Finite Group Databasebeta

← C2×#10594309 #11910215

Subgroups — C2×#10594309 #11910215

Order 1152.

2981 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64094C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×C3×#882C211yesmaximal, characteristic, complemented
4C2×#63983C211yesmaximal, characteristic, complemented
5C2×#63977C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#63959C211yesmaximal, characteristic, complemented
8C2×#63922C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×#63915C211yesmaximal, characteristic, complemented
11C2×#63913C211yesmaximal, characteristic, complemented
12C2×#63907C211yesmaximal, characteristic, complemented
13C2×#63863C211yesmaximal, characteristic, complemented
14C2×#63860C211yesmaximal, characteristic, complemented
15C2×#63852C211yesmaximal, characteristic, complemented
16#10594309C2116yesmaximal, direct product factor
17C2×#5683—31nomaximal
18C2×#5594—31nomaximal
19C24×C3×D3C2211yescharacteristic, complemented
20C23×D32C2211yescharacteristic, complemented
21C22×#638C2211yescharacteristic
22C22×#634C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic, complemented
28C22×#627C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic, complemented
34C2×#3757C2211yescharacteristic, complemented
35C2×#3752C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic, complemented
37C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
38#64094C2218yescomplemented
39C2×C3×#217C2211yescharacteristic, complemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×C4×Dic3C2211yescharacteristic, complemented
45C3×#885C2218yescomplemented
46C3×#882C2218yescomplemented
47#63983C2218yescomplemented
48#63977C2218yescomplemented
49#63976C2218yescomplemented
50C2×#3722C2211yescharacteristic, complemented
51C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59#63959C2218yescomplemented
60C2×Dic32C2211yescharacteristic, complemented
61#63922C2218yescomplemented
62#63922C2218yescomplemented
63#63915C2218yescomplemented
64#63913C2218yescomplemented
65#63907C2218yescomplemented
66#63863C2218yescomplemented
67#63860C2218yescomplemented
68#63852C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#120—31no—
71C2×#953—31no—
72C2×#953—31no—
73C2×#947—31no—
74C2×#947—31no—
75C2×#937—31no—
76C2×#937—31no—
77C2×#937—31no—
78C2×#937—31no—
79C2×#937—31no—
80C2×#936—31no—
81C2×#936—31no—
82C2×#936—31no—
83#5683—316no—
84#5594—316no—
85C2×#885—31no—
86C2×#885—31no—
87C2×#885—31no—
88C2×#885—31no—
89C2×#885—31no—
90C2×#885—31no—
91C2×#885—31no—
92C2×#885—31no—
93C2×#885—31no—
94C2×#885—61no—
95C2×#885D311yescharacteristic, complemented
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—31no—
99C2×#882D311yescharacteristic, complemented
100C2×#875—31no—
101C2×#875—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3—42no—
105C23×C3×D3—42no—
106C23×C3×D3—42no—
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yescomplemented
112C22×D32—42no—
113C22×D32—42no—
114C22×D32—42no—
115C22×D32C2314yescomplemented
116C22×C32×C4C2311yescharacteristic
