Finite Group Databasebeta

← C2×#10594368 #11901168

Subgroups — C2×#10594368 #11901168

Order 1152.

3441 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64105C211yesmaximal, characteristic, complemented
4C2×C3×#896C211yesmaximal, characteristic, complemented
5C2×C3×#895C211yesmaximal, characteristic, complemented
6C2×#63912C211yesmaximal, characteristic, complemented
7C2×#63906C211yesmaximal, characteristic, complemented
8C2×#63906C211yesmaximal, characteristic, complemented
9C2×#63896C211yesmaximal, characteristic, complemented
10C2×#63887C211yesmaximal, characteristic, complemented
11C2×#63886C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10594368C2116yesmaximal, direct product factor
17C2×#5629—31nomaximal
18C2×#5597—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic
35C22×D3×Dic3C2211yescharacteristic
36C22×D3×Dic3C2211yescharacteristic
37C22×D3×Dic3C2211yescharacteristic
38C2×#3796—28no—
39C2×#3796C2218yescomplemented
40C2×#3795—28no—
41C2×#3795C2218yescomplemented
42C2×C32×C4⋊C4C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3750C2211yescharacteristic
46C2×#3750C2211yescharacteristic
47#64105C2218yescomplemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic
52C2×C3×Dic3⋊C4C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54C3×#896C2218yescomplemented
55C3×#895C2218yescomplemented
56C2×#3724C2211yescharacteristic
57C2×Dic3⋊Dic3C2211yescharacteristic
58C2×Dic3⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61#63912C2218yescomplemented
62#63906C2218yescomplemented
63#63906C2218yescomplemented
64#63896C2218yescomplemented
65#63887C2218yescomplemented
66#63886C2218yescomplemented
67#63886C2218yescomplemented
68#63885C2218yescomplemented
69#63885C2218yescomplemented
70D3×Dic3⋊C4C2218yescomplemented
71C22×#239—31no—
72C22×#237—31no—
73C22×#237—31no—
74C22×#235—31no—
75C2×C3×C22⋊Q8—31no—
76C2×C3×#121—31no—
77C2×#946—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#939—31no—
82C2×#930—31no—
83C2×#930—31no—
84C22×Dic3⋊C4—31no—
85#5629—316no—
86#5597—316no—
87C2×#896—31no—
88C2×#896—31no—
89C2×#896—31no—
90C2×#896—61no—
91C2×#896D311yescharacteristic, complemented
92C2×#895—31no—
93C2×#895—31no—
94C2×#895D311yescharacteristic, complemented
95C2×D3×C4⋊C4—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#884—31no—
99C2×#884—31no—
100C2×#884—31no—
101C2×#884—31no—
102C2×#878—31no—
103C2×#878—31no—
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4×C3⋊D3—24no—
116C2×C4×C3⋊D3C2314yes—
117C2×#634—24no—
118C2×#634C2314yes—
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×D12—24no—
124C2×C3×D12—24no—
125C2×C3×D12—42no—
126C2×C3×D12C2314yes—
127C2×C3×D12C2314yes—
128C2×C3×D12C2314yes—
129C2×C3×C4×D3—24no—
130C2×C3×C4×D3—42no—
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2314yes—
133C2×C3×Dic6—24no—
134C2×C3×Dic6C2314yes—
135C2×#626—24no—
136C2×#626—24no—
137C2×#626—42no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#625—24no—
144C2×#625—24no—
145C2×#625—42no—
146C2×#625C2314yes—
147C2×#625C2314yes—
148C2×#625C2314yes—
149C2×D3×Dic3—24no—
150C2×D3×Dic3—24no—
151C2×D3×Dic3—42no—
152C2×D3×Dic3D418yescomplemented
