Finite Group Databasebeta

← C2×#10595227 #11902732

Subgroups — C2×#10595227 #11902732

Order 1152.

3685 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64148C211yesmaximal, characteristic, complemented
4C2×C3×#940C211yesmaximal, characteristic, complemented
5C2×C3×#939C211yesmaximal, characteristic, complemented
6C2×#63979C211yesmaximal, characteristic, complemented
7C2×#63979C211yesmaximal, characteristic, complemented
8C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
9C2×Dic3×#67C211yesmaximal, characteristic, complemented
10C2×#63970C211yesmaximal, characteristic, complemented
11C2×#63958C211yesmaximal, characteristic, complemented
12#10595227C2116yesmaximal, direct product factor
13C2×#63886C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×#63880C211yesmaximal, characteristic, complemented
16C2×#63837C211yesmaximal, characteristic, complemented
17C2×#5718—31nomaximal
18C2×#5599—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic
29C23×C3×Dic3C2211yescharacteristic
30C22×C3×D12C2211yescharacteristic
31C22×#627C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic
35C22×#625C2211yescharacteristic
36C22×#625C2211yescharacteristic
37C22×#624C2211yescharacteristic
38C2×#3805—28no—
39C2×#3805C2218yescomplemented
40C2×#3804—28no—
41C2×#3804C2218yescomplemented
42C22×D3×Dic3C2211yescharacteristic
43C22×D3×Dic3C2211yescharacteristic
44C22×D3×Dic3C2211yescharacteristic
45C2×#3757C2211yescharacteristic
46#64148C2218yescomplemented
47C2×#3752C2211yescharacteristic
48C2×#3750C2211yescharacteristic
49C2×C3×#217C2211yescharacteristic
50C3×#940C2218yescomplemented
51C3×#939C2218yescomplemented
52C2×C3×(C2×D3)⋊C4C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54C2×C3×C4×Dic3C2211yescharacteristic
55#63979C2218yescomplemented
56#63979C2218yescomplemented
57#67⋊Dic3C2218yescomplemented
58Dic3×#67C2218yescomplemented
59#63970C2218yescomplemented
60C2×Dic3⋊Dic3C2211yescharacteristic
61C2×Dic3⋊Dic3C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2211yescharacteristic
63C2×(C2×D3)⋊Dic3C2211yescharacteristic
64#63958C2218yescomplemented
65C2×Dic32C2211yescharacteristic
66C2×Dic32C2211yescharacteristic
67#63886C2218yescomplemented
68#63885C2218yescomplemented
69#63880C2218yescomplemented
70#63837C2218yescomplemented
71C22×#237—31no—
72C22×#237—31no—
73C22×#237—31no—
74C22×#235—31no—
75C2×C3×#127—31no—
76C2×C3×#121—31no—
77C2×#940—31no—
78C2×#940—31no—
79C2×#940—31no—
80C2×#940—31no—
81C2×#940D311yescharacteristic, complemented
82C2×#939—31no—
83C2×#939—31no—
84C2×#939—31no—
85C2×#939—31no—
86C2×#939—31no—
87C2×#939—61no—
88C2×#939D311yescharacteristic, complemented
89C2×#938—31no—
90C2×#938—31no—
91C2×D4×Dic3—31no—
92C2×D4×Dic3—31no—
93C2×C4×#67—31no—
94#5718—316no—
95#5599—316no—
96C2×#895—31no—
97C2×#887—31no—
98C2×#884—31no—
99C2×#884—31no—
100C2×#67⋊C4—31no—
101C2×#67⋊C4—31no—
102C2×C4×D12—31no—
103C2×C4×Dic6—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C2×C32×D4—42no—