117C22×C32×C4C2311yescharacteristic
118C2×#638—42no—
119C2×#638C2314yes—
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C2×#634—42no—
124C2×#634C2314yescomplemented
125C2×C3×#67—42no—
126C2×C3×#67—42no—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C2×C3×D12—42no—
134C2×C3×D12—42no—
135C2×C3×D12C2314yes—
136C2×C3×D12C2314yes—
137C2×C3×Dic6—42no—
138C2×C3×Dic6C2314yescomplemented
139C2×#627—42no—
140C2×#627C2314yescomplemented
141C2×#626—42no—
142C2×#626—42no—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#625—42no—
146C2×#625—42no—
147C2×#625C2314yes—
148C2×#625C2314yes—
149C32×C22⋊C4C2314yescomplemented
150#3757C2314yescomplemented
151#3752C2314yescomplemented
152#3752C2314yescomplemented
153C4×C3⋊Dic3C2314yescomplemented
154C3×#217C2314yescomplemented
155C3×(C2×D3)⋊C4C2314yescomplemented
156C3×(C2×D3)⋊C4C2314yescomplemented
157C3×(C2×D3)⋊C4C2314yescomplemented
158C3×(C2×D3)⋊C4C2314yescomplemented
159C3×C4×Dic3C2314yescomplemented
160#3722C2314yescomplemented
161(C2×D3)⋊Dic3C2314yescomplemented
162(C2×D3)⋊Dic3C2314yescomplemented
163(C2×D3)⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yescomplemented
165(C2×D3)⋊Dic3C2314yescomplemented
166(C2×D3)⋊Dic3C2314yescomplemented
167(C2×D3)⋊Dic3C2314yescomplemented
168(C2×D3)⋊Dic3C2314yescomplemented
169Dic32C2314yescomplemented
170C2×H(3,𝔽4)—91noSylow
171C25×C3—31no—
172C24×D3—31no—
173C24×D3—31no—
174C24×D3C2×D311yescharacteristic, complemented
175C22×C3×Q8—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—61no—
189C22×#67C2×D311yescharacteristic
190C22×#67C2×D311yescharacteristic
191C22×D12—31no—
192C22×D12—31no—
193C22×D12C2×D311yescharacteristic
194C22×D12C2×D311yescharacteristic
195C22×Dic6—31no—
196C22×Dic6—31no—
197C22×Dic6—31no—
198C22×Dic6—31no—
199C22×Dic6—61no—
200C22×Dic6C2×D311yescharacteristic, complemented
201C3×#124—38no—
202C3×#120—38no—
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, complemented
210C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
211C2×C3×C42—31no—
212#953—38no—
213#953—38no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217—31no—
218C2×#217—31no—
219C2×#217—31no—
220C2×#217—31no—
221C2×#217—31no—
222C2×#217—31no—
223C2×#217—31no—
224C2×#217—61no—
225C2×#217C2×D311yescharacteristic, complemented
226#947—38no—
227#947—38no—
228#937—38no—
229#937—38no—
230#937—38no—
231#937—38no—
232#937—38no—
233#936—38no—
234#936—38no—
235#936—38no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—61no—
251C2×(C2×D3)⋊C4—61no—
252C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
253C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
254C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
255C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3—31no—
259C2×C4×Dic3—31no—
260C2×C4×Dic3—61no—
261C2×C4×Dic3C2×D311yescharacteristic, complemented
262#885—38no—
263#885—38no—
264#885—38no—
265#885—38no—
266#885—38no—
267#885—38no—
268#885—38no—
269#885—38no—
270#885—38no—
271#885—68no—
272#885C2×D318yescomplemented
273#882—38no—
274#882—38no—
275#882—38no—
276#882C2×D318yescomplemented
