Finite Group Databasebeta

← C2×#10595138 #11900442

Subgroups — C2×#10595138 #11900442

Order 1152.

4091 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#624C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63975C211yesmaximal, characteristic, complemented
8C2×Dic3×#67C211yesmaximal, characteristic, complemented
9C2×#63964C211yesmaximal, characteristic, complemented
10C2×#63958C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595138C2116yesmaximal, direct product factor
13C2×#63895C211yesmaximal, characteristic, complemented
14C2×#63880C211yesmaximal, characteristic, complemented
15C2×#63854C211yesmaximal, characteristic, complemented
16C2×#63836C211yesmaximal, characteristic, complemented
17C2×#5606—31nomaximal
18C2×#5547—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C23×C3×Dic3C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic, complemented
28C22×#627C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#624—28no—
32C22×#624C2211yescharacteristic
33C22×#624C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C22×#624C2211yescharacteristic
36C22×#624C2218yescomplemented
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C2×#3757C2211yescharacteristic
41#64146C2218yescomplemented
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×C3×#217C2211yescharacteristic
45C2×C3×#217C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C3×#939C2218yescomplemented
48C3×D4×Dic3C2218yescomplemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C2×C3×C4×Dic3C2211yescharacteristic, complemented
53#63981C2218yescomplemented
54#63975C2218yescomplemented
55Dic3×#67C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60#63964C2218yescomplemented
61C2×#3722C2211yescharacteristic
62C2×#3722C2211yescharacteristic
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63958C2218yescomplemented
65C2×Dic32C2211yescharacteristic, complemented
66#63952C2218yescomplemented
67#63895C2218yescomplemented
68#63880C2218yescomplemented
69#63854C2218yescomplemented
70#63836C2218yescomplemented
71C22×#237—31no—
72C22×#235—31no—
73C23×C4×D3—31no—
74C23×C4×D3—31no—
75C2×C3×#121—31no—
76C2×C3×C4×D4—31no—
77C2×#939D311yescharacteristic, complemented
78C2×#938—31no—
79C2×#937—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#937—61no—
83C2×D4×Dic3—31no—
84C2×D4×Dic3D311yescharacteristic, complemented
85C2×C4×#67—31no—
86C2×C4×#67—31no—
87C2×#924—31no—
88#5606—316no—
89#5547—316no—
90C2×#897—31no—
91C2×#896—31no—
92C2×#894—31no—
93C2×#892—31no—
94C2×#884—31no—
95C2×#883—31no—
96C2×#883—31no—
97C2×#883—31no—
98C2×#882—31no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4—31no—
101C2×#878—31no—
102C2×C4×D12—31no—
103C2×#872—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3—24no—
107C23×C3⋊D3—24no—
108C23×C3⋊D3—24no—
109C23×C3⋊D3C2314yes—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C2×C32×D4—24no—
114C2×C32×D4C2314yes—