111C2×C32×D4C2314yes—
112C22×C32×C4C2311yescharacteristic
113C2×#638—24no—
114C2×#638—42no—
115C2×#638C2314yes—
116C2×#638C2314yes—
117C22×C3⋊Dic3—24no—
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2314yes—
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C2×C3×#67—24no—
123C2×C3×#67—24no—
124C2×C3×#67—24no—
125C2×C3×#67—24no—
126C2×C3×#67—24no—
127C2×C3×#67—42no—
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C2×C3×#67C2314yes—
132C2×C3×#67C2314yes—
133C2×C3×#67C2314yes—
134C22×C3×Dic3—24no—
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2314yes—
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C2×C3×D12—42no—
142C2×C3×D12C2314yes—
143C2×#627D418yescomplemented
144C2×#627C2314yes—
145C2×#626—24no—
146C2×#626—24no—
147C2×#626—42no—
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#625—24no—
152C2×#625—42no—
153C2×#625C2314yes—
154C2×#625C2314yes—
155C2×#624—24no—
156C2×#624C2314yes—
157#3805—232no—
158#3804—232no—
159C2×D3×Dic3—24no—
160C2×D3×Dic3—24no—
161C2×D3×Dic3—24no—
162C2×D3×Dic3C2314yes—
163C2×D3×Dic3C2314yes—
164C2×D3×Dic3C2314yes—
165#3757C2314yes—
166#3752C2314yes—
167#3750C2314yes—
168C3×#217C2314yes—
169C3×(C2×D3)⋊C4C2314yes—
170C3×Dic3⋊C4C2314yes—
171C3×C4×Dic3C2314yes—
172Dic3⋊Dic3C2314yes—
173Dic3⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175(C2×D3)⋊Dic3C2314yes—
176Dic32C2314yes—
177Dic32C2314yes—
178C2×#550—91noSylow
179C22×C3×D4—21no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4C2×D311yescharacteristic
188C22×C3×D4C2×D311yescharacteristic
189C23×C3×C4—31no—
190C22×#67—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—31no—
200C22×#67—31no—
201C22×#67—61no—
202C22×#67—61no—
203C22×#67C2×D311yescharacteristic
204C22×#67C2×D311yescharacteristic
205C22×#67C2×D311yescharacteristic
206C22×#67C2×D311yescharacteristic
207C22×#67C2×D311yescharacteristic
208C22×#67C2×D311yescharacteristic
209C23×Dic3—31no—
210C23×Dic3—31no—
211C23×Dic3—31no—
212C23×Dic3—31no—
213C23×Dic3—31no—
214C23×Dic3—61no—
215C23×Dic3C2×D311yescharacteristic
216C2×#237—38no—
217C2×#237—38no—
218C2×#237—38no—
219C2×#237—68no—
220C2×#237—68no—
221C2×#237—68no—
222C2×#235—38no—
223C2×#235—68no—
224C22×D12—31no—
225C22×D12—31no—
226C22×D12—31no—
227C22×D12C2×D311yescharacteristic
228C22×C4×D3—31no—
229C22×C4×D3—31no—
230C22×C4×D3—31no—
231C22×C4×D3—31no—
232C22×C4×D3—31no—
233C22×Dic6—31no—
234C22×Dic6—31no—
235C3×#127—38no—
236C3×#121—38no—
237C2×C3×C4⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×C3×C42—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—31no—
244C2×#217—31no—
245C2×#217—61no—
246C2×#217C2×D311yescharacteristic
247#940—38no—
248#940—38no—
249#940—38no—
250#940—38no—
251#940C2×D318yescomplemented
252#939—38no—
253#939—38no—
254#939—38no—
255#939—38no—
256#939—38no—
257#939—68no—
258#939C2×D318yescomplemented
259#938—38no—
260#938—38no—
261D4×Dic3—38no—
262D4×Dic3—38no—
263C4×#67—38no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—31no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—31no—
