
1049C2×C4—364no—
1050C2×C4C22×D3212yes—
1051C2×C3—24no—
1052C2×C3—24no—
1053C2×C3—24no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—44no—
1058C2×C3—42no—
1059C2×C3—42no—
1060C2×C3—64no—
1061C2×C3—82no—
1062C2×C3—122no—
1063C2×C3#555014yescomplemented
1064C2×C3#559114yescomplemented
1065C2×C3C22×#23511yescharacteristic
1066C2×C3C22×D3×D411yescharacteristic
1067C2×C3C22×D3×D411yescharacteristic
1068C2×C3C22×#23711yescharacteristic
1069C2×C3C2×#100411yescharacteristic
1070C2×C3C2×#100911yescharacteristic
1071D3—24no—
1072D3—42no—
1073D3—64no—
1074D3—64no—
1075D3—124no—
1076D3—124no—
1077D3—122no—
1078D3—122no—
1079C22—28no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—34no—
1086C22—44no—
1087C22—68no—
1088C22—62no—
1089C22—62no—
1090C22—62no—
1091C22—62no—
1092C22—62no—
1093C22—94no—
1094C22—1216no—
1095C22—124no—
1096C22—188no—
1097C22—182no—
1098C22—182no—
1099C22—182no—
1100C22—182no—
1101C22—182no—
1102C22—3616no—
1103C22—364no—
1104C22D32×D412yes—
1105C22#6431412yes—
1106C22C2×#380412yes—
1107C22C2×#380414yescomplemented
1108C22C23×D3211yescharacteristic
1109C4—22no—
1110C4—34no—
1111C4—62no—
1112C4—62no—
1113C4—62no—
1114C4—62no—
1115C4—62no—
1116C4—182no—
1117C4—182no—
1118C3—21no—
1119C3C2×#555011yescharacteristic, complemented
1120C3C2×#559111yescharacteristic, complemented
1121C2—24no—
1122C2—42no—
1123C2—64no—
1124C2—122no—
1125C2—184no—
1126C2—362no—
1127C2#1059513514yesdirect product factor
1128C2C2×D32×D411yescharacteristic
1129C2C2×#6431411yescharacteristic
1130C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×#626C2semidirect
2. C22×#3804C2semidirect
3. C2×#64146C2semidirect
4. C2×C3×#937C2semidirect
5. C2×C3×D4×Dic3C2semidirect
6. C2×#63978C2semidirect
7. C2×#63974C2semidirect
8. C2×#63971C2semidirect
9. C2×D3×#217C2semidirect
10. C2×#63964C2semidirect
11. C2×#63958C2semidirect
12. #10595135C2direct (N × H)
13. C2×#63890C2semidirect
14. C2×#63880C2semidirect
15. C2×#63854C2semidirect
16. C2×#63852C2semidirect
22. C22×#638C22semidirect
23. C22×#638C22semidirect
24. C22×C3×#67C22semidirect
25. C22×C3×#67C22semidirect
27. C23×C3×Dic3C22semidirect
28. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#624C22semidirect
36. C22×#624C22semidirect
38. C2×#3804C22semidirect
39. C22×D3×Dic3C22semidirect
40. C22×D3×Dic3C22semidirect
42. #64146C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
47. C2×C3×#217C22semidirect
48. C3×#937C22semidirect
49. C3×D4×Dic3C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×C4⋊Dic3C22semidirect
53. C2×C3×C4×Dic3C22semidirect
54. #63978C22semidirect
55. #63974C22semidirect
56. #63971C22semidirect
57. D3×#217C22semidirect
58. C2×#3724C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. C2×Dic3⋊Dic3C22semidirect
61. #63964C22semidirect
62. C2×#3722C22semidirect
63. C2×#3722C22semidirect
64. C2×(C2×D3)⋊Dic3C22semidirect
65. C2×(C2×D3)⋊Dic3C22semidirect
66. #63958C22semidirect
67. #63890C22semidirect
68. #63880C22semidirect
69. #63854C22semidirect
70. #63852C22semidirect
84. C2×#937D3semidirect
85. C2×D4×Dic3D3semidirect
123. C2×#638C23semidirect
124. C2×#638C23semidirect
129. C2×C3×#67C23semidirect
130. C2×C3×#67C23semidirect
140. C22×C3×Dic3C23semidirect
142. C2×#627C23semidirect
147. C2×#626D4semidirect
154. C2×#624C23semidirect
155. C2×#624C23semidirect
159. C2×D3×Dic3C23semidirect
160. C2×D3×Dic3C23semidirect
162. #3752C23semidirect
163. #3752C23semidirect
166. C3×#217C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×C4⋊Dic3C23semidirect
170. C3×C4×Dic3C23semidirect
171. #3724C23semidirect
172. Dic3⋊Dic3C23semidirect
173. Dic3⋊Dic3C23semidirect
174. #3722C23semidirect
175. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
203. C22×#67C2×D3semidirect
204. C22×#67C2×D3semidirect
208. C23×Dic3C2×D3semidirect
244. C2×#217C2×D3semidirect
251. #937C2×D3semidirect
252. D4×Dic3C2×D3semidirect
266. C2×(C2×D3)⋊C4C2×D3semidirect
267. C2×(C2×D3)⋊C4C2×D3semidirect
270. C2×C4⋊Dic3C2×D3semidirect
276. C2×C4×Dic3C2×D3semidirect
296. C23×C32#41semidirect
353. #626C2×D4semidirect
456. C2×#67C22×D3semidirect
457. C2×#67C22×D3semidirect
477. C22×Dic3C22×D3semidirect
519. #217C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
536. C4⋊Dic3C22×D3semidirect
541. C4×Dic3C22×D3semidirect
551. C22×C32C2×#41semidirect
664. C23×C3#235semidirect
665. C23×C3#237semidirect
799. C2×C32#546semidirect
917. C22×C3C2×#235semidirect
921. C22×C3C2×#237semidirect
983. C32C2×#546semidirect
1013. C23#3804semidirect
1063. C2×C3#5550semidirect
1064. C2×C3#5591semidirect
1107. C22C2×#3804semidirect
1119. C3C2×#5550semidirect
1120. C3C2×#5591semidirect
1127. C2#10595135direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6262
C22×#38042
C2×#641462
C2×C3×#9372
C2×C3×D4×Dic32
C2×#639782
C2×#639742
C2×#639712
C2×D3×#2172
C2×#639642
C2×#639582
#105951352
C2×#638902
C2×#638802
C2×#638542
C2×#638522
C2×#55913
C2×#55503