115C22×C32×C4C2311yescharacteristic
116C2×#638—24no—
117C2×#638—24no—
118C2×#638C2314yes—
119C2×#638C2314yes—
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C2×C3×#67—24no—
123C2×C3×#67—24no—
124C2×C3×#67C2314yes—
125C2×C3×#67C2314yescomplemented
126C22×C3×Dic3—24no—
127C22×C3×Dic3—24no—
128C22×C3×Dic3—24no—
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2314yes—
135C22×C3×Dic3C2314yes—
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2314yescomplemented
139C2×#627—24no—
140C2×#627C2314yescomplemented
141C2×#626—24no—
142C2×#626—24no—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#624—24no—
146C2×#624—24no—
147C2×#624—24no—
148C2×#624—232no—
149C2×#624D418yescomplemented
150C2×#624C2314yes—
151C2×#624C2314yes—
152C2×#624C2314yes—
153C2×#624C2314yes—
154#3804—232no—
155C2×D3×Dic3—24no—
156C2×D3×Dic3C2314yescomplemented
157#3757C2314yes—
158#3752C2314yes—
159#3752C2314yes—
160C3×#217C2314yes—
161C3×#217C2314yescomplemented
162C3×#217C2314yescomplemented
163C3×(C2×D3)⋊C4C2314yescomplemented
164C3×C4⋊Dic3C2314yescomplemented
165C3×Dic3⋊C4C2314yescomplemented
166C3×C4×Dic3C2314yescomplemented
167#3724C2314yescomplemented
168Dic3⋊Dic3C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171#3722C2314yes—
172#3722C2314yes—
173(C2×D3)⋊Dic3C2314yescomplemented
174Dic32C2314yescomplemented
175C2×#525—91noSylow
176C24×D3—31no—
177C24×D3—31no—
178C24×D3—61no—
179C22×C3×D4—21no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4C2×D311yescharacteristic
183C22×C3×D4C2×D311yescharacteristic
184C23×C3×C4—31no—
185C23×C3×C4—31no—
186C23×C3×C4—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—61no—
194C22×#67—61no—
195C22×#67C2×D311yescharacteristic
196C22×#67C2×D311yescharacteristic, complemented
197C23×Dic3—31no—
198C23×Dic3C2×D311yescharacteristic
199C23×Dic3C2×D311yescharacteristic
200C23×Dic3C2×D311yescharacteristic, complemented
201C2×#237—38no—
202C2×#237—68no—
203C2×#235—38no—
204C2×#235—68no—
205C22×D12—31no—
206C22×D12—31no—
207C22×C4×D3—31no—
208C22×C4×D3—31no—
209C22×C4×D3—31no—
210C22×C4×D3—31no—
211C22×C4×D3—31no—
212C22×C4×D3—31no—
213C22×C4×D3—31no—
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—38no—
217C22×C4×D3—38no—
218C22×C4×D3—68no—
219C22×C4×D3—68no—
220C22×Dic6—31no—
221C22×Dic6—31no—
222C3×#121—38no—
223C3×C4×D4—38no—
224C2×C3×C4⋊C4—31no—
225C2×C3×C4⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C42—31no—
231C2×#217—31no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—61no—
235C2×#217C2×D311yescharacteristic
236C2×#217C2×D311yescharacteristic, complemented
237C2×#217C2×D311yescharacteristic, complemented
238#939C2×D318yescomplemented
239#938—38no—
240#937—38no—
241#937—38no—
242#937—38no—
243#937—68no—
244D4×Dic3—38no—
245D4×Dic3C2×D318yescomplemented
246C4×#67—38no—
247C4×#67—38no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—61no—
258C2×(C2×D3)⋊C4—61no—
259C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