268C2×(C2×D3)⋊C4—61no—
269C2×(C2×D3)⋊C4C2×D311yescharacteristic
270C2×C4⋊Dic3—31no—
271C2×C4⋊Dic3—31no—
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×Dic3⋊C4—61no—
277C2×Dic3⋊C4C2×D311yescharacteristic
278C2×C4×Dic3—31no—
279C2×C4×Dic3—31no—
280C2×C4×Dic3—31no—
281C2×C4×Dic3—31no—
282C2×C4×Dic3C2×D311yescharacteristic
283#895—38no—
284#887—38no—
285#884—38no—
286#884—38no—
287#67⋊C4—38no—
288#67⋊C4—38no—
289C4×D12—38no—
290C4×Dic6—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32C2412yes—
298C23×C32C2412yes—
299C23×C32C2411yescharacteristic
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3C2412yes—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—22no—
313C22×C3×D3C2412yes—
314C22×C3×D3C2412yes—
315C22×C3×D3C2412yes—
316C32×D4—44no—
317C2×C32×C4—22no—
318C2×C32×C4C2412yes—
319#638—28no—
320#638—44no—
321C2×C3⋊Dic3—22no—
322C2×C3⋊Dic3—22no—
323C2×C3⋊Dic3—28no—
324C2×C3⋊Dic3C2×D414yes—
325C2×C3⋊Dic3C2412yes—
326C2×C3⋊Dic3C2412yes—
327C2×C3⋊Dic3C2412yes—
328C3×#67—28no—
329C3×#67—28no—
330C3×#67—28no—
331C3×#67—28no—
332C3×#67—28no—
333C3×#67—44no—
334C2×C3×Dic3—22no—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—28no—
337C2×C3×Dic3C2×D414yes—
338C2×C3×Dic3C2×D414yes—
339C2×C3×Dic3#4114yescomplemented
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C3×D12—44no—
346#627C2×D4116yescomplemented
347#626—28no—
348#626—28no—
349#626—44no—
350#625—28no—
351#625—44no—
352#624—28no—
353D3×Dic3—28no—
354D3×Dic3—28no—
355D3×Dic3—28no—
356C22×#41—91no—
357C22×#41—91no—
358#550—916no—
359C2×#127—31no—
360C2×#127—91no—
361C2×#127—91no—
362C2×#121—31no—
363C2×#121—91no—
364C2×#121—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×C4×Q8—91no—
369C2×C4×D4—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C24×C3—21no—
373C24×C3—21no—
374C24×C3—31no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3C22×D311yescharacteristic
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C24×C3C22×D311yescharacteristic
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—61no—
384C23×D3C22×D311yescharacteristic
385C23×D3C22×D311yescharacteristic
386C23×D3C22×D311yescharacteristic
387C2×C3×D4—24no—
388C2×C3×D4—34no—
389C2×C3×D4—34no—
390C2×C3×D4—34no—
391C2×C3×D4—34no—
392C2×C3×D4—34no—
393C2×C3×D4—34no—
394C2×C3×D4—34no—
395C2×C3×D4—42no—
396C2×C3×D4—42no—
397C2×C3×D4—44no—
398C2×C3×D4—64no—
399C2×C3×D4—64no—
400C2×C3×D4—64no—
401C2×C3×D4—64no—
402C2×C3×D4—64no—
403C2×C3×D4—122no—
404C2×C3×D4—122no—
405C2×C3×D4C22×D314yes—
406C2×C3×D4C22×D314yes—
407C22×C3×C4—21no—
408C22×C3×C4—31no—
409C22×C3×C4—31no—
410C22×C3×C4—31no—
411C22×C3×C4—31no—
412C22×C3×C4—31no—
413C22×C3×C4—34no—
414C22×C3×C4—64no—
415C22×C3×C4C22×D311yescharacteristic
416C22×C3×C4C22×D311yescharacteristic
417C2×#67—24no—
418C2×#67—24no—
419C2×#67—24no—
420C2×#67—24no—
421C2×#67—24no—
422C2×#67—34no—
423C2×#67—34no—
424C2×#67—34no—
425C2×#67—34no—
426C2×#67—34no—
