Finite Group Databasebeta

← C2×#10594066 #11900447

Subgroups — C2×#10594066 #11900447

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×#3799C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×#878C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63978C211yesmaximal, characteristic, complemented
8C2×#63952C211yesmaximal, characteristic, complemented
9C2×#63910C211yesmaximal, characteristic, complemented
10C2×#63904C211yesmaximal, characteristic, complemented
11C2×#63897C211yesmaximal, characteristic, complemented
12C2×#63894C211yesmaximal, characteristic, complemented
13C2×#63888C211yesmaximal, characteristic, complemented
14C2×#63854C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594066C2116yesmaximal, direct product factor
17C2×#5627—31nomaximal
18C2×#5547—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×Dic6C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic, complemented
31C22×#624—28no—
32C22×#624C2211yescharacteristic
33C22×#624C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C22×#624C2211yescharacteristic
36C22×#624C2218yescomplemented
37C22×#624C2211yescharacteristic, complemented
38C2×#3799—28no—
39C2×#3799C2218yescomplemented
40C2×C32×C22⋊C4C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43#64091C2218yescomplemented
44C2×C3×#217C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C3×C4×Dic3C2211yescharacteristic, complemented
51C3×#67⋊C4C2218yescomplemented
52C3×#878C2218yescomplemented
53#63981C2218yescomplemented
54#63978C2218yescomplemented
55C2×#3724C2211yescharacteristic, complemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×#3722C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×Dic32C2211yescharacteristic, complemented
63#63952C2218yescomplemented
64#63910C2218yescomplemented
65#63904C2218yescomplemented
66#63897C2218yescomplemented
67#63894C2218yescomplemented
68#63888C2218yescomplemented
69#63854C2218yescomplemented
70#63836C2218yescomplemented
71C22×#239—31no—
72C22×#235—31no—
73C23×C4×D3—31no—
74C23×C4×D3—31no—
75C2×C3×C22⋊Q8—31no—
76C2×C3×C4×D4—31no—
77C2×#946—31no—
78C2×#939—31no—
79C2×#937—31no—
80C2×#930—31no—
81C2×C4×#67—31no—
82C2×C4×#67—31no—
83#5627—316no—
84#5547—316no—
85C2×#896—31no—
86C2×#895—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#894—31no—
90C2×#893—31no—
91C2×#893—31no—
92C2×#892—31no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—61no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4D311yescharacteristic, complemented
101C2×#878D311yescharacteristic, complemented
102C2×C4×D12—31no—
103C2×#872—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—24no—
108C23×C3⋊D3C2314yes—
109C23×C3⋊D3C2311yescharacteristic
110C23×C3⋊D3C2311yescharacteristic
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C2×#638—24no—
116C2×#638C2314yes—
117C22×C3⋊Dic3C2311yescharacteristic
118C2×C4⋊(C3⋊D3)—24no—
119C2×C4⋊(C3⋊D3)—24no—
120C2×C4⋊(C3⋊D3)C2314yes—
121C2×C4⋊(C3⋊D3)C2314yes—
122C2×C3×#67—24no—
123C2×C3×#67C2314yes—
124C22×C3×Dic3—24no—
125C22×C3×Dic3—24no—
126C22×C3×Dic3C2314yes—
127C22×C3×Dic3C2314yes—