153C2×D3×Dic3C2314yes—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2314yes—
156C2×D3×Dic3C2314yes—
157#3796—232no—
158#3795—232no—
159C32×C4⋊C4C2314yes—
160#3752C2314yes—
161#3752C2314yes—
162#3750C2314yes—
163#3750C2314yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2314yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2314yes—
170#3724C2314yes—
171Dic3⋊Dic3C2314yes—
172Dic3⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175C2×#537—91noSylow
176C22×C3×Q8—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C23×C3×C4—31no—
181C23×C3×C4—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C23×Dic3—31no—
193C23×Dic3—31no—
194C23×Dic3—31no—
195C23×Dic3—31no—
196C2×#239—38no—
197C2×#239—68no—
198C2×#237—38no—
199C2×#237—38no—
200C2×#237—68no—
201C2×#237—68no—
202C2×#235—38no—
203C2×#235—68no—
204C22×D12—31no—
205C22×D12—31no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12C2×D311yescharacteristic
209C22×D12C2×D311yescharacteristic
210C22×D12C2×D311yescharacteristic
211C22×C4×D3—31no—
212C22×C4×D3—31no—
213C22×C4×D3—31no—
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3—61no—
218C22×C4×D3C2×D311yescharacteristic
219C22×C4×D3C2×D311yescharacteristic
220C22×Dic6—31no—
221C22×Dic6—31no—
222C22×Dic6—61no—
223C22×Dic6C2×D311yescharacteristic
224C3×C22⋊Q8—38no—
225C3×#121—38no—
226C2×C3×C4⋊C4—21no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4C2×D311yescharacteristic
230C2×C3×C4⋊C4C2×D311yescharacteristic
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×#217—31no—
236C2×#217—31no—
237#946—38no—
238#939—38no—
239#939—38no—
240#939—38no—
241#939—38no—
242#930—38no—
243#930—38no—
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—61no—
251C2×(C2×D3)⋊C4—61no—
252C2×(C2×D3)⋊C4C2×D311yescharacteristic
253C2×(C2×D3)⋊C4C2×D311yescharacteristic
254C2×(C2×D3)⋊C4C2×D311yescharacteristic
255C2×(C2×D3)⋊C4C2×D311yescharacteristic
256C2×C4⋊Dic3—31no—
257C2×C4⋊Dic3—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—31no—
262C2×Dic3⋊C4—31no—
263C2×Dic3⋊C4—31no—
264C2×Dic3⋊C4—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—38no—
267C2×Dic3⋊C4—61no—
268C2×Dic3⋊C4—61no—
269C2×Dic3⋊C4C2×D311yescharacteristic
270C2×Dic3⋊C4C2×D311yescharacteristic
271#896—38no—
272#896—38no—
273#896—38no—
274#896—68no—
275#896C2×D318yescomplemented
276#895—38no—
277#895—38no—
278#895C2×D318yescomplemented
279D3×C4⋊C4—38no—
280#884—38no—
281#884—38no—
282#884—38no—
283#884—38no—
284#884—38no—
285#884—38no—
286#878—38no—
287#878—38no—
288C23×C32C2411yescharacteristic
289C22×C3⋊D3—22no—
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3C2412yes—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3C2×D414yes—
305C22×C3×D3C2412yes—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C22×C3×D3C2412yes—
309C2×C32×C4—22no—
310C2×C32×C4—22no—
311C2×C32×C4—22no—
312C2×C32×C4C2412yes—
313C2×C32×C4C2412yes—
314C2×C32×C4C2412yes—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3—22no—
317C2×C3⋊Dic3C2×D414yes—
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
320C2×C3⋊Dic3C2412yes—
321C4×C3⋊D3—28no—
