Finite Group Databasebeta

← C2×#10594301 #11901347

Subgroups — C2×#10594301 #11901347

Order 1152.

2843 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64095C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×C3×#884C211yesmaximal, characteristic, complemented
4C2×#63983C211yesmaximal, characteristic, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63922C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#63907C211yesmaximal, characteristic, complemented
11C2×Dic3×D12C211yesmaximal, characteristic, complemented
12C2×#63891C211yesmaximal, characteristic, complemented
13C2×#63868C211yesmaximal, characteristic, complemented
14C2×#63861C211yesmaximal, characteristic, complemented
15C2×#63856C211yesmaximal, characteristic, complemented
16#10594301C2116yesmaximal, direct product factor
17C2×#5678—31nomaximal
18C2×#5617—31nomaximal
19C23×D32C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic, complemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37#64095C2218yescomplemented
38C2×C3×#217C2211yescharacteristic, complemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×C4×Dic3C2211yescharacteristic, complemented
44C3×#885C2218yescomplemented
45C3×#884C2218yescomplemented
46#63983C2218yescomplemented
47#63980C2218yescomplemented
48#67⋊Dic3C2218yescomplemented
49#63971C2218yescomplemented
50C2×#3724C2211yescharacteristic, complemented
51C2×#3724C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63922C2218yescomplemented
62D3×(C2×D3)⋊C4C2218yescomplemented
63#63907C2218yescomplemented
64Dic3×D12C2218yescomplemented
65#63891C2218yescomplemented
66#63868C2218yescomplemented
67#63861C2218yescomplemented
68#63856C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#121—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#937—31no—
77C2×#937—31no—
78C2×#937—31no—
79C2×D4×Dic3—31no—
80C2×D4×Dic3—31no—
81C22×(C2×D3)⋊C4—31no—
82C2×#924—31no—
83#5678—316no—
84#5617—316no—
85C2×#898—31no—
86C2×#898—31no—
87C2×#886—31no—
88C2×#886—31no—
89C2×#886—31no—
90C2×#886—61no—
91C2×#885—31no—
92C2×#885D311yescharacteristic, complemented
93C2×#884—31no—
94C2×#884D311yescharacteristic, complemented
95C2×#883—31no—
96C2×#882—31no—
97C2×#67⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×#879—31no—
100C2×#876—31no—
101C2×C4×D12—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×D32—24no—
108C22×D32—42no—
109C22×D32—42no—
110C22×D32C2314yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C2×#638—42no—
114C2×#638C2314yes—
115C22×C3⋊Dic3—42no—
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2314yescomplemented
120C2×C3×#67—24no—
121C2×C3×#67—42no—
122C2×C3×#67—42no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C2×C3×#67C2314yescomplemented
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×D12—24no—
132C2×C3×D12C2314yes—
133C2×C3×C4×D3—42no—
134C2×C3×C4×D3C2314yes—
135C2×C3×Dic6—42no—
136C2×C3×Dic6C2314yescomplemented
137C2×#626—42no—
138C2×#626C2314yes—
139C2×#625—42no—
140C2×#625C2314yes—
141C2×D3×Dic3—42no—
142C2×D3×Dic3—42no—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yescomplemented
145C32×C22⋊C4C2314yescomplemented
146#3752C2314yes—
147#3752C2314yes—
148C4⋊(C3⋊Dic3)C2314yescomplemented
149C4⋊(C3⋊Dic3)C2314yescomplemented
150C3×#217C2314yescomplemented
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155C3×C4×Dic3C2314yescomplemented
156#3724C2314yescomplemented
157#3724C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×Q8—31no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C23×C3×C4—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—61no—
182C22×#67C2×D311yescharacteristic
