Finite Group Databasebeta

← C2×#10594234 #11910193

Subgroups — C2×#10594234 #11910193

Order 1152.

2811 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64088C211yesmaximal, characteristic, complemented
2C2×C3×#884C211yesmaximal, characteristic, complemented
3C2×C3×#882C211yesmaximal, characteristic, complemented
4C2×#63976C211yesmaximal, characteristic, complemented
5C2×#63976C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×#63970C211yesmaximal, characteristic, complemented
8C2×#63914C211yesmaximal, characteristic, complemented
9C2×#63908C211yesmaximal, characteristic, complemented
10C2×#63905C211yesmaximal, characteristic, complemented
11C2×#63891C211yesmaximal, characteristic, complemented
12C2×#63885C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63884C211yesmaximal, characteristic, complemented
15C2×#63862C211yesmaximal, characteristic, complemented
16#10594234C2116yesmaximal, direct product factor
17C2×#5620—31nomaximal
18C2×#5595—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×#625C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×#625C2211yescharacteristic, complemented
32C22×#625C2211yescharacteristic, complemented
33C22×D3×Dic3C2211yescharacteristic, complemented
34C22×D3×Dic3C2211yescharacteristic, complemented
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37C2×#3757C2211yescharacteristic
38C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C2×#3750C2211yescharacteristic, complemented
40C2×#3750C2211yescharacteristic, complemented
41C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
42#64088C2218yescomplemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×#884C2218yescomplemented
48C3×#882C2218yescomplemented
49#63976C2218yescomplemented
50#63976C2218yescomplemented
51#63970C2218yescomplemented
52#63970C2218yescomplemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×Dic3⋊Dic3C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63914C2218yescomplemented
62#63908C2218yescomplemented
63#63905C2218yescomplemented
64#63891C2218yescomplemented
65#63885C2218yescomplemented
66#63885C2218yescomplemented
67#63884C2218yescomplemented
68#63862C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×#120—31no—
71C2×#953—31no—
72C2×#953—31no—
73C2×#940—31no—
74C2×#940—31no—
75C2×#939—31no—
76C2×#939—31no—
77C2×#939—31no—
78C2×#939—31no—
79C2×#938—31no—
80C2×#938—31no—
81C2×#938—31no—
82C2×#937—31no—
83C2×#937—31no—
84C2×#935—31no—
85C2×#930—31no—
86C2×#929—31no—
87#5620—316no—
88#5595—316no—
89C2×#898—31no—
90C2×#894—31no—
91C2×#886—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884D311yescharacteristic, complemented
95C2×#883—31no—
96C2×#883—31no—
97C2×#882D311yescharacteristic, complemented
98C2×#879—31no—
99C2×#879—31no—
100C2×#879—31no—
101C2×#879—61no—
102C24×C32C2311yescharacteristic
103C23×C3×D3—42no—
104C23×C3×D3—42no—
105C23×C3×D3—42no—
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C2×C3×#67—42no—
119C2×C3×#67—42no—
120C2×C3×#67—42no—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×D12—42no—
128C2×C3×D12—42no—
129C2×C3×D12—42no—
130C2×C3×D12C2314yes—
131C2×C3×D12C2314yes—
132C2×C3×D12C2314yescomplemented
133C2×C3×C4×D3—42no—
134C2×C3×C4×D3C2314yescomplemented
135C2×#625—42no—
136C2×#625—42no—
137C2×#625—42no—
138C2×#625—42no—
139C2×#625—42no—
140C2×#625—42no—
141C2×#625C2314yes—
142C2×#625C2314yes—
143C2×#625C2314yes—
144C2×#625C2314yes—
145C2×#625C2314yescomplemented
146C2×#625C2314yescomplemented
147C2×D3×Dic3—42no—
148C2×D3×Dic3—42no—
149C2×D3×Dic3C2314yescomplemented
150C2×D3×Dic3C2314yescomplemented
151C32×C22⋊C4C2314yes—
152#3757C2314yes—
153#3757C2314yes—
154C4⋊(C3⋊Dic3)C2314yescomplemented
155#3750C2314yescomplemented
156#3750C2314yescomplemented
157C4×C3⋊Dic3C2314yescomplemented
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yescomplemented
161C3×Dic3⋊C4C2314yescomplemented
162Dic3⋊Dic3C2314yescomplemented
163Dic3⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yescomplemented
169(C2×D3)⋊Dic3C2314yescomplemented
170C2×#560—91noSylow
171C25×C3—31no—
172C24×D3C2×D311yescharacteristic
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C23×C3×C4—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—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67C2×D311yescharacteristic
193C22×#67C2×D311yescharacteristic
194C22×#67C2×D311yescharacteristic
195C23×Dic3—31no—
196C23×Dic3—31no—
197C22×D12C2×D311yescharacteristic
198C22×D12C2×D311yescharacteristic
199C22×D12C2×D311yescharacteristic, complemented
200C22×C4×D3—31no—
201C22×C4×D3—31no—
202C22×C4×D3C2×D311yescharacteristic, complemented
203C3×#121—38no—