322#634—28no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3C2×D414yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C3×D12—28no—
332C3×D12—28no—
333C3×D12—44no—
334C3×C4×D3—28no—
335C3×C4×D3—44no—
336C3×Dic6—28no—
337#626—28no—
338#626—28no—
339#626—44no—
340#626—44no—
341#625—28no—
342#625—28no—
343#625—44no—
344D3×Dic3—28no—
345D3×Dic3—28no—
346D3×Dic3—44no—
347D3×Dic3C2×D4116yescomplemented
348C22×#41—91no—
349C22×#41—91no—
350#537—916no—
351C2×C22⋊Q8—31no—
352C2×C22⋊Q8—91no—
353C2×C22⋊Q8—91no—
354C2×C22⋊Q8—91no—
355C2×#121—31no—
356C2×#121—91no—
357C2×#121—91no—
358C2×#121—91no—
359C2×#121—91no—
360C2×#121—91no—
361C2×#121—91no—
362C2×#121—91no—
363C22×C4⋊C4—91no—
364C24×C3—31no—
365C24×C3—31no—
366C24×C3—31no—
367C24×C3—31no—
368C23×D3—31no—
369C23×D3—31no—
370C23×D3—61no—
371C23×D3C22×D311yescharacteristic
372C23×D3C22×D311yescharacteristic
373C23×D3C22×D311yescharacteristic
374C23×D3C22×D311yescharacteristic
375C2×C3×Q8—34no—
376C2×C3×Q8—64no—
377C2×C3×D4—34no—
378C2×C3×D4—34no—
379C2×C3×D4—34no—
380C2×C3×D4—64no—
381C2×C3×D4—64no—
382C2×C3×D4—122no—
383C22×C3×C4—21no—
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—34no—
391C22×C3×C4—34no—
392C22×C3×C4—64no—
393C22×C3×C4—122no—
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—64no—
411C2×#67—64no—
412C2×#67—64no—
413C2×#67—64no—
414C2×#67—64no—
415C2×#67—64no—
416C2×#67—122no—
417C2×#67—122no—
418C2×#67—122no—
419C2×#67—122no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—38no—
423C22×Dic3—34no—
424C22×Dic3—31no—
425C22×Dic3—31no—
426C22×Dic3—31no—
427C22×Dic3—31no—
428C22×Dic3—34no—
429C22×Dic3—34no—
430C22×Dic3—34no—
431C22×Dic3—61no—
432C22×Dic3—61no—
433C22×Dic3—61no—
434C22×Dic3—64no—
435C22×Dic3—64no—
436C22×Dic3—122no—
437C22×Dic3C22×D311yescharacteristic
438C22×Dic3C22×D311yescharacteristic
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441#239—632no—
442#237—632no—
443#237—632no—
444#235—632no—
445C2×D12—24no—
446C2×D12—24no—
447C2×D12—34no—
448C2×D12—34no—
449C2×D12—34no—
450C2×D12—34no—
451C2×D12—42no—
452C2×D12—64no—
453C2×D12—64no—
454C2×D12—122no—
455C2×D12—122no—
456C2×D12C22×D314yes—
457C2×D12C22×D314yes—
458C2×D12C22×D314yes—
459C2×C4×D3—24no—
460C2×C4×D3—38no—
461C2×C4×D3—34no—
462C2×C4×D3—34no—
463C2×C4×D3—34no—
464C2×C4×D3—34no—
465C2×C4×D3—34no—
466C2×C4×D3—34no—
467C2×C4×D3—42no—
468C2×C4×D3—64no—
469C2×C4×D3—64no—
470C2×C4×D3—64no—
471C2×C4×D3—64no—
472C2×C4×D3—64no—
473C2×C4×D3—124no—
474C2×C4×D3—122no—
475C2×C4×D3C22×D314yes—
476C2×C4×D3C22×D314yes—
477C2×Dic6—24no—
478C2×Dic6—34no—
479C2×Dic6—34no—
480C2×Dic6—64no—
481C2×Dic6—64no—
482C2×Dic6—64no—
483C2×Dic6—124no—
484C2×Dic6C22×D314yes—
485C3×C4⋊C4—24no—
486C3×C4⋊C4—34no—
487C3×C4⋊C4—34no—
488C3×C4⋊C4C22×D314yes—
489C3×C4⋊C4C22×D314yes—
490C3×C22⋊C4—34no—
491C3×C22⋊C4—34no—
492C3×C22⋊C4—34no—
493C3×C22⋊C4—34no—
494#217—34no—
495#217—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—64no—
503(C2×D3)⋊C4—64no—
504(C2×D3)⋊C4C22×D314yes—
505(C2×D3)⋊C4C22×D314yes—
506(C2×D3)⋊C4C22×D314yes—
507(C2×D3)⋊C4C22×D314yes—
508C4⋊Dic3—34no—
509C4⋊Dic3—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—64no—
519Dic3⋊C4—64no—
520Dic3⋊C4C22×D314yes—
521Dic3⋊C4C22×D314yes—