277#875—38no—
278#875—38no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32C2412yes—
283C23×C32C2411yescharacteristic
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3C2412yes—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
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—44no—
301C22×C3×D3—44no—
302C22×C3×D3—44no—
303C22×C3×D3—416no—
304C22×C3×D3C2412yes—
305C22×C3×D3C2412yes—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C2×D32—44no—
309C2×D32—44no—
310C2×D32—44no—
311C2×D32—416no—
312C2×C32×C4—22no—
313C2×C32×C4—22no—
314C2×C32×C4C2412yes—
315C2×C32×C4C2412yes—
316#638—44no—
317C2×C3⋊Dic3—22no—
318C2×C3⋊Dic3—22no—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3C2412yes—
321C2×C3⋊Dic3C2412yes—
322C2×C3⋊Dic3C2412yes—
323#634—44no—
324C3×#67—44no—
325C3×#67—44no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C3×D12—44no—
335C3×D12—44no—
336C3×Dic6—44no—
337#627—44no—
338#626—44no—
339#626—44no—
340#625—44no—
341#625—44no—
342H(3,𝔽4)—916no—
343C2×#124—31no—
344C2×#124—91no—
345C2×#124—91no—
346C2×#124—91no—
347C2×#124—91no—
348C2×#124—91no—
349C2×#124—91no—
350C2×#124—91no—
351C2×#124—91no—
352C2×#120—31no—
353C2×#120—91no—
354C2×#120—91no—
355C2×#120—91no—
356C2×#120—91no—
357C2×#120—91no—
358C24×C3—21no—
359C24×C3—31no—
360C24×C3—31no—
361C24×C3—31no—
362C24×C3—31no—
363C24×C3—34no—
364C24×C3—122no—
365C24×C3—122no—
366C24×C3—122no—
367C24×C3C22×D311yescharacteristic
368C24×C3C22×D311yescharacteristic
369C23×D3—31no—
370C23×D3—31no—
371C23×D3—34no—
372C23×D3—34no—
373C23×D3—42no—
374C23×D3—42no—
375C23×D3—42no—
376C23×D3—61no—
377C23×D3—122no—
378C23×D3—122no—
379C23×D3—122no—
380C23×D3—122no—
381C23×D3—122no—
382C23×D3—122no—
383C23×D3C22×D311yescharacteristic
384C23×D3C22×D311yescharacteristic
385C23×D3C22×D311yescharacteristic
386C23×D3C22×D311yescharacteristic
387C23×D3C22×D314yescomplemented
388C2×C3×Q8—34no—
389C2×C3×Q8—122no—
390C2×C3×D4—34no—
391C2×C3×D4—34no—
392C2×C3×D4—34no—
393C2×C3×D4—34no—
394C2×C3×D4—122no—
395C2×C3×D4—122no—
396C2×C3×D4—122no—
397C2×C3×D4—122no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C22×C3×C4C22×D311yescharacteristic
407C22×C3×C4C22×D311yescharacteristic
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—34no—
416C2×#67—42no—
417C2×#67—42no—
418C2×#67—64no—
419C2×#67—122no—
420C2×#67—122no—
421C2×#67—122no—
422C2×#67—122no—
423C2×#67—122no—
424C2×#67—122no—
425C2×#67—122no—
426C2×#67—122no—
427C2×#67—124no—
428C2×#67C22×D314yes—
429C2×#67C22×D314yes—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—31no—
435C22×Dic3—31no—
436C22×Dic3—61no—
437C22×Dic3—61no—
438C22×Dic3—61no—
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441C22×Dic3C22×D311yescharacteristic
442C22×Dic3C22×D311yescharacteristic
443C2×D12—34no—
444C2×D12—34no—
445C2×D12—42no—
446C2×D12—42no—
447C2×D12—122no—
448C2×D12—122no—
449C2×D12C22×D314yes—
450C2×D12C22×D314yes—
451C2×Dic6—34no—
452C2×Dic6—34no—
453C2×Dic6—34no—
454C2×Dic6—34no—
455C2×Dic6—42no—
456C2×Dic6—64no—
457C2×Dic6—122no—
458C2×Dic6—122no—
459C2×Dic6—122no—
