Finite Group Databasebeta

← C2×#10594162 #11901319

Subgroups — C2×#10594162 #11901319

Order 1152.

3003 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63975C211yesmaximal, characteristic, complemented
6C2×#63974C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63910C211yesmaximal, characteristic, complemented
10C2×#63894C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63888C211yesmaximal, characteristic, complemented
13C2×#63880C211yesmaximal, characteristic, complemented
14C2×#63868C211yesmaximal, characteristic, complemented
15C2×#63864C211yesmaximal, characteristic, complemented
16#10594162C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5678—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic, complemented
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic, complemented
28C22×#624C2211yescharacteristic
29C22×#624C2211yescharacteristic
30C22×#624C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35#64091C2218yescomplemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×C4×Dic3C2211yescharacteristic, complemented
45C2×C3×C4×Dic3C2211yescharacteristic, complemented
46C3×#885C2218yescomplemented
47C3×#879C2218yescomplemented
48#63981C2218yescomplemented
49#63975C2218yescomplemented
50#63974C2218yescomplemented
51#63971C2218yescomplemented
52C2×#3724C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×Dic3⋊Dic3C2211yescharacteristic, complemented
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×#3722C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic, complemented
61#63910C2218yescomplemented
62#63910C2218yescomplemented
63#63894C2218yescomplemented
64#63890C2218yescomplemented
65#63888C2218yescomplemented
66#63880C2218yescomplemented
67#63868C2218yescomplemented
68#63864C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#124—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#939—31no—
74C2×#937—31no—
75#5704—316no—
76#5678—316no—
77C2×#898—31no—
78C2×#896—31no—
79C2×#895—31no—
80C2×#895—31no—
81C2×#894—31no—
82C2×#893—31no—
83C2×#886—31no—
84C2×#885D311yescharacteristic, complemented
85C2×#884—31no—
86C2×#884—31no—
87C2×#884—31no—
88C2×#883—31no—
89C2×#883—31no—
90C2×#882—31no—
91C2×#882—31no—
92C2×#882—31no—
93C2×#882—61no—
94C2×#67⋊C4—31no—
95C2×D3×C22⋊C4—31no—
96C2×D3×C22⋊C4—31no—
97C2×#879D311yescharacteristic, complemented
98C2×#876—31no—
99C2×#875—31no—
100C2×C4×D12—31no—
101C2×C4×D12—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3—24no—
104C23×C3⋊D3—42no—
105C23×C3⋊D3—42no—
106C23×C3⋊D3C2311yescharacteristic
107C23×C3⋊D3C2311yescharacteristic
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3×D3C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C2×#638—42no—
114C2×#638C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C4⋊(C3⋊D3)—24no—
117C2×C4⋊(C3⋊D3)—42no—
118C2×C4⋊(C3⋊D3)C2314yes—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C3×#67—42no—
121C2×C3×#67C2314yes—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×Dic6—42no—
130C2×C3×Dic6C2314yescomplemented
131C2×#626—24no—
132C2×#626—42no—
133C2×#626—42no—
134C2×#626C2314yes—
135C2×#626C2314yes—
136C2×#626C2314yescomplemented
137C2×#624—42no—
138C2×#624—42no—
139C2×#624—42no—
140C2×#624C2314yes—
141C2×#624C2314yes—
142C2×#624C2314yescomplemented
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yescomplemented
145C32×C22⋊C4C2314yes—
146#3752C2314yes—
147#3752C2314yes—
148C3×#217C2314yes—
149C3×#217C2314yes—
150C3×#217C2314yes—
151C3×(C2×D3)⋊C4C2314yescomplemented
152C3×(C2×D3)⋊C4C2314yescomplemented
153C3×C4⋊Dic3C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156C3×C4×Dic3C2314yescomplemented
157C3×C4×Dic3C2314yescomplemented
158#3724C2314yescomplemented
159Dic3⋊Dic3C2314yescomplemented
160Dic3⋊Dic3C2314yescomplemented
161#3722C2314yes—