260C2×C4⋊Dic3—31no—
261C2×C4⋊Dic3—31no—
262C2×C4⋊Dic3—31no—
263C2×C4⋊Dic3C2×D311yescharacteristic, complemented
264#924—38no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4C2×D311yescharacteristic, complemented
271C2×C4×Dic3—31no—
272C2×C4×Dic3—31no—
273C2×C4×Dic3C2×D311yescharacteristic, complemented
274#897—38no—
275#896—38no—
276#894—38no—
277#892—38no—
278#884—38no—
279#883—38no—
280#883—38no—
281#883—38no—
282#882—38no—
283#67⋊C4—38no—
284#67⋊C4—38no—
285#878—38no—
286C4×D12—38no—
287#872—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32#4114yescomplemented
294C23×C32C2412yes—
295C23×C32C2412yes—
296C23×C32C2411yescharacteristic
297C22×C3⋊D3—232no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—28no—
303C22×C3⋊D3—28no—
304C22×C3⋊D3—28no—
305C22×C3⋊D3C2×D414yes—
306C22×C3⋊D3#4114yescomplemented
307C22×C3⋊D3C2412yes—
308C22×C3⋊D3C2412yes—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3C2412yes—
313C32×D4—28no—
314C2×C32×C4—22no—
315C2×C32×C4C2412yes—
316#638—28no—
317#638—28no—
318C2×C3⋊Dic3—22no—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3C2412yes—
321C2×C3⋊Dic3C2412yes—
322C3×#67—28no—
323C3×#67—28no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—28no—
330C2×C3×Dic3—28no—
331C2×C3×Dic3—28no—
332C2×C3×Dic3C2×D414yes—
333C2×C3×Dic3C2×D414yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C2×C3×Dic3C2412yes—
340C2×C3×Dic3C2412yes—
341#627—28no—
342#626—28no—
343#626—28no—
344#624—28no—
345#624—28no—
346#624—28no—
347#624C2×D4116yescomplemented
348D3×Dic3—28no—
349C22×#41—91no—
350C24×C4—91no—
351#525—916no—
352C2×#123—91no—
353C2×#123—91no—
354C2×C22⋊Q8—91no—
355C2×C22⋊Q8—91no—
356C2×#121—31no—
357C2×#121—91no—
358C2×#120—91no—
359C2×#120—91no—
360C2×C4×D4—31no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C2×C4×D4—91no—
364C2×#117—91no—
365C24×C3—21no—
366C24×C3—21no—
367C24×C3—31no—
368C24×C3C22×D311yescharacteristic
369C24×C3C22×D311yescharacteristic
370C24×C3C22×D311yescharacteristic
371C24×C3C22×D311yescharacteristic
372C23×D3—31no—
373C23×D3—31no—
374C23×D3—31no—
375C23×D3—31no—
376C23×D3—34no—
377C23×D3—34no—
378C23×D3—61no—
379C23×D3—61no—
380C23×D3—64no—
381C23×D3—64no—
382C23×D3—64no—
383C23×D3—64no—
384C23×D3—64no—
385C23×D3—64no—
386C23×D3—64no—
387C23×D3—124no—
388C23×D3—124no—
389C23×D3—124no—
390C23×D3C22×D311yescharacteristic
391C2×C3×D4—24no—
392C2×C3×D4—24no—
393C2×C3×D4—24no—
394C2×C3×D4—34no—
395C2×C3×D4—34no—
396C2×C3×D4—44no—
397C2×C3×D4—64no—
398C2×C3×D4—64no—
399C2×C3×D4C22×D314yes—
400C2×C3×D4C22×D314yes—
401C22×C3×C4—21no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—31no—
405C22×C3×C4—31no—
406C22×C3×C4—31no—
407C22×C3×C4—31no—
408C22×C3×C4—31no—
409C22×C3×C4—34no—
410C22×C3×C4—34no—
411C22×C3×C4—34no—
412C22×C3×C4—64no—
413C22×C3×C4—64no—
414C22×C3×C4—64no—
415C22×C3×C4C22×D311yescharacteristic
416C22×C3×C4C22×D311yescharacteristic