460C2×Dic6—122no—
461C2×Dic6—124no—
462C2×Dic6C22×D314yescomplemented
463C3×C22⋊C4—24no—
464C3×C22⋊C4—34no—
465C3×C22⋊C4—34no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4C22×D314yescomplemented
470C3×C22⋊C4C22×D314yescomplemented
471C3×C42—34no—
472#217—34no—
473#217—34no—
474#217—34no—
475#217—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480#217—34no—
481#217—34no—
482#217—64no—
483#217C22×D314yescomplemented
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—64no—
499(C2×D3)⋊C4—64no—
500(C2×D3)⋊C4C22×D314yescomplemented
501(C2×D3)⋊C4C22×D314yescomplemented
502(C2×D3)⋊C4C22×D314yescomplemented
503(C2×D3)⋊C4C22×D314yescomplemented
504C4×Dic3—34no—
505C4×Dic3—34no—
506C4×Dic3—34no—
507C4×Dic3—34no—
508C4×Dic3—64no—
509C4×Dic3C22×D314yescomplemented
510C22×C32—22no—
511C22×C32—22no—
512C22×C32—22no—
513C22×C32—44no—
514C22×C32H(5,𝔽2)12yes—
515C22×C32H(5,𝔽2)12yes—
516C22×C32H(5,𝔽2)12yes—
517C22×C32C2511yescharacteristic
518C2×C3⋊D3—22no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—22no—
521C2×C3⋊D3—44no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—416no—
535C2×C3×D3—44no—
536C2×C3×D3—44no—
537C2×C3×D3—44no—
538C2×C3×D3—44no—
539D32—416no—
540C32×C4—22no—
541C32×C4—22no—
542C3⋊Dic3—22no—
543C3⋊Dic3—22no—
544C3⋊Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C25—31no—
550C25—91no—
551C22×Q8—31no—
552C22×Q8—91no—
553C22×Q8—91no—
554C22×D4—31no—
555C22×D4—31no—
556C22×D4—31no—
557C22×D4—31no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—91no—
562C22×D4—91no—
563#124—38no—
564#124—98no—
565#124—98no—
566#124—98no—
567#124—98no—
568#124—98no—
569#124—98no—
570#124—98no—
571#124—98no—
572#120—38no—
573#120—98no—
574#120—98no—
575#120—98no—
576#120—98no—
577#120—98no—
578C2×C22⋊C4—31no—
579C2×C22⋊C4—31no—
580C2×C22⋊C4—31no—
581C2×C22⋊C4—31no—
582C2×C22⋊C4—31no—
583C2×C22⋊C4—91no—
584C2×C22⋊C4—91no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4—91no—
587C2×C22⋊C4—91no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—91no—
590C2×C22⋊C4—91no—
591C2×C22⋊C4—91no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4D3211yescharacteristic, complemented
596C2×C42—31no—
597C2×C42—91no—
598C2×C42—91no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—21no—
607C23×C3—32no—
608C23×C3—32no—
609C23×C3—32no—
610C23×C3—32no—
611C23×C3—42no—
612C23×C3—42no—
613C23×C3—42no—
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×C3—62no—
626C23×C3—124no—
627C23×C3—124no—
628C23×C3—124no—
629C23×C3—1216no—
630C23×C3C23×D312yes—
631C23×C3C23×D312yes—
632C23×C3C23×D311yescharacteristic
633C23×C3C23×D311yescharacteristic
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—22no—
643C22×D3—22no—
644C22×D3—22no—
645C22×D3—22no—
646C22×D3—32no—
647C22×D3—32no—
648C22×D3—44no—
649C22×D3—44no—
650C22×D3—44no—
651C22×D3—416no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—62no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—62no—
658C22×D3—62no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—124no—
663C22×D3—124no—
664C22×D3—124no—
665C22×D3—124no—