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×C4×D3—24no—
136C2×C3×C4×D3C2314yescomplemented
137C2×C3×Dic6—24no—
138C2×C3×Dic6C2314yescomplemented
139C2×#626—24no—
140C2×#626—24no—
141C2×#626—24no—
142C2×#626C2314yes—
143C2×#626C2314yes—
144C2×#626C2314yescomplemented
145C2×#624—24no—
146C2×#624—24no—
147C2×#624—24no—
148C2×#624—24no—
149C2×#624—232no—
150C2×#624D418yescomplemented
151C2×#624C2314yes—
152C2×#624C2314yes—
153C2×#624C2314yes—
154C2×#624C2314yes—
155C2×#624C2314yescomplemented
156#3799—232no—
157C32×C22⋊C4C2314yes—
158#3752C2314yes—
159#3752C2314yes—
160C3×#217C2314yes—
161C3×(C2×D3)⋊C4C2314yescomplemented
162C3×C4⋊Dic3C2314yescomplemented
163C3×Dic3⋊C4C2314yescomplemented
164C3×Dic3⋊C4C2314yescomplemented
165C3×Dic3⋊C4C2314yescomplemented
166C3×C4×Dic3C2314yescomplemented
167#3724C2314yescomplemented
168Dic3⋊Dic3C2314yescomplemented
169#3722C2314yes—
170#3722C2314yes—
171#3722C2314yescomplemented
172#3722C2314yescomplemented
173(C2×D3)⋊Dic3C2314yescomplemented
174Dic32C2314yescomplemented
175C2×#525—91noSylow
176C24×D3—31no—
177C24×D3—31no—
178C24×D3—61no—
179C22×C3×Q8—31no—
180C22×C3×D4—31no—
181C23×C3×C4—31no—
182C23×C3×C4—31no—
183C23×C3×C4—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—61no—
190C22×#67C2×D311yescharacteristic
191C23×Dic3C2×D311yescharacteristic
192C23×Dic3C2×D311yescharacteristic
193C2×#239—38no—
194C2×#239—68no—
195C2×#235—38no—
196C2×#235—68no—
197C22×D12—31no—
198C22×D12—31no—
199C22×D12—31no—
200C22×D12—31no—
201C22×D12—31no—
202C22×D12—31no—
203C22×D12—31no—
204C22×D12—61no—
205C22×D12—61no—
206C22×C4×D3—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—38no—
215C22×C4×D3—38no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—68no—
219C22×C4×D3—68no—
220C22×C4×D3C2×D311yescharacteristic, complemented
221C22×Dic6C2×D311yescharacteristic, complemented
222C3×C22⋊Q8—38no—
223C3×C4×D4—38no—
224C2×C3×C4⋊C4—31no—
225C2×C3×C4⋊C4—31no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C22⋊C4—21no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4C2×D311yescharacteristic
232C2×C3×C22⋊C4C2×D311yescharacteristic
233C2×C3×C42—31no—
234C2×#217—31no—
235C2×#217C2×D311yescharacteristic
236#946—38no—
237#939—38no—
238#937—38no—
239#930—38no—
240C4×#67—38no—
241C4×#67—38no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
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—61no—
256C2×(C2×D3)⋊C4—61no—
257C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
258C2×C4⋊Dic3—31no—
259C2×C4⋊Dic3C2×D311yescharacteristic, complemented
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—31no—
262C2×Dic3⋊C4—31no—
263C2×Dic3⋊C4C2×D311yescharacteristic, complemented
264C2×Dic3⋊C4C2×D311yescharacteristic, complemented
265C2×Dic3⋊C4C2×D311yescharacteristic, complemented
266C2×C4×Dic3—31no—
267C2×C4×Dic3—31no—
268C2×C4×Dic3C2×D311yescharacteristic, complemented
269#896—38no—
270#895—38no—
271#894—38no—
272#894—38no—
273#894—38no—
274#893—38no—
275#893—38no—
276#892—38no—
277#884—38no—
278#883—38no—
279#882—38no—
280#882—38no—
281#882—38no—
282#882—68no—
283#67⋊C4—38no—