427C2×#67—34no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—42no—
434C2×#67—64no—
435C2×#67—64no—
436C2×#67—64no—
437C2×#67—64no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—124no—
443C2×#67—122no—
444C2×#67—122no—
445C2×#67—122no—
446C2×#67—122no—
447C2×#67—122no—
448C2×#67—124no—
449C2×#67C22×D314yes—
450C2×#67C22×D314yes—
451C2×#67C22×D314yes—
452C2×#67C22×D314yes—
453C2×#67C22×D314yes—
454C2×#67C22×D314yes—
455C22×Dic3—24no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—34no—
459C22×Dic3—31no—
460C22×Dic3—31no—
461C22×Dic3—31no—
462C22×Dic3—31no—
463C22×Dic3—34no—
464C22×Dic3—34no—
465C22×Dic3—34no—
466C22×Dic3—34no—
467C22×Dic3—61no—
468C22×Dic3—61no—
469C22×Dic3—61no—
470C22×Dic3—64no—
471C22×Dic3—64no—
472C22×Dic3—64no—
473C22×Dic3—64no—
474C22×Dic3—64no—
475C22×Dic3—64no—
476C22×Dic3—124no—
477C22×Dic3C22×D311yescharacteristic
478C22×Dic3C22×D311yescharacteristic
479C22×Dic3C22×D314yes—
480C22×Dic3C22×D311yescharacteristic
481C22×Dic3C22×D311yescharacteristic
482C22×Dic3C22×D311yescharacteristic
483#237—632no—
484#237—632no—
485#237—632no—
486#235—632no—
487C2×D12—34no—
488C2×D12—34no—
489C2×D12—34no—
490C2×D12—42no—
491C2×D12—64no—
492C2×D12—64no—
493C2×D12—122no—
494C2×D12C22×D314yes—
495C2×C4×D3—34no—
496C2×C4×D3—34no—
497C2×C4×D3—34no—
498C2×C4×D3—34no—
499C2×C4×D3—34no—
500C2×C4×D3—64no—
501C2×C4×D3—64no—
502C2×C4×D3—64no—
503C2×C4×D3—64no—
504C2×C4×D3—64no—
505C2×Dic6—38no—
506C2×Dic6—38no—
507C2×Dic6—34no—
508C2×Dic6—34no—
509C3×C4⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4—34no—
512C3×C42—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—34no—
517#217—64no—
518#217C22×D314yes—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—64no—
524(C2×D3)⋊C4C22×D314yes—
525C4⋊Dic3—34no—
526C4⋊Dic3—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—64no—
532Dic3⋊C4C22×D314yes—
533C4×Dic3—34no—
534C4×Dic3—34no—
535C4×Dic3—34no—
536C4×Dic3—34no—
537C4×Dic3C22×D314yes—
538C22×C32—22no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—44no—
545C22×C32—44no—
546C22×C32C22×D412yes—
547C22×C32C2×#4112yes—
548C22×C32H(5,𝔽2)12yes—
549C22×C32C2511yescharacteristic
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—44no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—44no—
564C2×C3×D3—44no—
565C2×C3×D3—44no—
566C32×C4—22no—
567C3⋊Dic3—22no—
568C3⋊Dic3—22no—
569C3⋊Dic3C22×D414yes—
570C3×Dic3—22no—
571C3×Dic3—22no—
572C3×Dic3C22×D414yes—
573C3×Dic3C22×D414yes—
574C3×Dic3C2×#4114yescomplemented
575C2×#41—98no—
576C2×#41—98no—
577C2×#41—188no—
578C2×#41—188no—
579C22×Q8—91no—
580C22×D4—31no—
581C22×D4—31no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4D3211yescharacteristic
595C23×C4—31no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601#127—38no—
602#127—98no—
603#127—98no—
604#121—38no—
605#121—98no—
606#121—98no—
607#121—98no—
608#121—98no—
609#121—98no—
610C4×Q8—98no—
611C4×D4—98no—
612C4×D4—98no—