522C22×C32C22×D412yes—
523C22×C32H(5,𝔽2)12yes—
524C22×C322−1+412yes—
525C22×C32C2511yescharacteristic
526C2×C3⋊D3—22no—
527C2×C3⋊D3—22no—
528C2×C3⋊D3—22no—
529C2×C3⋊D3—44no—
530C2×C3×D3—28no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—44no—
543C2×C3×D3—44no—
544C2×C3×D3—44no—
545C2×C3×D3C22×D414yes—
546C32×C4—22no—
547C32×C4—22no—
548C32×C4—22no—
549C3⋊Dic3—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3C22×D414yes—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3C22×D414yes—
556C2×#41—98no—
557C2×#41—98no—
558C2×#41—188no—
559C2×#41—188no—
560C22×Q8—31no—
561C22×Q8—91no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—91no—
566C22×D4—91no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C23×C4—31no—
573C23×C4—31no—
574C23×C4—91no—
575C23×C4—91no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—91no—
579C22⋊Q8—38no—
580C22⋊Q8—98no—
581C22⋊Q8—98no—
582C22⋊Q8—98no—
583#121—38no—
584#121—98no—
585#121—98no—
586#121—98no—
587#121—98no—
588#121—98no—
589#121—98no—
590#121—98no—
591C2×C4⋊C4—31no—
592C2×C4⋊C4—31no—
593C2×C4⋊C4—98no—
594C2×C4⋊C4—91no—
595C2×C4⋊C4—91no—
596C2×C4⋊C4—91no—
597C2×C4⋊C4—91no—
598C2×C4⋊C4—91no—
599C2×C4⋊C4D3211yescharacteristic
600C2×C22⋊C4—31no—
601C2×C22⋊C4—31no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—31no—
604C2×C22⋊C4—91no—
605C2×C22⋊C4—91no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4—91no—
608C23×C3—21no—
609C23×C3—34no—
610C23×C3—32no—
611C23×C3—32no—
612C23×C3—32no—
613C23×C3—32no—
614C23×C3—62no—
615C23×C3—62no—
616C23×C3—62no—
617C23×C3—62no—
618C23×C3—62no—
619C23×C3—62no—
620C23×C3—62no—
621C23×C3—62no—
622C23×C3—62no—
623C23×C3—62no—
624C23×C3—62no—
625C23×C3C23×D311yescharacteristic
626C23×C3C23×D311yescharacteristic
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—32no—
639C22×D3—32no—
640C22×D3—62no—
641C22×D3—64no—
642C22×D3—62no—
643C22×D3—62no—
644C22×D3—62no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3D3×D414yes—
651C22×D3C23×D312yes—
652C22×D3C23×D312yes—
653C22×D3C23×D312yes—
654C22×D3C23×D312yes—
655C3×Q8—68no—
656C3×D4—68no—
657C3×D4—68no—
658C3×D4—124no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—34no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—42no—
674C2×C3×C4—42no—
675C2×C3×C4—42no—
676C2×C3×C4—68no—
677C2×C3×C4—62no—
678C2×C3×C4—62no—
679C2×C3×C4—62no—
680C2×C3×C4—124no—
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D312yes—
683C2×C3×C4C23×D312yes—
684C2×C3×C4C23×D312yes—
685C2×C3×C4C23×D312yes—
686C2×C3×C4C23×D312yes—
687#67—68no—
688#67—68no—
689#67—68no—
690#67—68no—
691#67—68no—
692#67—68no—
693#67—124no—
694#67—124no—
695#67—124no—
696#67—124no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—34no—
701C2×Dic3—34no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—316no—
705C2×Dic3—32no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—32no—
709C2×Dic3—64no—
710C2×Dic3—62no—
711C2×Dic3—62no—
712C2×Dic3—62no—
713C2×Dic3—68no—
714C2×Dic3—62no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—68no—
719C2×Dic3—122no—
720C2×Dic3—122no—
721C2×Dic3—124no—
722C2×Dic3D3×D414yes—
723C2×Dic3C23×D312yes—
724C2×Dic3C23×D312yes—