284#67⋊C4C2×D318yescomplemented
285#878C2×D318yescomplemented
286C4×D12—38no—
287#872—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32#4114yescomplemented
291C23×C32C2412yes—
292C23×C32C2411yescharacteristic
293C22×C3⋊D3—232no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3—22no—
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—28no—
299C22×C3⋊D3—28no—
300C22×C3⋊D3—28no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—22no—
304C22×C3⋊D3C2×D414yes—
305C22×C3⋊D3#4114yescomplemented
306C22×C3⋊D3C2412yes—
307C22×C3⋊D3C2412yes—
308C22×C3⋊D3C2412yes—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3C2412yes—
313C2×C32×C4—22no—
314C2×C32×C4—22no—
315C2×C32×C4C2412yes—
316C2×C32×C4C2412yes—
317#638—28no—
318C2×C3⋊Dic3—22no—
319C2×C3⋊Dic3C2412yes—
320C4⋊(C3⋊D3)—28no—
321C4⋊(C3⋊D3)—28no—
322C3×#67—28no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—28no—
329C2×C3×Dic3—28no—
330C2×C3×Dic3C2×D414yes—
331C2×C3×Dic3C2×D414yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C3×C4×D3—28no—
340C3×Dic6—28no—
341#626—28no—
342#626—28no—
343#626—28no—
344#624—28no—
345#624—28no—
346#624—28no—
347#624—28no—
348#624C2×D4116yescomplemented
349C22×#41—91no—
350C24×C4—91no—
351#525—916no—
352C2×#123—91no—
353C2×#123—91no—
354C2×C22⋊Q8—31no—
355C2×C22⋊Q8—91no—
356C2×#121—91no—
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—31no—
367C24×C3C22×D311yescharacteristic
368C24×C3C22×D311yescharacteristic
369C23×D3—31no—
370C23×D3—31no—
371C23×D3—31no—
372C23×D3—31no—
373C23×D3—34no—
374C23×D3—34no—
375C23×D3—31no—
376C23×D3—31no—
377C23×D3—61no—
378C23×D3—61no—
379C23×D3—64no—
380C23×D3—61no—
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×Q8—34no—
392C2×C3×Q8—64no—
393C2×C3×D4—34no—
394C2×C3×D4—64no—
395C22×C3×C4—21no—
396C22×C3×C4—21no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—34no—
405C22×C3×C4—34no—
406C22×C3×C4—34no—
407C22×C3×C4—64no—
408C22×C3×C4—64no—
409C22×C3×C4—64no—
410C22×C3×C4C22×D311yescharacteristic
411C22×C3×C4C22×D311yescharacteristic
412C22×C3×C4C22×D311yescharacteristic
413C22×C3×C4C22×D311yescharacteristic
414C2×#67—24no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—64no—
421C2×#67—64no—
422C2×#67—64no—
423C2×#67—64no—
424C2×#67—64no—
425C2×#67—64no—
426C2×#67—124no—
427C2×#67C22×D314yes—
428C22×Dic3—24no—
429C22×Dic3—24no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—61no—
433C22×Dic3C22×D314yes—
434C22×Dic3C22×D314yes—
435C22×Dic3C22×D311yescharacteristic
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C22×Dic3C22×D311yescharacteristic
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441C22×Dic3C22×D311yescharacteristic
442#239—632no—
443#235—632no—
444C2×D12—34no—
445C2×D12—34no—
446C2×D12—34no—
447C2×D12—34no—
448C2×D12—34no—
449C2×D12—34no—
450C2×D12—34no—
451C2×D12—64no—
452C2×D12—64no—
453C2×D12—64no—
454C2×D12—64no—
455C2×D12—64no—
456C2×D12—64no—
457C2×D12—64no—
458C2×D12—64no—
459C2×D12—64no—
460C2×D12—124no—
461C2×D12—124no—
462C2×C4×D3—24no—
463C2×C4×D3—38no—
464C2×C4×D3—38no—
465C2×C4×D3—34no—
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×C4×D3—64no—