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—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C42—31no—
625C2×C42—91no—
626C2×C42—91no—
627C23×C3—24no—
628C23×C3—22no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
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—21no—
643C23×C3—32no—
644C23×C3—32no—
645C23×C3—32no—
646C23×C3—42no—
647C23×C3—42no—
648C23×C3—42no—
649C23×C3—42no—
650C23×C3—42no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3—62no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—62no—
660C23×C3C23×D312yes—
661C23×C3C23×D312yes—
662C23×C3C23×D312yes—
663C23×C3C23×D312yes—
664C23×C3C23×D311yescharacteristic
665C23×C3C23×D311yescharacteristic
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—22no—
675C22×D3—32no—
676C22×D3—32no—
677C22×D3—62no—
678C22×D3—62no—
679C22×D3—62no—
680C22×D3—62no—
681C22×D3—62no—
682C22×D3—62no—
683C22×D3—62no—
684C22×D3—122no—
685C22×D3—122no—
686C22×D3—122no—
687C22×D3C23×D312yes—
688C22×D3C23×D312yes—
689C22×D3C23×D312yes—
690C3×D4—44no—
691C3×D4—44no—
692C3×D4—48no—
693C3×D4—68no—
694C3×D4—68no—
695C3×D4—68no—
696C3×D4—68no—
697C3×D4—68no—
698C3×D4—124no—
699C3×D4—124no—
700C2×C3×C4—22no—
701C2×C3×C4—22no—
702C2×C3×C4—22no—
703C2×C3×C4—34no—
704C2×C3×C4—34no—
705C2×C3×C4—34no—
706C2×C3×C4—32no—
707C2×C3×C4—32no—
708C2×C3×C4—32no—
709C2×C3×C4—32no—
710C2×C3×C4—32no—
711C2×C3×C4—42no—
712C2×C3×C4—68no—
713C2×C3×C4—62no—
714C2×C3×C4—62no—
715C2×C3×C4C23×D312yes—
716C2×C3×C4C23×D312yes—
717#67—28no—
718#67—28no—
719#67—28no—
720#67—28no—
721#67—28no—
722#67—44no—
723#67—68no—
724#67—68no—
725#67—68no—
726#67—68no—
727#67—68no—
728#67—68no—
729#67—128no—
730#67—124no—
731#67—124no—
732#67—124no—
733#67—124no—
734#67—124no—
735#67—128no—
736C2×Dic3—22no—
737C2×Dic3—22no—
738C2×Dic3—28no—
739C2×Dic3—34no—
740C2×Dic3—34no—
741C2×Dic3—32no—
742C2×Dic3—32no—
743C2×Dic3—32no—
744C2×Dic3—32no—
745C2×Dic3—32no—
746C2×Dic3—32no—
747C2×Dic3—64no—
748C2×Dic3—62no—
749C2×Dic3—62no—
750C2×Dic3—62no—
751C2×Dic3—68no—
752C2×Dic3—68no—
753C2×Dic3—68no—
754C2×Dic3—62no—
755C2×Dic3—62no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—68no—
759C2×Dic3—68no—
760C2×Dic3—128no—
761C2×Dic3—122no—
762C2×Dic3—122no—
763C2×Dic3D3×D414yes—
764C2×Dic3D3×D414yes—
765C2×Dic3#23714yescomplemented
766C2×Dic3C23×D312yes—
767C2×Dic3C23×D312yes—
768C2×Dic3C23×D312yes—
769C2×Dic3C23×D312yes—
770C2×Dic3C23×D312yes—
771D12—44no—
772D12—68no—
773D12—68no—
774D12—124no—
775C4×D3—68no—
776C4×D3—68no—
777C4×D3—68no—
778C4×D3—68no—
779C4×D3—68no—
780Dic6—316no—
781Dic6—316no—
782C2×C32—42no—
783C2×C32—42no—
784C2×C32#55014yescomplemented
785C2×C32C23×D411yescharacteristic
786C2×C32C22×#4111yescharacteristic
787C2×C32C2×H(5,𝔽2)11yescharacteristic
788C3⋊D3—42no—
789C3×D3—42no—
790C3×D3—42no—
791C3×D3—42no—
792C24—31no—
793C24—31no—
794C24—31no—
795C24—91no—
796C24C2×D3211yescharacteristic
797C24C2×D3211yescharacteristic
798#41—1832no—
799#41—1832no—
800C2×Q8—94no—
801C2×Q8—98no—
802C2×D4—34no—