183C22×#67C2×D311yescharacteristic
184C22×#67C2×D311yescharacteristic, complemented
185C23×Dic3—31no—
186C23×Dic3—31no—
187C23×Dic3—31no—
188C23×Dic3—31no—
189C23×Dic3—61no—
190C22×D12—31no—
191C22×D12C2×D311yescharacteristic
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3C2×D311yescharacteristic
195C22×Dic6C2×D311yescharacteristic, complemented
196C3×#124—38no—
197C3×#121—38no—
198C2×C3×C4⋊C4—31no—
199C2×C3×C22⋊C4—21no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
205C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
206C2×C3×C42—31no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217C2×D311yescharacteristic, complemented
213#947—38no—
214#946—38no—
215#939—38no—
216#939—38no—
217#939—38no—
218#937—38no—
219#937—38no—
220#937—38no—
221D4×Dic3—38no—
222D4×Dic3—38no—
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—38no—
237C2×(C2×D3)⋊C4—61no—
238C2×(C2×D3)⋊C4—61no—
239C2×(C2×D3)⋊C4C2×D311yescharacteristic
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—61no—
248C2×C4⋊Dic3—61no—
249#924—38no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4C2×D311yescharacteristic, complemented
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3C2×D311yescharacteristic, complemented
259#898—38no—
260#898—38no—
261#886—38no—
262#886—38no—
263#886—38no—
264#886—68no—
265#885—38no—
266#885C2×D318yescomplemented
267#884—38no—
268#884C2×D318yescomplemented
269#883—38no—
270#882—38no—
271#67⋊C4—38no—
272D3×C22⋊C4—38no—
273#879—38no—
274#876—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⋊D3C2412yes—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3#4114yes—
294C22×C3×D3C2412yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×D32—28no—
298C2×D32—44no—
299C2×D32—44no—
300C2×D32—416no—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304C2×C32×C4C2412yes—
305#638—44no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—44no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C3×#67—28no—
314C3×#67—44no—
315C3×#67—44no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×D12—28no—
327C3×C4×D3—44no—
328C3×Dic6—44no—
329#626—44no—
330#625—44no—
331D3×Dic3—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—31no—
337C2×#124—91no—
338C2×#123—91no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—31no—
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×C3—31no—
352C24×C3—31no—
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—34no—
358C23×D3—34no—
359C23×D3—61no—
360C23×D3—64no—
361C23×D3—64no—
362C23×D3—122no—
363C23×D3—122no—
364C23×D3—122no—
365C23×D3—122no—
366C23×D3C22×D311yescharacteristic
367C23×D3C22×D311yescharacteristic
368C23×D3C22×D311yescharacteristic
369C2×C3×Q8—34no—
370C2×C3×Q8—122no—
371C2×C3×D4—34no—
372C2×C3×D4—34no—
373C2×C3×D4—34no—
374C2×C3×D4—34no—
375C2×C3×D4—64no—
376C2×C3×D4—64no—
377C2×C3×D4—122no—
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—34no—
387C22×C3×C4—122no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C2×#67—24no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—42no—
399C2×#67—42no—
400C2×#67—64no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—122no—
405C2×#67—122no—
406C2×#67—124no—
407C2×#67C22×D314yes—
408C2×#67C22×D314yes—
409C2×#67C22×D314yescomplemented
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—34no—
417C22×Dic3—34no—
418C22×Dic3—34no—
419C22×Dic3—34no—
420C22×Dic3—64no—
421C22×Dic3—61no—
422C22×Dic3—61no—
423C22×Dic3—61no—
424C22×Dic3—122no—
425C22×Dic3—122no—
426C22×Dic3—122no—
427C22×Dic3—122no—
428C22×Dic3—124no—
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D311yescharacteristic