417C2×#67—24no—
418C2×#67—24no—
419C2×#67—34no—
420C2×#67—34no—
421C2×#67—34no—
422C2×#67—34no—
423C2×#67—34no—
424C2×#67—34no—
425C2×#67—64no—
426C2×#67—64no—
427C2×#67—64no—
428C2×#67—64no—
429C2×#67—64no—
430C2×#67—64no—
431C2×#67—64no—
432C2×#67—64no—
433C2×#67—124no—
434C2×#67—124no—
435C2×#67C22×D314yes—
436C2×#67C22×D314yescomplemented
437C22×Dic3—24no—
438C22×Dic3—24no—
439C22×Dic3—24no—
440C22×Dic3—31no—
441C22×Dic3—31no—
442C22×Dic3—31no—
443C22×Dic3—31no—
444C22×Dic3—34no—
445C22×Dic3—61no—
446C22×Dic3—61no—
447C22×Dic3—64no—
448C22×Dic3C22×D314yes—
449C22×Dic3C22×D311yescharacteristic
450C22×Dic3C22×D311yescharacteristic
451C22×Dic3C22×D311yescharacteristic
452C22×Dic3C22×D311yescharacteristic
453C22×Dic3C22×D311yescharacteristic
454C22×Dic3C22×D314yes—
455C22×Dic3C22×D311yescharacteristic
456C22×Dic3C22×D311yescharacteristic
457C22×Dic3C22×D314yescomplemented
458#237—632no—
459#235—632no—
460C2×D12—34no—
461C2×D12—34no—
462C2×D12—64no—
463C2×D12—64no—
464C2×C4×D3—38no—
465C2×C4×D3—38no—
466C2×C4×D3—34no—
467C2×C4×D3—34no—
468C2×C4×D3—34no—
469C2×C4×D3—34no—
470C2×C4×D3—34no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—632no—
476C2×C4×D3—632no—
477C2×C4×D3—64no—
478C2×C4×D3—64no—
479C2×C4×D3—64no—
480C2×C4×D3—64no—
481C2×C4×D3—64no—
482C2×C4×D3—64no—
483C2×C4×D3—64no—
484C2×Dic6—34no—
485C2×Dic6—34no—
486C2×Dic6—64no—
487C2×Dic6—64no—
488C3×C4⋊C4—34no—
489C3×C4⋊C4—34no—
490C3×C22⋊C4—34no—
491C3×C22⋊C4—34no—
492C3×C22⋊C4—34no—
493C3×C22⋊C4—34no—
494C3×C42—34no—
495#217—34no—
496#217—34no—
497#217—34no—
498#217—64no—
499#217C22×D314yes—
500#217C22×D314yescomplemented
501#217C22×D314yescomplemented
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—34no—
508(C2×D3)⋊C4—34no—
509(C2×D3)⋊C4—34no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—64no—
512(C2×D3)⋊C4—64no—
513(C2×D3)⋊C4C22×D314yescomplemented
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—34no—
517C4⋊Dic3C22×D314yescomplemented
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4C22×D314yescomplemented
524C4×Dic3—34no—
525C4×Dic3—34no—
526C4×Dic3C22×D314yescomplemented
527C22×C32—28no—
528C22×C32—22no—
529C22×C32—22no—
530C22×C32—22no—
531C22×C32—22no—
532C22×C32—22no—
533C22×C32—44no—
534C22×C32C22×D412yes—
535C22×C32C2×#4112yes—
536C22×C32C2×#4112yes—
537C22×C32C2×#4114yescomplemented
538C22×C32C2511yescharacteristic
539C2×C3⋊D3—232no—
540C2×C3⋊D3—28no—
541C2×C3⋊D3—28no—
542C2×C3⋊D3—22no—
543C2×C3⋊D3—22no—
544C2×C3⋊D3—22no—
545C2×C3⋊D3—22no—
546C2×C3⋊D3C22×D414yes—
547C2×C3⋊D3C2×#4114yescomplemented
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3—44no—
552C32×C4—22no—
553C3⋊Dic3—22no—
554C3⋊Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3—22no—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3C22×D414yes—
561C3×Dic3C22×D414yes—
562C25—91no—
563C2×#41—98no—
564C2×#41—188no—