803C2×D4—34no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—34no—
808C2×D4—34no—
809C2×D4—42no—
810C2×D4—64no—
811C2×D4—64no—
812C2×D4—64no—
813C2×D4—64no—
814C2×D4—64no—
815C2×D4—94no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4—94no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—122no—
823C2×D4—122no—
824C2×D4—184no—
825C2×D4—184no—
826C2×D4—184no—
827C2×D4—184no—
828C2×D4—362no—
829C2×D4—362no—
830C2×D4—362no—
831C2×D4C2×D3214yes—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—31no—
835C22×C4—34no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—64no—
839C22×C4—94no—
840C22×C4—94no—
841C22×C4—94no—
842C22×C4—94no—
843C22×C4—91no—
844C22×C4—94no—
845C22×C4—91no—
846C22×C4—91no—
847C22×C4—184no—
848C22×C4—184no—
849C22×C4—184no—
850C22×C4—184no—
851C22×C4—184no—
852C22×C4C2×D3211yescharacteristic
853C4⋊C4—34no—
854C4⋊C4—94no—
855C4⋊C4—94no—
856C4⋊C4—94no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C42—34no—
864C42—94no—
865C42—94no—
866C22×C3—24no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—21no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—42no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—48no—
889C22×C3—44no—
890C22×C3—44no—
891C22×C3—44no—
892C22×C3—44no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—84no—
903C22×C3—124no—
904C22×C3—124no—
905C22×C3—124no—
906C22×C3C2×D3×D412yes—
907C22×C3C2×D3×D412yes—
908C22×C3C2×#23712yes—
909C22×C3#100412yes—
910C22×C3#100412yes—
911C22×C3D3×#4112yes—
912C22×C3C24×D311yescharacteristic
913C22×C3C24×D311yescharacteristic
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—44no—
924C2×D3—44no—
925C2×D3—44no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—122no—
933C2×D3—122no—
934C2×D3—122no—
935C2×D3—124no—
936C2×D3—124no—
937C2×D3—244no—
938C3×C4—22no—
939C3×C4—22no—
940C3×C4—34no—
941C3×C4—34no—
942C3×C4—34no—
943C3×C4—42no—
944C3×C4—62no—
945C3×C4—62no—
946Dic3—22no—
947Dic3—22no—
948Dic3—34no—
949Dic3—34no—
950Dic3—64no—
951Dic3—62no—
952Dic3—62no—
953Dic3—62no—
954Dic3—62no—
955Dic3—122no—
956Dic3—122no—
957Dic3C2×D3×D414yes—
958Dic3C2×D3×D414yes—
959Dic3C2×#23714yescomplemented
960C32C2×#55011yescharacteristic, complemented, Sylow
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—32no—
968C23—32no—
969C23—32no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—92no—
980C23—182no—
981C23—182no—
982C23—182no—
983C23C22×D3212yes—
984C23C22×D3212yes—
985C23C22×D3211yescharacteristic
986Q8—916no—
987D4—44no—
988D4—68no—
989D4—68no—
990D4—68no—
991D4—68no—
992D4—68no—
993D4—124no—
994D4—124no—
995D4—188no—
996D4—188no—
997D4—188no—
998D4—188no—
999D4—364no—
1000D4—364no—
1001D4—364no—
1002C2×C4—22no—
1003C2×C4—34no—
1004C2×C4—34no—
1005C2×C4—34no—
1006C2×C4—32no—
1007C2×C4—32no—
1008C2×C4—32no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—68no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—94no—
1015C2×C4—92no—
1016C2×C4—92no—
1017C2×C4—92no—
1018C2×C4—188no—
1019C2×C4—188no—
1020C2×C4—188no—