432C22×Dic3C22×D311yescharacteristic
433C22×Dic3C22×D311yescharacteristic
434C2×D12—24no—
435C2×D12—34no—
436C2×D12—122no—
437C2×D12C22×D314yes—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—42no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3C22×D314yes—
444C2×Dic6—42no—
445C2×Dic6C22×D314yescomplemented
446C3×C4⋊C4—34no—
447C3×C22⋊C4—24no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4C22×D314yescomplemented
453C3×C22⋊C4C22×D314yescomplemented
454C3×C42—34no—
455#217—34no—
456#217—34no—
457#217—34no—
458#217—34no—
459#217—34no—
460#217C22×D314yescomplemented
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
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—64no—
475(C2×D3)⋊C4—64no—
476(C2×D3)⋊C4C22×D314yes—
477(C2×D3)⋊C4C22×D314yes—
478(C2×D3)⋊C4C22×D314yescomplemented
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—64no—
485C4⋊Dic3—64no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4C22×D314yescomplemented
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3C22×D314yescomplemented
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—44no—
499C22×C32C2×#4112yes—
500C22×C32H(5,𝔽2)12yes—
501C22×C32H(5,𝔽2)12yes—
502C22×C32C2511yescharacteristic
503C2×C3⋊D3—22no—
504C2×C3⋊D3—22no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—44no—
507C2×C3×D3—28no—
508C2×C3×D3—22no—
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—44no—
517C2×C3×D3—44no—
518C2×C3×D3C2×#4114yes—
519D32—416no—
520C32×C4—22no—
521C32×C4—22no—
522C3⋊Dic3—22no—
523C3⋊Dic3—22no—
524C3⋊Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C25—91no—
531C22×Q8—31no—
532C22×D4—31no—
533C22×D4—31no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C23×C4—31no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543#126—98no—
544#126—98no—
545#124—38no—
546#124—98no—
547#123—98no—
548#123—98no—
549C22⋊Q8—98no—
550#121—38no—
551#121—98no—
552#121—98no—
553#120—98no—
554#120—98no—
555C4×D4—98no—
556C4×D4—98no—
557C2×C4⋊C4—31no—
558C2×C4⋊C4—91no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—98no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4D3211yescharacteristic, complemented
578C2×C42—31no—
579C2×C42—91no—
580C23×C3—24no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—21no—
589C23×C3—34no—
590C23×C3—32no—
591C23×C3—32no—
592C23×C3—32no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—62no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3—62no—
602C23×C3—62no—
603C23×C3C23×D312yes—
604C23×C3C23×D312yes—
605C23×C3C23×D311yescharacteristic
606C23×C3C23×D311yescharacteristic
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—32no—
616C22×D3—32no—
617C22×D3—62no—
618C22×D3—68no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—68no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—124no—
630C22×D3—124no—
631C22×D3—124no—
632C22×D3—124no—
633C22×D3—1216no—
634C22×D3—1216no—
635C22×D3#23714yes—
636C22×D3C23×D312yes—
637C22×D3C23×D312yes—
638C22×D3C23×D312yes—
639C3×Q8—124no—
640C3×D4—68no—
641C3×D4—68no—
642C3×D4—124no—
643C3×D4—124no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—42no—
656C2×C3×C4—42no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—124no—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667#67—28no—
668#67—44no—
669#67—44no—
670#67—124no—
671#67—124no—
672#67—124no—
673#67—124no—
674#67—124no—
675#67—128no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—122no—
697C2×Dic3—122no—
698C2×Dic3—122no—
699C2×Dic3—124no—
700C2×Dic3—124no—
701C2×Dic3—124no—
702C2×Dic3—124no—
703C2×Dic3—128no—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709D12—28no—
710D12—124no—