565C22×Q8—91no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4D3211yescharacteristic
573C23×C4—31no—
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—91no—
579C23×C4—91no—
580C23×C4—98no—
581C23×C4—91no—
582C23×C4—188no—
583#123—98no—
584#123—98no—
585C22⋊Q8—98no—
586C22⋊Q8—98no—
587#121—38no—
588#121—98no—
589#120—98no—
590#120—98no—
591C4×D4—38no—
592C4×D4—98no—
593C4×D4—98no—
594C4×D4—98no—
595#117—98no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—91no—
599C2×C4⋊C4—91no—
600C2×C4⋊C4—91no—
601C2×C4⋊C4—91no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—31no—
604C2×C22⋊C4—31no—
605C2×C22⋊C4—31no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4—91no—
608C2×C22⋊C4—91no—
609C2×C22⋊C4—91no—
610C2×C22⋊C4—91no—
611C2×C22⋊C4—91no—
612C2×C42—31no—
613C2×C42—91no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—22no—
625C23×C3—22no—
626C23×C3—21no—
627C23×C3—24no—
628C23×C3—32no—
629C23×C3—42no—
630C23×C3—42no—
631C23×C3—42no—
632C23×C3—42no—
633C23×C3—42no—
634C23×C3—62no—
635C23×C3—62no—
636C23×C3—62no—
637C23×C3#23514yescomplemented
638C23×C3#23714yescomplemented
639C23×C3C23×D312yes—
640C23×C3C23×D312yes—
641C23×C3C23×D312yes—
642C23×C3C23×D312yes—
643C23×C3C23×D311yescharacteristic
644C23×C3C23×D311yescharacteristic
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—34no—
649C22×D3—34no—
650C22×D3—34no—
651C22×D3—34no—
652C22×D3—32no—
653C22×D3—32no—
654C22×D3—32no—
655C22×D3—32no—
656C22×D3—64no—
657C22×D3—64no—
658C22×D3—62no—
659C22×D3—62no—
660C22×D3—68no—
661C22×D3—68no—
662C22×D3—68no—
663C22×D3—68no—
664C22×D3—632no—
665C22×D3—632no—
666C22×D3—62no—
667C22×D3—62no—
668C22×D3—68no—
669C22×D3—62no—
670C22×D3—62no—
671C22×D3—62no—
672C22×D3—62no—
673C22×D3—68no—
674C22×D3—62no—
675C22×D3—62no—
676C22×D3—128no—
677C22×D3—128no—
678C22×D3—122no—
679C22×D3—122no—
680C22×D3—122no—
681C22×D3—122no—
682C22×D3—128no—
683C22×D3—1232no—
684C22×D3C23×D312yes—
685C3×D4—28no—
686C3×D4—28no—
687C3×D4—48no—
688C3×D4—68no—
689C3×D4—68no—
690C2×C3×C4—22no—
691C2×C3×C4—22no—
692C2×C3×C4—22no—
693C2×C3×C4—34no—
694C2×C3×C4—34no—
695C2×C3×C4—32no—
696C2×C3×C4—32no—
697C2×C3×C4—32no—
698C2×C3×C4—32no—
699C2×C3×C4—32no—
700C2×C3×C4—32no—
701C2×C3×C4—32no—
702C2×C3×C4—42no—
703C2×C3×C4—68no—
704C2×C3×C4—68no—
705C2×C3×C4—68no—
706C2×C3×C4—62no—
707C2×C3×C4—62no—
708C2×C3×C4—62no—
709C2×C3×C4—62no—
710C2×C3×C4—62no—
711C2×C3×C4C23×D312yes—
712C2×C3×C4C23×D312yes—
713#67—28no—
714#67—28no—
715#67—68no—
716#67—68no—
717#67—68no—
718#67—68no—
719#67—68no—
720#67—68no—
721#67—128no—
722#67—128no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—22no—
726C2×Dic3—22no—
727C2×Dic3—22no—
728C2×Dic3—28no—
729C2×Dic3—28no—
730C2×Dic3—28no—
731C2×Dic3—32no—
732C2×Dic3—32no—
733C2×Dic3—32no—
734C2×Dic3—32no—
735C2×Dic3—62no—
736C2×Dic3—62no—
737C2×Dic3—62no—
738C2×Dic3—62no—
739C2×Dic3—62no—
740C2×Dic3—62no—
741C2×Dic3—68no—
742C2×Dic3—122no—
743C2×Dic3—122no—
744C2×Dic3D3×D414yes—