725C2×Dic3C23×D312yes—
726C2×Dic3C23×D312yes—
727D12—28no—
728D12—28no—
729D12—44no—
730D12—68no—
731D12—68no—
732D12—124no—
733D12—124no—
734C4×D3—28no—
735C4×D3—316no—
736C4×D3—44no—
737C4×D3—68no—
738C4×D3—68no—
739C4×D3—68no—
740C4×D3—68no—
741C4×D3—128no—
742C4×D3—124no—
743Dic6—28no—
744Dic6—68no—
745Dic6—68no—
746Dic6—128no—
747C2×C32#53714yescomplemented
748C2×C32C23×D411yescharacteristic
749C2×C32C2×H(5,𝔽2)11yescharacteristic
750C2×C32C2×2−1+411yescharacteristic
751C3⋊D3—42no—
752C3×D3—24no—
753C3×D3—42no—
754C3×D3—42no—
755C3×D3—42no—
756C24—31no—
757C24—31no—
758C24—31no—
759C24—31no—
760C24—91no—
761#41—1832no—
762#41—1832no—
763C2×Q8—34no—
764C2×Q8—64no—
765C2×Q8—94no—
766C2×Q8—184no—
767C2×D4—34no—
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—64no—
771C2×D4—64no—
772C2×D4—94no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—94no—
776C2×D4—94no—
777C2×D4—94no—
778C2×D4—94no—
779C2×D4—122no—
780C2×D4—184no—
781C2×D4—184no—
782C2×D4—184no—
783C2×D4—184no—
784C2×D4—362no—
785C2×D4—362no—
786C2×D4—362no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—34no—
792C22×C4—34no—
793C22×C4—64no—
794C22×C4—94no—
795C22×C4—98no—
796C22×C4—94no—
797C22×C4—94no—
798C22×C4—94no—
799C22×C4—91no—
800C22×C4—91no—
801C22×C4—91no—
802C22×C4—94no—
803C22×C4—122no—
804C22×C4—184no—
805C22×C4—184no—
806C22×C4—184no—
807C22×C4—362no—
808C22×C4C2×D3211yescharacteristic
809C22×C4C2×D3211yescharacteristic
810C22×C4C2×D3211yescharacteristic
811C4⋊C4—34no—
812C4⋊C4—34no—
813C4⋊C4—94no—
814C4⋊C4—94no—
815C4⋊C4—94no—
816C4⋊C4—94no—
817C4⋊C4—94no—
818C4⋊C4C2×D3214yes—
819C22⋊C4—34no—
820C22⋊C4—34no—
821C22⋊C4—34no—
822C22⋊C4—34no—
823C22⋊C4—94no—
824C22⋊C4—94no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—21no—
831C22×C3—34no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—68no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—124no—
845C22×C3—124no—
846C22×C3—124no—
847C22×C3C2×D3×D412yes—
848C22×C3C2×D3×D412yes—
849C22×C3#100412yes—
850C22×C3#100712yes—
851C22×C3#100912yes—
852C22×C3#101012yes—
853C22×C3C24×D311yescharacteristic
854C22×C3C24×D311yescharacteristic
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—28no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—44no—
868C2×D3—44no—
869C2×D3—44no—
870C2×D3—64no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—122no—
878C2×D3—122no—
879C2×D3—128no—
880C2×D3—124no—
881C2×D3—124no—
882C2×D3C2×D3×D414yes—
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—22no—
888C3×C4—22no—
889C3×C4—34no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—42no—
893C3×C4—62no—
894C3×C4—62no—
895C3×C4—62no—
896Dic3—22no—
897Dic3—22no—
898Dic3—22no—
899Dic3—34no—
900Dic3—34no—
901Dic3—64no—
902Dic3—62no—
903Dic3—62no—
904Dic3—62no—
905Dic3—62no—
906Dic3—122no—
907Dic3—122no—
908Dic3C2×D3×D414yes—
909C32C2×#53711yescharacteristic, complemented, Sylow
910C23—34no—
911C23—32no—
912C23—32no—
913C23—32no—
914C23—32no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—92no—
927C23—182no—
928C23—182no—
929C23—182no—
930C23C22×D3211yescharacteristic
931Q8—68no—
932Q8—188no—
933D4—68no—
934D4—68no—
935D4—124no—
936D4—188no—