485C2×C4×D3C22×D314yescomplemented
486C2×Dic6—24no—
487C2×Dic6C22×D314yescomplemented
488C3×C4⋊C4—34no—
489C3×C4⋊C4—34no—
490C3×C4⋊C4—34no—
491C3×C4⋊C4—34no—
492C3×C22⋊C4—24no—
493C3×C22⋊C4—34no—
494C3×C22⋊C4—34no—
495C3×C22⋊C4C22×D314yes—
496C3×C22⋊C4C22×D314yes—
497C3×C42—34no—
498#217—34no—
499#217C22×D314yes—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
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—34no—
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—64no—
514(C2×D3)⋊C4—64no—
515(C2×D3)⋊C4C22×D314yescomplemented
516C4⋊Dic3—34no—
517C4⋊Dic3C22×D314yescomplemented
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4C22×D314yescomplemented
522Dic3⋊C4C22×D314yescomplemented
523Dic3⋊C4C22×D314yescomplemented
524C4×Dic3—34no—
525C4×Dic3—34no—
526C4×Dic3C22×D314yescomplemented
527C22×C32—28no—
528C22×C32—22no—
529C22×C32—22no—
530C22×C32C22×D412yes—
531C22×C32C2×#4112yes—
532C22×C32C2×#4112yes—
533C22×C32C2×#4114yescomplemented
534C22×C32C2511yescharacteristic
535C2×C3⋊D3—232no—
536C2×C3⋊D3—28no—
537C2×C3⋊D3—28no—
538C2×C3⋊D3—22no—
539C2×C3⋊D3—22no—
540C2×C3⋊D3—22no—
541C2×C3⋊D3—22no—
542C2×C3⋊D3—22no—
543C2×C3⋊D3—22no—
544C2×C3⋊D3—22no—
545C2×C3⋊D3—44no—
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—
553C32×C4—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—31no—
566C22×D4—31no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4—91no—
573C23×C4—31no—
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—91no—
579C23×C4—91no—
580C23×C4—91no—
581C23×C4—98no—
582C23×C4—188no—
583#123—98no—
584#123—98no—
585C22⋊Q8—38no—
586C22⋊Q8—98no—
587#121—98no—
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—31no—
599C2×C4⋊C4—31no—
600C2×C4⋊C4—91no—
601C2×C4⋊C4—91no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—31no—
604C2×C22⋊C4—91no—
605C2×C22⋊C4—91no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4—91no—
608C2×C22⋊C4—91no—
609C2×C22⋊C4—91no—
610C2×C22⋊C4—91no—
611C2×C22⋊C4D3211yescharacteristic
612C2×C42—31no—
613C2×C42—91no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—22no—
619C23×C3—21no—
620C23×C3—24no—
621C23×C3—32no—
622C23×C3—42no—
623C23×C3—42no—
624C23×C3—62no—
625C23×C3—62no—
626C23×C3—62no—
627C23×C3#23514yescomplemented
628C23×C3#23914yescomplemented
629C23×C3C23×D312yes—
630C23×C3C23×D312yes—
631C23×C3C23×D311yescharacteristic
632C23×C3C23×D311yescharacteristic
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—34no—
637C22×D3—34no—
638C22×D3—34no—
639C22×D3—34no—
640C22×D3—32no—
641C22×D3—32no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—32no—
645C22×D3—32no—
646C22×D3—64no—
647C22×D3—64no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—68no—
652C22×D3—68no—
653C22×D3—68no—
654C22×D3—68no—
655C22×D3—632no—
656C22×D3—632no—
657C22×D3—62no—
658C22×D3—62no—
659C22×D3—68no—
660C22×D3—62no—
661C22×D3—62no—
662C22×D3—62no—
663C22×D3—62no—
664C22×D3—68no—
665C22×D3—62no—
666C22×D3—62no—
667C22×D3—62no—
668C22×D3—62no—
669C22×D3—62no—
670C22×D3—62no—
671C22×D3—62no—
672C22×D3—62no—
673C22×D3—128no—
674C22×D3—128no—
675C22×D3—122no—