745C2×Dic3D3×D414yes—
746C2×Dic3C23×D312yes—
747C2×Dic3C23×D312yes—
748C2×Dic3C23×D312yes—
749C2×Dic3C23×D312yes—
750C2×Dic3C23×D312yes—
751C2×Dic3C23×D312yes—
752C2×Dic3C23×D312yes—
753D12—68no—
754D12—68no—
755C4×D3—316no—
756C4×D3—316no—
757C4×D3—68no—
758C4×D3—68no—
759C4×D3—68no—
760C4×D3—68no—
761C4×D3—68no—
762C4×D3—68no—
763C4×D3—68no—
764Dic6—68no—
765Dic6—68no—
766C2×C32—24no—
767C2×C32—42no—
768C2×C32#52514yescomplemented
769C2×C32C23×D411yescharacteristic
770C2×C32C22×#4111yescharacteristic
771C2×C32C22×#4111yescharacteristic
772C3⋊D3—24no—
773C3⋊D3—24no—
774C3×D3—42no—
775C24—31no—
776C24—91no—
777C24—91no—
778C24—94no—
779C24—184no—
780C24—184no—
781C24—184no—
782C24C2×D3211yescharacteristic
783C24C2×D3211yescharacteristic
784#41—1832no—
785C2×Q8—94no—
786C2×Q8—184no—
787C2×D4—24no—
788C2×D4—34no—
789C2×D4—34no—
790C2×D4—64no—
791C2×D4—64no—
792C2×D4—94no—
793C2×D4—94no—
794C2×D4—94no—
795C2×D4—94no—
796C2×D4—184no—
797C2×D4—184no—
798C2×D4—184no—
799C2×D4—184no—
800C2×D4C2×D3214yes—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—34no—
804C22×C4—34no—
805C22×C4—34no—
806C22×C4—31no—
807C22×C4—31no—
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—31no—
811C22×C4—64no—
812C22×C4—64no—
813C22×C4—64no—
814C22×C4—94no—
815C22×C4—98no—
816C22×C4—94no—
817C22×C4—94no—
818C22×C4—94no—
819C22×C4—94no—
820C22×C4—91no—
821C22×C4—91no—
822C22×C4—184no—
823C22×C4—184no—
824C22×C4—184no—
825C22×C4—1832no—
826C22×C4—184no—
827C22×C4C2×D3211yescharacteristic
828C4⋊C4—34no—
829C4⋊C4—34no—
830C4⋊C4—94no—
831C4⋊C4—94no—
832C4⋊C4—94no—
833C4⋊C4—94no—
834C22⋊C4—34no—
835C22⋊C4—34no—
836C22⋊C4—34no—
837C22⋊C4—34no—
838C22⋊C4—94no—
839C22⋊C4—94no—
840C22⋊C4—94no—
841C22⋊C4—94no—
842C22⋊C4—94no—
843C22⋊C4—94no—
844C42—34no—
845C42—94no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—28no—
851C22×C3—28no—
852C22×C3—22no—
853C22×C3—22no—
854C22×C3—22no—
855C22×C3—22no—
856C22×C3—22no—
857C22×C3—22no—
858C22×C3—22no—
859C22×C3—22no—
860C22×C3—22no—
861C22×C3—24no—
862C22×C3—21no—
863C22×C3—42no—
864C22×C3—42no—
865C22×C3—48no—
866C22×C3—42no—
867C22×C3—42no—
868C22×C3—42no—
869C22×C3—44no—
870C22×C3—44no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—62no—
874C22×C3—84no—
875C22×C3—124no—
876C22×C3C2×#23512yes—
877C22×C3C2×#23514yescomplemented
878C22×C3C2×D3×D412yes—
879C22×C3C2×D3×D412yes—
880C22×C3C2×#23712yes—
881C22×C3C2×#23714yescomplemented
882C22×C3D3×#4112yes—
883C22×C3D3×#4112yes—
884C22×C3C24×D311yescharacteristic
885C22×C3C24×D311yescharacteristic
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—34no—
890C2×D3—34no—
891C2×D3—34no—
892C2×D3—34no—
893C2×D3—44no—
894C2×D3—64no—
895C2×D3—64no—
896C2×D3—632no—
897C2×D3—632no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—68no—
907C2×D3—68no—
908C2×D3—68no—
909C2×D3—68no—
910C2×D3—122no—
911C2×D3—122no—
912C2×D3—128no—
913C2×D3—128no—
914C2×D3—122no—