711C4×D3—44no—
712C4×D3—124no—
713C4×D3—124no—
714Dic6—44no—
715C2×C32—42no—
716C2×C32#53814yescomplemented
717C2×C32C22×#4111yescharacteristic
718C2×C32C2×H(5,𝔽2)11yescharacteristic
719C2×C32C2×H(5,𝔽2)11yescharacteristic
720C3⋊D3—42no—
721C3×D3—24no—
722C3×D3—42no—
723C3×D3—42no—
724C24—31no—
725C24—31no—
726C24—31no—
727C24—94no—
728C24—91no—
729C24—184no—
730C24—362no—
731C24—362no—
732C24C2×D3211yescharacteristic
733C2×Q8—34no—
734C2×Q8—122no—
735C2×D4—34no—
736C2×D4—34no—
737C2×D4—34no—
738C2×D4—34no—
739C2×D4—64no—
740C2×D4—64no—
741C2×D4—94no—
742C2×D4—94no—
743C2×D4—94no—
744C2×D4—122no—
745C2×D4—122no—
746C2×D4—362no—
747C2×D4—362no—
748C2×D4—362no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—34no—
755C22×C4—94no—
756C22×C4—94no—
757C22×C4—91no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—94no—
761C22×C4—122no—
762C22×C4—362no—
763C22×C4—362no—
764C22×C4—362no—
765C22×C4C2×D3211yescharacteristic
766C22×C4C2×D3211yescharacteristic
767C4⋊C4—34no—
768C4⋊C4—94no—
769C4⋊C4—94no—
770C4⋊C4—94no—
771C4⋊C4—94no—
772C4⋊C4—94no—
773C22⋊C4—34no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4C2×D3214yescomplemented
787C42—34no—
788C42—94no—
789C22×C3—24no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—21no—
800C22×C3—34no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—48no—
804C22×C3—44no—
805C22×C3—44no—
806C22×C3—68no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—124no—
816C22×C3—124no—
817C22×C3C2×#23712yes—
818C22×C3#100412yes—
819C22×C3#100412yes—
820C22×C3D3×#4112yes—
821C22×C3#100912yes—
822C22×C3#100912yes—
823C22×C3C24×D311yescharacteristic
824C22×C3C24×D311yescharacteristic
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—28no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—44no—
835C2×D3—44no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—1216no—
846C2×D3—1216no—
847C2×D3—124no—
848C2×D3—124no—
849C2×D3—244no—
850C2×D3C2×#23714yes—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—62no—
858C3×C4—62no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4—62no—
862Dic3—22no—
863Dic3—22no—
864Dic3—22no—
865Dic3—22no—
866Dic3—22no—
867Dic3—62no—
868Dic3—62no—
869Dic3—62no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—122no—
874Dic3—122no—
875Dic3—122no—
876C32C2×#53811yescharacteristic, complemented, Sylow
877C23—22no—
878C23—22no—
879C23—22no—
880C23—34no—
881C23—32no—
882C23—32no—
883C23—32no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—92no—
893C23—188no—
894C23—182no—
895C23—182no—
896C23—182no—
897C23—364no—
898C23—364no—
899C23—3616no—
900C23C22×D3212yes—
901C23C22×D3211yescharacteristic
902Q8—124no—
903D4—68no—
904D4—68no—
905D4—124no—
906D4—124no—
907D4—364no—
908D4—364no—
909D4—364no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—32no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—92no—
923C2×C4—92no—
924C2×C4—92no—
925C2×C4—124no—
926C2×C4—182no—
927C2×C4—182no—
928C2×C4—182no—
929C2×C4—364no—
930C2×C4—364no—
931C2×C4—364no—
932C2×C4C22×D3212yes—
933C2×C4C22×D3212yes—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—24no—
938C2×C3—44no—
939C2×C3—42no—
940C2×C3—42no—
941C2×C3—64no—
942C2×C3—122no—
943C2×C3—122no—
944C2×C3#561714yescomplemented
945C2×C3#567814yescomplemented
946C2×C3C22×#23711yescharacteristic
947C2×C3C2×#100411yescharacteristic
948C2×C3C2×#100411yescharacteristic
949C2×C3C2×D3×#4111yescharacteristic
950C2×C3C2×#100911yescharacteristic
951C2×C3C2×#100911yescharacteristic
952D3—24no—
953D3—42no—
954D3—42no—
955D3—122no—
956D3—122no—
957D3—242no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—34no—