676C22×D3—122no—
677C22×D3—128no—
678C22×D3—122no—
679C22×D3—122no—
680C22×D3—1232no—
681C22×D3—122no—
682C22×D3—122no—
683C22×D3—122no—
684C22×D3C23×D312yes—
685C3×Q8—68no—
686C3×D4—68no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
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—42no—
704C2×C3×C4—68no—
705C2×C3×C4—68no—
706C2×C3×C4—68no—
707C2×C3×C4—62no—
708C2×C3×C4—62no—
709C2×C3×C4—62no—
710C2×C3×C4—62no—
711C2×C3×C4—62no—
712C2×C3×C4C23×D312yes—
713C2×C3×C4C23×D312yes—
714C2×C3×C4C23×D312yes—
715C2×C3×C4C23×D312yes—
716#67—28no—
717#67—68no—
718#67—68no—
719#67—68no—
720#67—68no—
721#67—68no—
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—32no—
731C2×Dic3—32no—
732C2×Dic3—62no—
733C2×Dic3—62no—
734C2×Dic3—62no—
735C2×Dic3—122no—
736C2×Dic3D3×D414yes—
737C2×Dic3D3×D414yes—
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D312yes—
740C2×Dic3C23×D312yes—
741C2×Dic3C23×D312yes—
742C2×Dic3C23×D312yes—
743C2×Dic3C23×D312yes—
744C2×Dic3C23×D312yes—
745D12—68no—
746D12—68no—
747D12—68no—
748D12—68no—
749D12—68no—
750D12—68no—
751D12—68no—
752D12—128no—
753D12—128no—
754C4×D3—28no—
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—
764C4×D3—68no—
765Dic6—28no—
766C2×C32—24no—
767C2×C32#52514yescomplemented
768C2×C32C23×D411yescharacteristic
769C2×C32C22×#4111yescharacteristic
770C2×C32C22×#4111yescharacteristic
771C3⋊D3—24no—
772C3⋊D3—24no—
773C3⋊D3—42no—
774C3×D3—42no—
775C24—31no—
776C24—91no—
777C24—91no—
778C24—94no—
779C24—91no—
780C24—184no—
781C24—184no—
782C24—184no—
783C24C2×D3211yescharacteristic
784#41—1832no—
785C2×Q8—34no—
786C2×Q8—64no—
787C2×D4—34no—
788C2×D4—64no—
789C2×D4—94no—
790C2×D4—94no—
791C2×D4—94no—
792C2×D4—94no—
793C2×D4—94no—
794C2×D4—94no—
795C2×D4—184no—
796C2×D4—184no—
797C2×D4—184no—
798C2×D4—184no—
799C2×D4—184no—
800C2×D4—184no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—34no—
804C22×C4—34no—
805C22×C4—31no—
806C22×C4—31no—
807C22×C4—31no—
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—34no—
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—184no—
822C22×C4—184no—
823C22×C4—184no—
824C22×C4—1832no—
825C22×C4—184no—
826C22×C4C2×D3211yescharacteristic
827C22×C4C2×D3211yescharacteristic
828C4⋊C4—34no—
829C4⋊C4—34no—
830C4⋊C4—34no—
831C4⋊C4—34no—
832C4⋊C4—94no—
833C4⋊C4—94no—
834C22⋊C4—34no—
835C22⋊C4—34no—
836C22⋊C4—94no—
837C22⋊C4—94no—
838C22⋊C4—94no—
839C22⋊C4—94no—
840C22⋊C4—94no—
841C22⋊C4—94no—
842C22⋊C4—94no—
843C22⋊C4C2×D3214yes—
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—24no—
854C22×C3—22no—
855C22×C3—22no—
856C22×C3—21no—
857C22×C3—48no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—124no—
864C22×C3C2×#23512yes—
865C22×C3C2×#23514yescomplemented
866C22×C3C2×D3×D412yes—
867C22×C3C2×D3×D412yes—
868C22×C3C2×#23912yes—
869C22×C3C2×#23914yescomplemented
870C22×C3D3×#4112yes—
871C22×C3D3×#4112yes—
872C22×C3C24×D311yescharacteristic
873C22×C3C24×D311yescharacteristic
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—34no—
878C2×D3—34no—
879C2×D3—34no—
880C2×D3—34no—
881C2×D3—44no—
882C2×D3—64no—
883C2×D3—64no—