1021C2×C4—188no—
1022C2×C4—188no—
1023C2×C4—182no—
1024C2×C4—182no—
1025C2×C4C22×D3212yes—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—24no—
1030C2×C3—44no—
1031C2×C3—42no—
1032C2×C3—42no—
1033C2×C3—42no—
1034C2×C3—42no—
1035C2×C3—82no—
1036C2×C3—122no—
1037C2×C3—122no—
1038C2×C3—122no—
1039C2×C3#559914yescomplemented
1040C2×C3#571814yescomplemented
1041C2×C3C22×D3×D411yescharacteristic
1042C2×C3C22×D3×D411yescharacteristic
1043C2×C3C22×#23711yescharacteristic
1044C2×C3C2×#100411yescharacteristic
1045C2×C3C2×#100411yescharacteristic
1046C2×C3C2×D3×#4111yescharacteristic
1047D3—42no—
1048D3—42no—
1049D3—42no—
1050D3—122no—
1051D3—122no—
1052D3—242no—
1053C22—22no—
1054C22—22no—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—44no—
1060C22—44no—
1061C22—62no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—62no—
1070C22—124no—
1071C22—124no—
1072C22—124no—
1073C22—182no—
1074C22—182no—
1075C22—182no—
1076C22—364no—
1077C22D32×D412yes—
1078C22D3×#23712yes—
1079C22#6433012yes—
1080C22C23×D3211yescharacteristic
1081C4—22no—
1082C4—34no—
1083C4—34no—
1084C4—34no—
1085C4—62no—
1086C4—62no—
1087C4—94no—
1088C4—182no—
1089C4—182no—
1090C3—21no—
1091C3C2×#559911yescharacteristic, complemented
1092C3C2×#571811yescharacteristic, complemented
1093C2—42no—
1094C2—42no—
1095C2—122no—
1096C2—122no—
1097C2—122no—
1098C2—362no—
1099C2#1059522714yesdirect product factor
1100C2C2×D32×D411yescharacteristic
1101C2C2×D3×#23711yescharacteristic
1102C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C22×#3804C2semidirect
3. C2×#64148C2semidirect
4. C2×C3×#940C2semidirect
5. C2×C3×#939C2semidirect
6. C2×#63979C2semidirect
7. C2×#63979C2semidirect
8. C2×#67⋊Dic3C2semidirect
9. C2×Dic3×#67C2semidirect
10. C2×#63970C2semidirect
11. C2×#63958C2semidirect
12. #10595227C2direct (N × H)
13. C2×#63886C2semidirect
14. C2×#63885C2semidirect
15. C2×#63880C2semidirect
16. C2×#63837C2semidirect
39. C2×#3805C22semidirect
41. C2×#3804C22semidirect
46. #64148C22semidirect
50. C3×#940C22semidirect
51. C3×#939C22semidirect
55. #63979C22semidirect
56. #63979C22semidirect
57. #67⋊Dic3C22semidirect
58. Dic3×#67C22semidirect
59. #63970C22semidirect
64. #63958C22semidirect
67. #63886C22semidirect
68. #63885C22semidirect
69. #63880C22semidirect
70. #63837C22semidirect
81. C2×#940D3semidirect
88. C2×#939D3semidirect
143. C2×#627D4semidirect
251. #940C2×D3semidirect
258. #939C2×D3semidirect
339. C2×C3×Dic3#41semidirect
346. #627C2×D4semidirect
574. C3×Dic3C2×#41semidirect
765. C2×Dic3#237semidirect
784. C2×C32#550semidirect
959. Dic3C2×#237semidirect
960. C32C2×#550semidirect
1039. C2×C3#5599semidirect
1040. C2×C3#5718semidirect
1091. C3C2×#5599semidirect
1092. C3C2×#5718semidirect
1099. C2#10595227direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C22×#38042
C2×#641482
C2×C3×#9402
C2×C3×#9392
C2×#639792
C2×#67⋊Dic32
C2×Dic3×#672
C2×#639702
C2×#639582
#105952272
C2×#638862
C2×#638852
C2×#638802
C2×#638372
C2×#57183
C2×#55993