666C22×D3—124no—
667C22×D3—124no—
668C22×D3—1216no—
669C22×D3—1216no—
670C22×D3C23×D312yes—
671C22×D3C23×D312yes—
672C22×D3C23×D312yes—
673C22×D3C23×D312yes—
674C3×Q8—124no—
675C3×D4—124no—
676C3×D4—124no—
677C3×D4—124no—
678C3×D4—124no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—32no—
686C2×C3×C4—32no—
687C2×C3×C4—32no—
688C2×C3×C4—32no—
689C2×C3×C4—42no—
690C2×C3×C4—42no—
691C2×C3×C4—62no—
692C2×C3×C4—62no—
693C2×C3×C4—62no—
694C2×C3×C4—62no—
695C2×C3×C4C23×D312yes—
696C2×C3×C4C23×D312yes—
697C2×C3×C4C23×D312yes—
698C2×C3×C4C23×D312yes—
699#67—44no—
700#67—44no—
701#67—124no—
702#67—124no—
703#67—124no—
704#67—124no—
705#67—124no—
706#67—124no—
707#67—124no—
708#67—124no—
709#67—128no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—62no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—64no—
724C2×Dic3—62no—
725C2×Dic3—62no—
726C2×Dic3—62no—
727C2×Dic3—62no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—122no—
731C2×Dic3—122no—
732C2×Dic3C23×D312yes—
733C2×Dic3C23×D312yes—
734C2×Dic3C23×D312yes—
735C2×Dic3C23×D312yes—
736D12—44no—
737D12—44no—
738D12—124no—
739D12—124no—
740Dic6—44no—
741Dic6—124no—
742Dic6—124no—
743Dic6—124no—
744Dic6—124no—
745Dic6—128no—
746C2×C32—42no—
747C2×C32H(3,𝔽4)14yescomplemented
748C2×C32C2×H(5,𝔽2)11yescharacteristic
749C2×C32C2×H(5,𝔽2)11yescharacteristic
750C2×C32C2×H(5,𝔽2)11yescharacteristic
751C3⋊D3—42no—
752C3×D3—42no—
753C3×D3—42no—
754C3×D3—42no—
755C3×D3—42no—
756C24—31no—
757C24—31no—
758C24—31no—
759C24—31no—
760C24—34no—
761C24—94no—
762C24—91no—
763C24—122no—
764C24—122no—
765C24—122no—
766C24—362no—
767C24—362no—
768C24—362no—
769C24C2×D3211yescharacteristic
770C2×Q8—34no—
771C2×Q8—94no—
772C2×Q8—94no—
773C2×Q8—122no—
774C2×Q8—362no—
775C2×Q8—362no—
776C2×D4—34no—
777C2×D4—34no—
778C2×D4—34no—
779C2×D4—34no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—94no—
784C2×D4—94no—
785C2×D4—122no—
786C2×D4—122no—
787C2×D4—122no—
788C2×D4—122no—
789C2×D4—362no—
790C2×D4—362no—
791C2×D4—362no—
792C2×D4—362no—
793C2×D4—362no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—91no—
799C22×C4—91no—
800C22×C4—91no—
801C22×C4C2×D3211yescharacteristic
802C22×C4C2×D3211yescharacteristic
803C22⋊C4—34no—
804C22⋊C4—34no—
805C22⋊C4—34no—
806C22⋊C4—34no—
807C22⋊C4—34no—
808C22⋊C4—94no—
809C22⋊C4—94no—
810C22⋊C4—94no—
811C22⋊C4—94no—
812C22⋊C4—94no—
813C22⋊C4—94no—
814C22⋊C4—94no—
815C22⋊C4—94no—
816C22⋊C4—94no—
817C22⋊C4—94no—
818C22⋊C4—94no—
819C22⋊C4—94no—
820C22⋊C4C2×D3214yescomplemented
821C42—34no—
822C42—94no—
823C42—94no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—21no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—44no—
838C22×C3—44no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—84no—
852C22×C3—1216no—
853C22×C3—124no—
854C22×C3—124no—
855C22×C3—124no—
856C22×C3—124no—
857C22×C3#100412yes—
858C22×C3#100412yes—
859C22×C3#100412yes—
860C22×C3#100412yes—
861C22×C3#100912yes—
862C22×C3#100912yes—
863C22×C3C24×D311yescharacteristic
864C22×C3C24×D311yescharacteristic
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—416no—