884C2×D3—632no—
885C2×D3—632no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—68no—
895C2×D3—68no—
896C2×D3—68no—
897C2×D3—68no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—128no—
905C2×D3—128no—
906C2×D3—122no—
907C2×D3—122no—
908C2×D3—122no—
909C2×D3—122no—
910C2×D3—1232no—
911C2×D3—122no—
912C2×D3—122no—
913C2×D3—122no—
914C2×D3—124no—
915C2×D3—124no—
916C2×D3—244no—
917C3×C4—22no—
918C3×C4—22no—
919C3×C4—22no—
920C3×C4—22no—
921C3×C4—34no—
922C3×C4—34no—
923C3×C4—42no—
924C3×C4—42no—
925C3×C4—62no—
926C3×C4—62no—
927C3×C4—62no—
928C3×C4—62no—
929C3×C4—62no—
930Dic3—22no—
931Dic3—22no—
932Dic3—22no—
933Dic3—22no—
934Dic3—22no—
935Dic3—62no—
936Dic3—62no—
937Dic3—122no—
938Dic3C2×D3×D414yes—
939Dic3C2×D3×D414yes—
940C32C2×#52511yescharacteristic, complemented, Sylow
941C23—22no—
942C23—22no—
943C23—32no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—94no—
948C23—94no—
949C23—92no—
950C23—92no—
951C23—92no—
952C23—188no—
953C23—188no—
954C23—1832no—
955C23—182no—
956C23—182no—
957C23—188no—
958C23—182no—
959C23—182no—
960C23—182no—
961C23—182no—
962C23—182no—
963C23#379914yescomplemented
964C23C22×D3212yes—
965C23C22×D3211yescharacteristic
966Q8—68no—
967D4—68no—
968D4—188no—
969D4—188no—
970D4—188no—
971D4—188no—
972D4—188no—
973D4—188no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—34no—
977C2×C4—34no—
978C2×C4—32no—
979C2×C4—32no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—32no—
984C2×C4—32no—
985C2×C4—68no—
986C2×C4—68no—
987C2×C4—68no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—916no—
994C2×C4—92no—
995C2×C4—188no—
996C2×C4—188no—
997C2×C4—188no—
998C2×C4—188no—
999C2×C4—182no—
1000C2×C4C22×D3212yes—
1001C2×C4C22×D3212yes—
1002C2×C3—24no—
1003C2×C3—24no—
1004C2×C3—24no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—44no—
1009C2×C3—122no—
1010C2×C3#554714yescomplemented
1011C2×C3#562714yescomplemented
1012C2×C3C22×#23511yescharacteristic
1013C2×C3C22×D3×D411yescharacteristic
1014C2×C3C22×D3×D411yescharacteristic
1015C2×C3C22×#23911yescharacteristic
1016C2×C3C2×D3×#4111yescharacteristic
1017C2×C3C2×D3×#4111yescharacteristic
1018D3—42no—
1019D3—64no—
1020D3—64no—
1021D3—64no—
1022D3—64no—
1023D3—124no—
1024D3—124no—
1025D3—122no—
1026D3—122no—
1027D3—242no—
1028C22—28no—
1029C22—22no—
1030C22—22no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—94no—
1035C22—94no—
1036C22—124no—
1037C22—1832no—
1038C22—188no—
1039C22—188no—
1040C22—182no—
1041C22—182no—
1042C22—182no—
1043C22—182no—
1044C22—182no—
1045C22—182no—
1046C22—182no—
1047C22—364no—
1048C22C2×#379912yes—
1049C22C2×#379914yescomplemented
1050C22D32×D412yes—
1051C22#6431212yes—
1052C22C23×D3211yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—34no—
1056C4—34no—
1057C4—62no—
1058C4—62no—
1059C4—62no—
1060C4—62no—
1061C4—62no—
1062C4—182no—
1063C3—21no—
1064C3C2×#554711yescharacteristic, complemented
1065C3C2×#562711yescharacteristic, complemented
1066C2—24no—
1067C2—122no—
1068C2—184no—
1069C2—184no—
1070C2—362no—
1071C2#1059406614yesdirect product factor
1072C2C22×#379911yescharacteristic