162#3722C2314yes—
163#3722C2314yes—
164#3722C2314yes—
165#3722C2314yescomplemented
166#3722C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C24×D3—61no—
171C22×C3×Q8—31no—
172C22×C3×D4—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—61no—
179C22×#67C2×D311yescharacteristic
180C23×Dic3—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—61no—
189C22×D12—61no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×Dic6C2×D311yescharacteristic, complemented
198C3×#126—38no—
199C3×#124—38no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C22⋊C4—21no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4C2×D311yescharacteristic
210C2×C3×C22⋊C4C2×D311yescharacteristic
211C2×C3×C42—31no—
212C2×C3×C42—31no—
213C2×#217C2×D311yescharacteristic
214C2×#217C2×D311yescharacteristic
215C2×#217C2×D311yescharacteristic
216#947—38no—
217#946—38no—
218#939—38no—
219#937—38no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—61no—
237C2×(C2×D3)⋊C4—61no—
238C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
239C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3—31no—
242C2×C4⋊Dic3C2×D311yescharacteristic, complemented
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4C2×D311yescharacteristic, complemented
248C2×Dic3⋊C4C2×D311yescharacteristic, complemented
249C2×C4×Dic3C2×D311yescharacteristic, complemented
250C2×C4×Dic3C2×D311yescharacteristic, complemented
251#898—38no—
252#896—38no—
253#895—38no—
254#895—38no—
255#894—38no—
256#893—38no—
257#886—38no—
258#885C2×D318yescomplemented
259#884—38no—
260#884—38no—
261#884—38no—
262#883—38no—
263#883—38no—
264#882—38no—
265#882—38no—
266#882—38no—
267#882—68no—
268#67⋊C4—38no—
269D3×C22⋊C4—38no—
270D3×C22⋊C4—38no—
271#879C2×D318yescomplemented
272#876—38no—
273#875—38no—
274C4×D12—38no—
275C4×D12—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32C2412yes—
280C23×C32C2411yescharacteristic
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—22no—
289C22×C3⋊D3—28no—
290C22×C3⋊D3—44no—
291C22×C3⋊D3—44no—
292C22×C3⋊D3—416no—
293C22×C3⋊D3#4114yes—
294C22×C3⋊D3C2412yes—
295C22×C3⋊D3C2412yes—
296C22×C3⋊D3C2412yes—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3C2412yes—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304C2×C32×C4C2412yes—
305#638—44no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3C2412yes—
308C4⋊(C3⋊D3)—28no—
309C4⋊(C3⋊D3)—44no—
310C3×#67—44no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C3×Dic6—44no—
326#626—28no—
327#626—44no—
328#626—44no—
329#624—44no—
330#624—44no—
331#624—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—31no—
335C2×#126—91no—
336C2×#124—31no—
337C2×#124—91no—
338C2×#123—91no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—91no—
345C2×#120—91no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3C22×D311yescharacteristic
352C24×C3C22×D311yescharacteristic
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—31no—
359C23×D3—34no—
360C23×D3—34no—
361C23×D3—61no—
362C23×D3—61no—
363C23×D3—64no—
364C23×D3—61no—
365C23×D3—64no—
366C23×D3—64no—
367C23×D3—124no—
368C23×D3—122no—
369C23×D3—122no—
370C23×D3—122no—
371C23×D3—122no—
372C23×D3—124no—
373C23×D3—124no—
374C23×D3C22×D311yescharacteristic
375C2×C3×Q8—34no—
376C2×C3×Q8—122no—
377C2×C3×D4—34no—
378C2×C3×D4—122no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—42no—
398C2×#67—64no—
399C2×#67—64no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—124no—
405C2×#67C22×D314yes—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—34no—
409C22×Dic3—61no—
410C22×Dic3—122no—
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D311yescharacteristic
417C22×Dic3C22×D311yescharacteristic
418C2×D12—34no—
419C2×D12—34no—
420C2×D12—34no—
421C2×D12—34no—
422C2×D12—34no—
423C2×D12—34no—
424C2×D12—34no—
425C2×D12—64no—
426C2×D12—64no—