878C2×D3—44no—
879C2×D3—44no—
880C2×D3—44no—
881C2×D3—44no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—122no—
889C2×D3—122no—
890C2×D3—122no—
891C2×D3—1216no—
892C2×D3—1216no—
893C2×D3—124no—
894C2×D3—124no—
895C2×D3—244no—
896C3×C4—22no—
897C3×C4—22no—
898C3×C4—22no—
899C3×C4—22no—
900C3×C4—42no—
901C3×C4—42no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—62no—
906Dic3—22no—
907Dic3—22no—
908Dic3—22no—
909Dic3—22no—
910Dic3—64no—
911Dic3—62no—
912Dic3—62no—
913Dic3—62no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—122no—
918Dic3—122no—
919C32C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
920C23—22no—
921C23—22no—
922C23—22no—
923C23—32no—
924C23—32no—
925C23—32no—
926C23—32no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—92no—
940C23—124no—
941C23—124no—
942C23—124no—
943C23—1216no—
944C23—182no—
945C23—182no—
946C23—182no—
947C23—364no—
948C23—364no—
949C23—364no—
950C23—3616no—
951C23C22×D3212yes—
952C23C22×D3211yescharacteristic
953Q8—124no—
954Q8—364no—
955Q8—364no—
956D4—124no—
957D4—124no—
958D4—124no—
959D4—124no—
960D4—364no—
961D4—364no—
962D4—364no—
963D4—364no—
964D4—364no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—92no—
976C2×C4—92no—
977C2×C4—92no—
978C2×C4—182no—
979C2×C4—182no—
980C2×C4—182no—
981C2×C4C22×D3212yes—
982C2×C4C22×D3212yes—
983C2×C3—24no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—42no—
988C2×C3—42no—
989C2×C3—82no—
990C2×C3—122no—
991C2×C3—122no—
992C2×C3—122no—
993C2×C3—122no—
994C2×C3#559414yescomplemented
995C2×C3#568314yescomplemented
996C2×C3C2×#100411yescharacteristic
997C2×C3C2×#100411yescharacteristic
998C2×C3C2×#100411yescharacteristic
999C2×C3C2×#100411yescharacteristic
1000C2×C3C2×#100911yescharacteristic
1001C2×C3C2×#100911yescharacteristic
1002D3—42no—
1003D3—42no—
1004D3—42no—
1005D3—42no—
1006D3—122no—
1007D3—122no—
1008D3—242no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—44no—
1013C22—62no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—1216no—
1026C22—124no—
1027C22—124no—
1028C22—124no—
1029C22—124no—
1030C22—182no—
1031C22—182no—
1032C22—182no—
1033C22—3616no—
1034C22—364no—
1035C22#6430712yes—
1036C22#6431312yes—
1037C22#6431412yes—
1038C22C23×D3211yescharacteristic
1039C4—22no—
1040C4—22no—
1041C4—62no—
1042C4—62no—
1043C4—62no—
1044C4—62no—
1045C4—182no—
1046C4—182no—
1047C4—182no—
1048C3—21no—
1049C3C2×#559411yescharacteristic, complemented
1050C3C2×#568311yescharacteristic, complemented
1051C2—42no—
1052C2—122no—
1053C2—122no—
1054C2—122no—
1055C2—122no—
1056C2—362no—
1057C2#1059430914yesdirect product factor
1058C2C2×#6430711yescharacteristic
1059C2C2×#6431311yescharacteristic
1060C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×H(3,𝔽4)
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×#64094C2semidirect
2. C2×C3×#885C2semidirect
3. C2×C3×#882C2semidirect
4. C2×#63983C2semidirect
5. C2×#63977C2semidirect
6. C2×#63976C2semidirect
7. C2×#63959C2semidirect
8. C2×#63922C2semidirect
9. C2×#63922C2semidirect
10. C2×#63915C2semidirect