1073C2C2×D32×D411yescharacteristic
1074C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#624C2semidirect
2. C22×#3799C2semidirect
3. C2×#64091C2semidirect
4. C2×C3×#67⋊C4C2semidirect
5. C2×C3×#878C2semidirect
6. C2×#63981C2semidirect
7. C2×#63978C2semidirect
8. C2×#63952C2semidirect
9. C2×#63910C2semidirect
10. C2×#63904C2semidirect
11. C2×#63897C2semidirect
12. C2×#63894C2semidirect
13. C2×#63888C2semidirect
14. C2×#63854C2semidirect
15. C2×#63836C2semidirect
16. #10594066C2direct (N × H)
26. C22×C3×C4×D3C22semidirect
27. C22×C3×Dic6C22semidirect
30. C22×#626C22semidirect
36. C22×#624C22semidirect
37. C22×#624C22semidirect
39. C2×#3799C22semidirect
43. #64091C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×C4⋊Dic3C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. C2×C3×C4×Dic3C22semidirect
51. C3×#67⋊C4C22semidirect
52. C3×#878C22semidirect
53. #63981C22semidirect
54. #63978C22semidirect
55. C2×#3724C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
59. C2×#3722C22semidirect
60. C2×#3722C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×Dic32C22semidirect
63. #63952C22semidirect
64. #63910C22semidirect
65. #63904C22semidirect
66. #63897C22semidirect
67. #63894C22semidirect
68. #63888C22semidirect
69. #63854C22semidirect
70. #63836C22semidirect
100. C2×#67⋊C4D3semidirect
101. C2×#878D3semidirect
136. C2×C3×C4×D3C23semidirect
138. C2×C3×Dic6C23semidirect
144. C2×#626C23semidirect
150. C2×#624D4semidirect
155. C2×#624C23semidirect
161. C3×(C2×D3)⋊C4C23semidirect
162. C3×C4⋊Dic3C23semidirect
163. C3×Dic3⋊C4C23semidirect
164. C3×Dic3⋊C4C23semidirect
165. C3×Dic3⋊C4C23semidirect
166. C3×C4×Dic3C23semidirect
167. #3724C23semidirect
168. Dic3⋊Dic3C23semidirect
171. #3722C23semidirect
172. #3722C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. Dic32C23semidirect
220. C22×C4×D3C2×D3semidirect
221. C22×Dic6C2×D3semidirect
257. C2×(C2×D3)⋊C4C2×D3semidirect
259. C2×C4⋊Dic3C2×D3semidirect
263. C2×Dic3⋊C4C2×D3semidirect
264. C2×Dic3⋊C4C2×D3semidirect
265. C2×Dic3⋊C4C2×D3semidirect
268. C2×C4×Dic3C2×D3semidirect
284. #67⋊C4C2×D3semidirect
285. #878C2×D3semidirect
290. C23×C32#41semidirect
305. C22×C3⋊D3#41semidirect
348. #624C2×D4semidirect
485. C2×C4×D3C22×D3semidirect
487. C2×Dic6C22×D3semidirect
515. (C2×D3)⋊C4C22×D3semidirect
517. C4⋊Dic3C22×D3semidirect
521. Dic3⋊C4C22×D3semidirect
522. Dic3⋊C4C22×D3semidirect
523. Dic3⋊C4C22×D3semidirect
526. C4×Dic3C22×D3semidirect
533. C22×C32C2×#41semidirect
547. C2×C3⋊D3C2×#41semidirect
627. C23×C3#235semidirect
628. C23×C3#239semidirect
767. C2×C32#525semidirect
865. C22×C3C2×#235semidirect
869. C22×C3C2×#239semidirect
940. C32C2×#525semidirect
963. C23#3799semidirect
1010. C2×C3#5547semidirect
1011. C2×C3#5627semidirect
1049. C22C2×#3799semidirect
1064. C3C2×#5547semidirect
1065. C3C2×#5627semidirect
1071. C2#10594066direct (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×#37992
C2×#640912
C2×C3×#67⋊C42
C2×C3×#8782
C2×#639812
C2×#639782
C2×#639522
C2×#639102
C2×#639042
C2×#638972
C2×#638942
C2×#638882
C2×#638542
C2×#638362
#105940662
C2×#56273
C2×#55473