915C2×D3—122no—
916C2×D3—1232no—
917C3×C4—22no—
918C3×C4—22no—
919C3×C4—34no—
920C3×C4—34no—
921C3×C4—42no—
922C3×C4—62no—
923C3×C4—62no—
924C3×C4—62no—
925C3×C4—62no—
926C3×C4—62no—
927Dic3—22no—
928Dic3—22no—
929Dic3—22no—
930Dic3—22no—
931Dic3—22no—
932Dic3—62no—
933Dic3—62no—
934Dic3—62no—
935Dic3—62no—
936Dic3—122no—
937Dic3—122no—
938Dic3C2×D3×D414yes—
939Dic3C2×D3×D414yes—
940C32C2×#52511yescharacteristic, complemented, Sylow
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—32no—
947C23—62no—
948C23—62no—
949C23—62no—
950C23—94no—
951C23—94no—
952C23—92no—
953C23—92no—
954C23—188no—
955C23—188no—
956C23—1832no—
957C23—182no—
958C23—182no—
959C23—182no—
960C23—182no—
961C23—188no—
962C23#380414yescomplemented
963C23C22×D3212yes—
964C23C22×D3212yes—
965C23C22×D3211yescharacteristic
966Q8—188no—
967D4—28no—
968D4—68no—
969D4—68no—
970D4—188no—
971D4—188no—
972D4—188no—
973D4—188no—
974C2×C4—22no—
975C2×C4—34no—
976C2×C4—34no—
977C2×C4—32no—
978C2×C4—32no—
979C2×C4—32no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—32no—
984C2×C4—68no—
985C2×C4—68no—
986C2×C4—68no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—916no—
993C2×C4—92no—
994C2×C4—92no—
995C2×C4—188no—
996C2×C4—188no—
997C2×C4—188no—
998C2×C4—188no—
999C2×C4—182no—
1000C2×C4—182no—
1001C2×C4C22×D3212yes—
1002C2×C3—24no—
1003C2×C3—24no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—24no—
1007C2×C3—21no—
1008C2×C3—44no—
1009C2×C3—42no—
1010C2×C3—42no—
1011C2×C3—82no—
1012C2×C3—122no—
1013C2×C3#554714yescomplemented
1014C2×C3#560614yescomplemented
1015C2×C3C22×#23511yescharacteristic
1016C2×C3C22×D3×D411yescharacteristic
1017C2×C3C22×D3×D411yescharacteristic
1018C2×C3C22×#23711yescharacteristic
1019C2×C3C2×D3×#4111yescharacteristic
1020C2×C3C2×D3×#4111yescharacteristic
1021D3—42no—
1022D3—64no—
1023D3—64no—
1024D3—64no—
1025D3—64no—
1026D3—124no—
1027D3—124no—
1028C22—22no—
1029C22—22no—
1030C22—28no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—44no—
1035C22—62no—
1036C22—62no—
1037C22—62no—
1038C22—94no—
1039C22—94no—
1040C22—124no—
1041C22—1832no—
1042C22—182no—
1043C22—182no—
1044C22—188no—
1045C22—188no—
1046C22—182no—
1047C22—182no—
1048C22D32×D412yes—
1049C22#6431212yes—
1050C22C2×#380412yes—
1051C22C2×#380414yescomplemented
1052C22C23×D3211yescharacteristic
1053C4—22no—
1054C4—34no—
1055C4—34no—
1056C4—62no—
1057C4—62no—
1058C4—62no—
1059C4—62no—
1060C4—62no—
1061C4—182no—
1062C4—182no—
1063C3—21no—
1064C3C2×#554711yescharacteristic, complemented
1065C3C2×#560611yescharacteristic, complemented
1066C2—24no—
1067C2—42no—
1068C2—122no—
1069C2—184no—
1070C2—184no—
1071C2#1059513814yesdirect product factor
1072C2C2×D32×D411yescharacteristic
1073C2C2×#6431211yescharacteristic
1074C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×#624C2semidirect
2. C22×#3804C2semidirect
3. C2×#64146C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×D4×Dic3C2semidirect