427C2×D12—64no—
428C2×D12—64no—
429C2×D12—64no—
430C2×D12—124no—
431C2×D12—122no—
432C2×D12—122no—
433C2×D12—124no—
434C2×D12—122no—
435C2×D12—122no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—34no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—122no—
446C2×C4×D3—122no—
447C2×C4×D3—122no—
448C2×C4×D3—122no—
449C2×C4×D3—122no—
450C2×Dic6—42no—
451C2×Dic6C22×D314yescomplemented
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C22⋊C4—24no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—34no—
460C3×C22⋊C4—34no—
461C3×C22⋊C4C22×D314yes—
462C3×C22⋊C4C22×D314yes—
463C3×C42—34no—
464C3×C42—34no—
465#217C22×D314yes—
466#217C22×D314yes—
467#217C22×D314yes—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—64no—
485(C2×D3)⋊C4—64no—
486(C2×D3)⋊C4C22×D314yescomplemented
487(C2×D3)⋊C4C22×D314yescomplemented
488C4⋊Dic3—34no—
489C4⋊Dic3—34no—
490C4⋊Dic3C22×D314yescomplemented
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4C22×D314yescomplemented
496Dic3⋊C4C22×D314yescomplemented
497C4×Dic3C22×D314yescomplemented
498C4×Dic3C22×D314yescomplemented
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—44no—
503C22×C32C2×#4112yes—
504C22×C32H(5,𝔽2)12yes—
505C22×C32H(5,𝔽2)12yes—
506C22×C32C2511yescharacteristic
507C2×C3⋊D3—22no—
508C2×C3⋊D3—28no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—22no—
512C2×C3⋊D3—22no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—22no—
515C2×C3⋊D3—22no—
516C2×C3⋊D3—416no—
517C2×C3⋊D3—44no—
518C2×C3⋊D3—44no—
519C2×C3⋊D3C2×#4114yes—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—44no—
524C32×C4—22no—
525C32×C4—22no—
526C3⋊Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—22no—
534C25—91no—
535C22×Q8—31no—
536C22×D4—31no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C22×D4—91no—
542C22×D4—91no—
543C23×C4—91no—
544C23×C4—91no—
545C23×C4—91no—
546C23×C4—91no—
547#126—38no—
548#126—98no—
549#124—38no—
550#124—98no—
551#123—98no—
552#123—98no—
553C22⋊Q8—98no—
554#121—98no—
555#121—98no—
556#121—98no—
557#120—98no—
558#120—98no—
559C4×D4—98no—
560C4×D4—98no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C4⋊C4—91no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—98no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C22⋊C4—91no—
580C2×C22⋊C4—91no—
581C2×C22⋊C4D3211yescharacteristic
582C2×C42—31no—
583C2×C42—31no—
584C23×C3—24no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—21no—
593C23×C3—32no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3C23×D312yes—
600C23×C3C23×D312yes—
601C23×C3C23×D311yescharacteristic
602C23×C3C23×D311yescharacteristic
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—34no—
607C22×D3—34no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—32no—
614C22×D3—64no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—68no—
619C22×D3—68no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—64no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—62no—
634C22×D3—62no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—128no—
638C22×D3—122no—
639C22×D3—122no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3—122no—
643C22×D3—122no—
644C22×D3—122no—
645C22×D3—124no—
646C22×D3—124no—
647C22×D3—124no—
648C22×D3—124no—
649C22×D3—128no—
650C22×D3—1216no—
651C22×D3—1216no—
652C22×D3—128no—
653C22×D3—1232no—
654C22×D3C23×D312yes—
655C3×Q8—124no—
656C3×D4—124no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—42no—
671C2×C3×C4—42no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—62no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—62no—
679C2×C3×C4C23×D312yes—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D312yes—
683#67—44no—
684#67—68no—
685#67—124no—
686#67—124no—
687#67—124no—
688#67—124no—
689#67—128no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—122no—