962C22—44no—
963C22—62no—
964C22—62no—
965C22—68no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—62no—
970C22—62no—
971C22—62no—
972C22—124no—
973C22—124no—
974C22—182no—
975C22—182no—
976C22—182no—
977C22—3616no—
978C22—364no—
979C22#6430812yes—
980C22D3×#23712yes—
981C22#6431312yes—
982C22C23×D3211yescharacteristic
983C4—22no—
984C4—22no—
985C4—62no—
986C4—62no—
987C4—62no—
988C4—62no—
989C4—62no—
990C4—182no—
991C4—182no—
992C4—182no—
993C3—21no—
994C3C2×#561711yescharacteristic, complemented
995C3C2×#567811yescharacteristic, complemented
996C2—42no—
997C2—64no—
998C2—122no—
999C2—122no—
1000C2—362no—
1001C2#1059430114yesdirect product factor
1002C2C2×#6430811yescharacteristic
1003C2C2×D3×#23711yescharacteristic
1004C2C2×#6431311yescharacteristic
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×#64095C2semidirect
2. C2×C3×#885C2semidirect
3. C2×C3×#884C2semidirect
4. C2×#63983C2semidirect
5. C2×#63980C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C2×#63971C2semidirect
8. C2×#63922C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×#63907C2semidirect
11. C2×Dic3×D12C2semidirect
12. C2×#63891C2semidirect
13. C2×#63868C2semidirect
14. C2×#63861C2semidirect
15. C2×#63856C2semidirect
16. #10594301C2direct (N × H)
21. C23×C3⋊Dic3C22semidirect
24. C22×C3×#67C22semidirect
27. C22×C3×Dic6C22semidirect
31. C22×D3×Dic3C22semidirect
32. C2×C32×C22⋊C4C22semidirect
35. C2×C4⋊(C3⋊Dic3)C22semidirect
36. C2×C4⋊(C3⋊Dic3)C22semidirect
37. #64095C22semidirect
38. C2×C3×#217C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×C4×Dic3C22semidirect
44. C3×#885C22semidirect
45. C3×#884C22semidirect
46. #63983C22semidirect
47. #63980C22semidirect
48. #67⋊Dic3C22semidirect
49. #63971C22semidirect
50. C2×#3724C22semidirect
51. C2×#3724C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×Dic32C22semidirect
61. #63922C22semidirect
62. D3×(C2×D3)⋊C4C22semidirect
63. #63907C22semidirect
64. Dic3×D12C22semidirect
65. #63891C22semidirect
66. #63868C22semidirect
67. #63861C22semidirect
68. #63856C22semidirect
92. C2×#885D3semidirect
94. C2×#884D3semidirect
119. C22×C3⋊Dic3C23semidirect
125. C2×C3×#67C23semidirect
136. C2×C3×Dic6C23semidirect
144. C2×D3×Dic3C23semidirect
145. C32×C22⋊C4C23semidirect
148. C4⋊(C3⋊Dic3)C23semidirect
149. C4⋊(C3⋊Dic3)C23semidirect
150. C3×#217C23semidirect
153. C3×(C2×D3)⋊C4C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×C4×Dic3C23semidirect
156. #3724C23semidirect
157. #3724C23semidirect
158. Dic3⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
184. C22×#67C2×D3semidirect
195. C22×Dic6C2×D3semidirect
204. C2×C3×C22⋊C4C2×D3semidirect
205. C2×C3×C22⋊C4C2×D3semidirect
212. C2×#217C2×D3semidirect
241. C2×(C2×D3)⋊C4C2×D3semidirect
255. C2×Dic3⋊C4C2×D3semidirect
258. C2×C4×Dic3C2×D3semidirect
266. #885C2×D3semidirect
268. #884C2×D3semidirect
409. C2×#67C22×D3semidirect
445. C2×Dic6C22×D3semidirect
452. C3×C22⋊C4C22×D3semidirect
453. C3×C22⋊C4C22×D3semidirect
460. #217C22×D3semidirect
478. (C2×D3)⋊C4C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
494. C4×Dic3C22×D3semidirect
577. C2×C22⋊C4D32semidirect
716. C2×C32#538semidirect
786. C22⋊C4C2×D32semidirect
876. C32C2×#538semidirect
944. C2×C3#5617semidirect
945. C2×C3#5678semidirect
994. C3C2×#5617semidirect
995. C3C2×#5678semidirect
1001. C2#10594301direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640952
C2×C3×#8852
C2×C3×#8842
C2×#639832
C2×#639802
C2×#67⋊Dic32
C2×#639712
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639072
C2×Dic3×D122
C2×#638912
C2×#638682
C2×#638612
C2×#638562
#105943012
C2×#56783
C2×#56173