11. C2×#63913C2semidirect
12. C2×#63907C2semidirect
13. C2×#63863C2semidirect
14. C2×#63860C2semidirect
15. C2×#63852C2semidirect
16. #10594309C2direct (N × H)
19. C24×C3×D3C22semidirect
20. C23×D32C22semidirect
22. C22×#634C22semidirect
27. C22×C3×Dic6C22semidirect
28. C22×#627C22semidirect
33. C2×C32×C22⋊C4C22semidirect
34. C2×#3757C22semidirect
35. C2×#3752C22semidirect
36. C2×#3752C22semidirect
37. C2×C4×C3⋊Dic3C22semidirect
38. #64094C22semidirect
39. C2×C3×#217C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. C3×#885C22semidirect
46. C3×#882C22semidirect
47. #63983C22semidirect
48. #63977C22semidirect
49. #63976C22semidirect
50. C2×#3722C22semidirect
51. C2×(C2×D3)⋊Dic3C22semidirect
52. C2×(C2×D3)⋊Dic3C22semidirect
53. C2×(C2×D3)⋊Dic3C22semidirect
54. C2×(C2×D3)⋊Dic3C22semidirect
55. C2×(C2×D3)⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. #63959C22semidirect
60. C2×Dic32C22semidirect
61. #63922C22semidirect
62. #63922C22semidirect
63. #63915C22semidirect
64. #63913C22semidirect
65. #63907C22semidirect
66. #63863C22semidirect
67. #63860C22semidirect
68. #63852C22semidirect
95. C2×#885D3semidirect
99. C2×#882D3semidirect
111. C23×C3×D3C23semidirect
115. C22×D32C23semidirect
124. C2×#634C23semidirect
138. C2×C3×Dic6C23semidirect
140. C2×#627C23semidirect
149. C32×C22⋊C4C23semidirect
150. #3757C23semidirect
151. #3752C23semidirect
152. #3752C23semidirect
153. C4×C3⋊Dic3C23semidirect
154. C3×#217C23semidirect
155. C3×(C2×D3)⋊C4C23semidirect
156. C3×(C2×D3)⋊C4C23semidirect
157. C3×(C2×D3)⋊C4C23semidirect
158. C3×(C2×D3)⋊C4C23semidirect
159. C3×C4×Dic3C23semidirect
160. #3722C23semidirect
161. (C2×D3)⋊Dic3C23semidirect
162. (C2×D3)⋊Dic3C23semidirect
163. (C2×D3)⋊Dic3C23semidirect
164. (C2×D3)⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. (C2×D3)⋊Dic3C23semidirect
167. (C2×D3)⋊Dic3C23semidirect
168. (C2×D3)⋊Dic3C23semidirect
169. Dic32C23semidirect
174. C24×D3C2×D3semidirect
200. C22×Dic6C2×D3semidirect
209. C2×C3×C22⋊C4C2×D3semidirect
210. C2×C3×C22⋊C4C2×D3semidirect
225. C2×#217C2×D3semidirect
252. C2×(C2×D3)⋊C4C2×D3semidirect
253. C2×(C2×D3)⋊C4C2×D3semidirect
254. C2×(C2×D3)⋊C4C2×D3semidirect
255. C2×(C2×D3)⋊C4C2×D3semidirect
261. C2×C4×Dic3C2×D3semidirect
272. #885C2×D3semidirect
276. #882C2×D3semidirect
387. C23×D3C22×D3semidirect
462. C2×Dic6C22×D3semidirect
469. C3×C22⋊C4C22×D3semidirect
470. C3×C22⋊C4C22×D3semidirect
483. #217C22×D3semidirect
500. (C2×D3)⋊C4C22×D3semidirect
501. (C2×D3)⋊C4C22×D3semidirect
502. (C2×D3)⋊C4C22×D3semidirect
503. (C2×D3)⋊C4C22×D3semidirect
509. C4×Dic3C22×D3semidirect
595. C2×C22⋊C4D32semidirect
747. C2×C32H(3,𝔽4)semidirect
820. C22⋊C4C2×D32semidirect
919. C32C2×H(3,𝔽4)semidirect
994. C2×C3#5594semidirect
995. C2×C3#5683semidirect
1049. C3C2×#5594semidirect
1050. C3C2×#5683semidirect
1057. C2#10594309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640942
C2×C3×#8852
C2×C3×#8822
C2×#639832
C2×#639772
C2×#639762
C2×#639592
C2×#639222
C2×#639152
C2×#639132
C2×#639072
C2×#638632
C2×#638602
C2×#638522
#105943092
C2×#56833
C2×#55943