703C2×Dic3—124no—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D312yes—
711D12—68no—
712D12—68no—
713D12—68no—
714D12—128no—
715D12—124no—
716D12—124no—
717D12—128no—
718D12—124no—
719D12—124no—
720C4×D3—124no—
721C4×D3—124no—
722C4×D3—124no—
723C4×D3—124no—
724C4×D3—124no—
725C4×D3—124no—
726C4×D3—124no—
727Dic6—44no—
728C2×C32—42no—
729C2×C32#53814yescomplemented
730C2×C32C22×#4111yescharacteristic
731C2×C32C2×H(5,𝔽2)11yescharacteristic
732C2×C32C2×H(5,𝔽2)11yescharacteristic
733C3⋊D3—24no—
734C3⋊D3—42no—
735C3⋊D3—42no—
736C3×D3—42no—
737C24—31no—
738C24—91no—
739C24—91no—
740C24—91no—
741C24—94no—
742C24—184no—
743C24—362no—
744C24—362no—
745C24C2×D3211yescharacteristic
746C2×Q8—34no—
747C2×Q8—122no—
748C2×D4—34no—
749C2×D4—94no—
750C2×D4—94no—
751C2×D4—94no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—94no—
755C2×D4—122no—
756C2×D4—184no—
757C2×D4—184no—
758C2×D4—362no—
759C2×D4—362no—
760C2×D4—362no—
761C2×D4—362no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—94no—
770C22×C4—94no—
771C22×C4—94no—
772C22×C4—94no—
773C22×C4—91no—
774C22×C4—362no—
775C22×C4—362no—
776C22×C4—362no—
777C22×C4—362no—
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—34no—
781C4⋊C4—34no—
782C4⋊C4—34no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C22⋊C4—34no—
787C22⋊C4—34no—
788C22⋊C4—34no—
789C22⋊C4—34no—
790C22⋊C4—34no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—94no—
798C22⋊C4—94no—
799C22⋊C4C2×D3214yes—
800C42—34no—
801C42—34no—
802C22×C3—24no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—21no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—48no—
816C22×C3—44no—
817C22×C3—44no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—124no—
822C22×C3#100412yes—
823C22×C3D3×#4112yes—
824C22×C3D3×#4112yes—
825C22×C3#100912yes—
826C22×C3#100912yes—
827C22×C3#100912yes—
828C22×C3C24×D311yescharacteristic
829C22×C3C24×D311yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—34no—
834C2×D3—34no—
835C2×D3—44no—
836C2×D3—64no—
837C2×D3—68no—
838C2×D3—62no—
839C2×D3—68no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—64no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—122no—
857C2×D3—122no—
858C2×D3—128no—
859C2×D3—122no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—1216no—
865C2×D3—1216no—
866C2×D3—128no—
867C2×D3—1232no—
868C2×D3—124no—
869C2×D3—124no—
870C2×D3—124no—
871C2×D3—124no—
872C2×D3—244no—
873C3×C4—22no—
874C3×C4—22no—
875C3×C4—22no—
876C3×C4—22no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—62no—
880C3×C4—62no—
881C3×C4—62no—
882C3×C4—62no—
883C3×C4—62no—
884C3×C4—62no—
885C3×C4—62no—
886Dic3—22no—
887Dic3—22no—
888Dic3—22no—
889Dic3—22no—
890Dic3—22no—
891Dic3—22no—
892Dic3—22no—
893Dic3—62no—
894Dic3—62no—
895Dic3—122no—
896C32C2×#53811yescharacteristic, complemented, Sylow
897C23—22no—
898C23—22no—
899C23—22no—
900C23—32no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—94no—
905C23—92no—
906C23—92no—
907C23—92no—
908C23—188no—
909C23—182no—
910C23—182no—
911C23—182no—
912C23—182no—
913C23—182no—
914C23—182no—
915C23—182no—
916C23—182no—
917C23—364no—
918C23—364no—
919C23—3616no—
920C23C22×D3212yes—
921C23C22×D3211yescharacteristic
922Q8—124no—
923D4—124no—
924D4—188no—
925D4—188no—
926D4—364no—
927D4—364no—
928D4—364no—
929D4—364no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—32no—
933C2×C4—32no—
934C2×C4—32no—
935C2×C4—32no—
936C2×C4—32no—
937C2×C4—32no—
938C2×C4—32no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—62no—
946C2×C4—92no—
947C2×C4—182no—
948C2×C4—364no—
949C2×C4—364no—
950C2×C4—364no—
951C2×C4—364no—
952C2×C4C22×D3212yes—
953C2×C4C22×D3212yes—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—24no—
958C2×C3—44no—
959C2×C3—42no—
960C2×C3—42no—
961C2×C3—122no—
962C2×C3#567814yescomplemented