6. C2×#63981C2semidirect
7. C2×#63975C2semidirect
8. C2×Dic3×#67C2semidirect
9. C2×#63964C2semidirect
10. C2×#63958C2semidirect
11. C2×#63952C2semidirect
12. #10595138C2direct (N × H)
13. C2×#63895C2semidirect
14. C2×#63880C2semidirect
15. C2×#63854C2semidirect
16. C2×#63836C2semidirect
24. C22×C3×#67C22semidirect
27. C23×C3×Dic3C22semidirect
28. C22×#627C22semidirect
36. C22×#624C22semidirect
38. C2×#3804C22semidirect
39. C22×D3×Dic3C22semidirect
41. #64146C22semidirect
45. C2×C3×#217C22semidirect
46. C2×C3×#217C22semidirect
47. C3×#939C22semidirect
48. C3×D4×Dic3C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×C4⋊Dic3C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C2×C3×C4×Dic3C22semidirect
53. #63981C22semidirect
54. #63975C22semidirect
55. Dic3×#67C22semidirect
56. C2×#3724C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. #63964C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63958C22semidirect
65. C2×Dic32C22semidirect
66. #63952C22semidirect
67. #63895C22semidirect
68. #63880C22semidirect
69. #63854C22semidirect
70. #63836C22semidirect
77. C2×#939D3semidirect
84. C2×D4×Dic3D3semidirect
125. C2×C3×#67C23semidirect
138. C22×C3×Dic3C23semidirect
140. C2×#627C23semidirect
149. C2×#624D4semidirect
156. C2×D3×Dic3C23semidirect
161. C3×#217C23semidirect
162. C3×#217C23semidirect
163. C3×(C2×D3)⋊C4C23semidirect
164. C3×C4⋊Dic3C23semidirect
165. C3×Dic3⋊C4C23semidirect
166. C3×C4×Dic3C23semidirect
167. #3724C23semidirect
168. Dic3⋊Dic3C23semidirect
169. Dic3⋊Dic3C23semidirect
170. Dic3⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. Dic32C23semidirect
196. C22×#67C2×D3semidirect
200. C23×Dic3C2×D3semidirect
236. C2×#217C2×D3semidirect
237. C2×#217C2×D3semidirect
238. #939C2×D3semidirect
245. D4×Dic3C2×D3semidirect
259. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×C4⋊Dic3C2×D3semidirect
270. C2×Dic3⋊C4C2×D3semidirect
273. C2×C4×Dic3C2×D3semidirect
293. C23×C32#41semidirect
306. C22×C3⋊D3#41semidirect
347. #624C2×D4semidirect
436. C2×#67C22×D3semidirect
457. C22×Dic3C22×D3semidirect
500. #217C22×D3semidirect
501. #217C22×D3semidirect
513. (C2×D3)⋊C4C22×D3semidirect
517. C4⋊Dic3C22×D3semidirect
523. Dic3⋊C4C22×D3semidirect
526. C4×Dic3C22×D3semidirect
537. C22×C32C2×#41semidirect
547. C2×C3⋊D3C2×#41semidirect
637. C23×C3#235semidirect
638. C23×C3#237semidirect
768. C2×C32#525semidirect
877. C22×C3C2×#235semidirect
881. C22×C3C2×#237semidirect
940. C32C2×#525semidirect
962. C23#3804semidirect
1013. C2×C3#5547semidirect
1014. C2×C3#5606semidirect
1051. C22C2×#3804semidirect
1064. C3C2×#5547semidirect
1065. C3C2×#5606semidirect
1071. C2#10595138direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6242
C22×#38042
C2×#641462
C2×C3×#9392
C2×C3×D4×Dic32
C2×#639812
C2×#639752
C2×Dic3×#672
C2×#639642
C2×#639582
C2×#639522
#105951382
C2×#638952
C2×#638802
C2×#638542
C2×#638362
C2×#56063
C2×#55473