937D4—188no—
938D4—188no—
939D4—188no—
940D4—364no—
941D4—364no—
942D4—364no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—34no—
947C2×C4—32no—
948C2×C4—32no—
949C2×C4—32no—
950C2×C4—32no—
951C2×C4—68no—
952C2×C4—62no—
953C2×C4—62no—
954C2×C4—62no—
955C2×C4—916no—
956C2×C4—94no—
957C2×C4—92no—
958C2×C4—92no—
959C2×C4—92no—
960C2×C4—124no—
961C2×C4—188no—
962C2×C4—188no—
963C2×C4—188no—
964C2×C4—182no—
965C2×C4—182no—
966C2×C4—364no—
967C2×C4C22×D3212yes—
968C2×C4C22×D3212yes—
969C2×C4C22×D3212yes—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—24no—
973C2×C3—21no—
974C2×C3—64no—
975C2×C3—122no—
976C2×C3—122no—
977C2×C3—122no—
978C2×C3#559714yescomplemented
979C2×C3#562914yescomplemented
980C2×C3C22×D3×D411yescharacteristic
981C2×C3C22×D3×D411yescharacteristic
982C2×C3C2×#100411yescharacteristic
983C2×C3C2×#100711yescharacteristic
984C2×C3C2×#100911yescharacteristic
985C2×C3C2×#101011yescharacteristic
986D3—24no—
987D3—42no—
988D3—42no—
989D3—42no—
990D3—124no—
991D3—122no—
992D3—122no—
993C22—34no—
994C22—62no—
995C22—68no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—62no—
1005C22—62no—
1006C22—124no—
1007C22—124no—
1008C22—124no—
1009C22—182no—
1010C22—182no—
1011C22—182no—
1012C22—364no—
1013C22#6430712yes—
1014C22D32×D412yes—
1015C22#6431512yes—
1016C22C23×D3211yescharacteristic
1017C4—22no—
1018C4—22no—
1019C4—22no—
1020C4—34no—
1021C4—62no—
1022C4—62no—
1023C4—62no—
1024C4—94no—
1025C4—182no—
1026C4—182no—
1027C3—21no—
1028C3C2×#559711yescharacteristic, complemented
1029C3C2×#562911yescharacteristic, complemented
1030C2—64no—
1031C2—122no—
1032C2—122no—
1033C2—122no—
1034C2—362no—
1035C2#1059436814yesdirect product factor
1036C2C2×#6430711yescharacteristic
1037C2C2×D32×D411yescharacteristic
1038C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3796C2semidirect
2. C22×#3795C2semidirect
3. C2×#64105C2semidirect
4. C2×C3×#896C2semidirect
5. C2×C3×#895C2semidirect
6. C2×#63912C2semidirect
7. C2×#63906C2semidirect
8. C2×#63906C2semidirect
9. C2×#63896C2semidirect
10. C2×#63887C2semidirect
11. C2×#63886C2semidirect
12. C2×#63886C2semidirect
13. C2×#63885C2semidirect
14. C2×#63885C2semidirect
15. C2×D3×Dic3⋊C4C2semidirect
16. #10594368C2direct (N × H)
39. C2×#3796C22semidirect
41. C2×#3795C22semidirect
47. #64105C22semidirect
54. C3×#896C22semidirect
55. C3×#895C22semidirect
61. #63912C22semidirect
62. #63906C22semidirect
63. #63906C22semidirect
64. #63896C22semidirect
65. #63887C22semidirect
66. #63886C22semidirect
67. #63886C22semidirect
68. #63885C22semidirect
69. #63885C22semidirect
70. D3×Dic3⋊C4C22semidirect
91. C2×#896D3semidirect
94. C2×#895D3semidirect
152. C2×D3×Dic3D4semidirect
275. #896C2×D3semidirect
278. #895C2×D3semidirect
347. D3×Dic3C2×D4semidirect
747. C2×C32#537semidirect
909. C32C2×#537semidirect
978. C2×C3#5597semidirect
979. C2×C3#5629semidirect
1028. C3C2×#5597semidirect
1029. C3C2×#5629semidirect
1035. C2#10594368direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C22×#37952
C2×#641052
C2×C3×#8962
C2×C3×#8952
C2×#639122
C2×#639062
C2×#638962
C2×#638872
C2×#638862
C2×#638852
C2×D3×Dic3⋊C42
#105943682
C2×#56293
C2×#55973