963C2×C3#570414yescomplemented
964C2×C3C2×#100411yescharacteristic
965C2×C3C2×D3×#4111yescharacteristic
966C2×C3C2×D3×#4111yescharacteristic
967C2×C3C2×#100911yescharacteristic
968C2×C3C2×#100911yescharacteristic
969C2×C3C2×#100911yescharacteristic
970D3—42no—
971D3—64no—
972D3—64no—
973D3—124no—
974D3—124no—
975D3—122no—
976D3—122no—
977D3—122no—
978D3—122no—
979D3—242no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—44no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—94no—
988C22—124no—
989C22—182no—
990C22—182no—
991C22—188no—
992C22—182no—
993C22—182no—
994C22—182no—
995C22—182no—
996C22—182no—
997C22—182no—
998C22—3616no—
999C22—364no—
1000C22—364no—
1001C22#6430812yes—
1002C22#6431212yes—
1003C22#6431412yes—
1004C22C23×D3211yescharacteristic
1005C4—22no—
1006C4—22no—
1007C4—62no—
1008C4—62no—
1009C4—62no—
1010C4—62no—
1011C4—62no—
1012C4—62no—
1013C4—62no—
1014C4—182no—
1015C3—21no—
1016C3C2×#567811yescharacteristic, complemented
1017C3C2×#570411yescharacteristic, complemented
1018C2—42no—
1019C2—122no—
1020C2—184no—
1021C2—362no—
1022C2—362no—
1023C2#1059416214yesdirect product factor
1024C2C2×#6430811yescharacteristic
1025C2C2×#6431211yescharacteristic
1026C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64091C2semidirect
2. C2×C3×#885C2semidirect
3. C2×C3×#879C2semidirect
4. C2×#63981C2semidirect
5. C2×#63975C2semidirect
6. C2×#63974C2semidirect
7. C2×#63971C2semidirect
8. C2×#63910C2semidirect
9. C2×#63910C2semidirect
10. C2×#63894C2semidirect
11. C2×#63890C2semidirect
12. C2×#63888C2semidirect
13. C2×#63880C2semidirect
14. C2×#63868C2semidirect
15. C2×#63864C2semidirect
16. #10594162C2direct (N × H)
24. C22×C3×Dic6C22semidirect
27. C22×#626C22semidirect
30. C22×#624C22semidirect
31. C22×D3×Dic3C22semidirect
35. #64091C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. C2×C3×C4×Dic3C22semidirect
46. C3×#885C22semidirect
47. C3×#879C22semidirect
48. #63981C22semidirect
49. #63975C22semidirect
50. #63974C22semidirect
51. #63971C22semidirect
52. C2×#3724C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
59. C2×#3722C22semidirect
60. C2×#3722C22semidirect
61. #63910C22semidirect
62. #63910C22semidirect
63. #63894C22semidirect
64. #63890C22semidirect
65. #63888C22semidirect
66. #63880C22semidirect
67. #63868C22semidirect
68. #63864C22semidirect
84. C2×#885D3semidirect
97. C2×#879D3semidirect
130. C2×C3×Dic6C23semidirect
136. C2×#626C23semidirect
142. C2×#624C23semidirect
144. C2×D3×Dic3C23semidirect
151. C3×(C2×D3)⋊C4C23semidirect
152. C3×(C2×D3)⋊C4C23semidirect
153. C3×C4⋊Dic3C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. C3×C4×Dic3C23semidirect
157. C3×C4×Dic3C23semidirect
158. #3724C23semidirect
159. Dic3⋊Dic3C23semidirect
160. Dic3⋊Dic3C23semidirect
165. #3722C23semidirect
166. #3722C23semidirect
197. C22×Dic6C2×D3semidirect
238. C2×(C2×D3)⋊C4C2×D3semidirect
239. C2×(C2×D3)⋊C4C2×D3semidirect
242. C2×C4⋊Dic3C2×D3semidirect
247. C2×Dic3⋊C4C2×D3semidirect
248. C2×Dic3⋊C4C2×D3semidirect
249. C2×C4×Dic3C2×D3semidirect
250. C2×C4×Dic3C2×D3semidirect
258. #885C2×D3semidirect
271. #879C2×D3semidirect
451. C2×Dic6C22×D3semidirect
486. (C2×D3)⋊C4C22×D3semidirect
487. (C2×D3)⋊C4C22×D3semidirect
490. C4⋊Dic3C22×D3semidirect
495. Dic3⋊C4C22×D3semidirect
496. Dic3⋊C4C22×D3semidirect
497. C4×Dic3C22×D3semidirect
498. C4×Dic3C22×D3semidirect
729. C2×C32#538semidirect
896. C32C2×#538semidirect
962. C2×C3#5678semidirect
963. C2×C3#5704semidirect
1016. C3C2×#5678semidirect
1017. C3C2×#5704semidirect
1023. C2#10594162direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640912
C2×C3×#8852
C2×C3×#8792
C2×#639812
C2×#639752
C2×#639742
C2×#639712
C2×#639102
C2×#638942
C2×#638902
C2×#638882
C2×#638802
C2×#638682
C2×#638642
#105941622
C2×#57043
C2×#56783