204C3×#120—38no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C22⋊C4—21no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4—31no—
210C2×C3×C22⋊C4C2×D311yescharacteristic
211C2×C3×C22⋊C4C2×D311yescharacteristic
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×#217—61no—
226#940—38no—
227#940—38no—
228#939—38no—
229#939—38no—
230#939—38no—
231#939—38no—
232#938—38no—
233#938—38no—
234#938—38no—
235#937—38no—
236#937—38no—
237#935—38no—
238#930—38no—
239#929—38no—
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)⋊C4C2×D311yescharacteristic
247C2×(C2×D3)⋊C4C2×D311yescharacteristic
248C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
249C2×C4⋊Dic3—31no—
250C2×C4⋊Dic3—31no—
251C2×C4⋊Dic3—31no—
252C2×C4⋊Dic3—31no—
253C2×C4⋊Dic3—61no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—61no—
261C2×Dic3⋊C4—61no—
262C2×Dic3⋊C4C2×D311yescharacteristic, complemented
263C2×C4×Dic3—31no—
264C2×C4×Dic3—31no—
265C2×C4×Dic3—61no—
266#898—38no—
267#894—38no—
268#886—38no—
269#884—38no—
270#884—38no—
271#884C2×D318yescomplemented
272#883—38no—
273#883—38no—
274#882C2×D318yescomplemented
275#879—38no—
276#879—38no—
277#879—38no—
278#879—68no—
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×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—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—44no—
300C22×C3×D3—44no—
301C22×C3×D3—44no—
302C22×C3×D3—416no—
303C22×C3×D3C2412yes—
304C22×C3×D3C2412yes—
305C22×C3×D3C2412yes—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C2×C32×C4—22no—
309C2×C32×C4—22no—
310C2×C32×C4C2412yes—
311C2×C32×C4C2412yes—
312C2×C3⋊Dic3—22no—
313C2×C3⋊Dic3—22no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3C2412yes—
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
320C3×#67—44no—
321C3×#67—44no—
322C3×#67—44no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C3×D12—44no—
330C3×D12—44no—
331C3×D12—44no—
332C3×C4×D3—44no—
333#625—44no—
334#625—44no—
335#625—44no—
336#625—44no—
337#625—44no—
338#625—44no—
339D3×Dic3—44no—
340D3×Dic3—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—91no—
344C2×#126—91no—
345C2×#123—91no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#121—31no—
349C2×#121—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×#121—91no—
354C2×#120—31no—
355C2×#120—91no—
356C2×#120—91no—
357C24×C3—21no—
358C24×C3—31no—
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—42no—
370C23×D3—42no—
371C23×D3—42no—
372C23×D3C22×D311yescharacteristic
373C23×D3C22×D311yescharacteristic
374C23×D3C22×D311yescharacteristic
375C23×D3C22×D311yescharacteristic
376C23×D3C22×D311yescharacteristic
377C23×D3C22×D314yes—
378C2×C3×D4—34no—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—34no—
384C2×C3×D4—122no—
385C2×C3×D4—122no—
386C2×C3×D4—122no—
387C2×C3×D4—122no—
388C2×C3×D4—122no—
389C2×C3×D4—122no—
390C22×C3×C4—21no—
391C22×C3×C4—21no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—34no—
396C22×C3×C4—122no—
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
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—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—42no—
414C2×#67—42no—
415C2×#67—42no—
416C2×#67—122no—
417C2×#67—122no—
418C2×#67—122no—
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—122no—
428C2×#67C22×D314yes—
429C2×#67C22×D314yes—
430C2×#67C22×D314yes—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—31no—
435C22×Dic3—31no—
436C22×Dic3—31no—
437C22×Dic3—31no—
438C22×Dic3—31no—
439C22×Dic3—34no—
440C22×Dic3—34no—
441C22×Dic3—61no—
442C22×Dic3—61no—
443C22×Dic3—61no—
444C22×Dic3—61no—
445C22×Dic3—122no—
446C22×Dic3—122no—
447C22×Dic3C22×D311yescharacteristic
448C22×Dic3C22×D311yescharacteristic
449C22×Dic3C22×D311yescharacteristic
450C2×D12—42no—
451C2×D12—42no—
452C2×D12—42no—
453C2×D12C22×D314yes—
454C2×D12C22×D314yes—
455C2×D12C22×D314yescomplemented
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—42no—
459C2×C4×D3—122no—
460C2×C4×D3—122no—
461C2×C4×D3C22×D314yescomplemented
462C3×C4⋊C4—34no—
463C3×C22⋊C4—24no—
464C3×C22⋊C4—34no—
465C3×C22⋊C4—34no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4C22×D314yes—
468C3×C22⋊C4C22×D314yes—
469#217—34no—
470#217—34no—
471#217—34no—
472#217—34no—
473#217—34no—
474#217—34no—
475#217—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—64no—
480#217—64no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4C22×D314yes—
488(C2×D3)⋊C4C22×D314yes—
489(C2×D3)⋊C4C22×D314yescomplemented
490C4⋊Dic3—34no—
491C4⋊Dic3—34no—
492C4⋊Dic3—34no—
493C4⋊Dic3—34no—
494C4⋊Dic3—64no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—64no—
502Dic3⋊C4—64no—
503Dic3⋊C4C22×D314yescomplemented
504C4×Dic3—34no—
505C4×Dic3—34no—
506C4×Dic3—64no—
507C22×C32—22no—
508C22×C32—22no—
509C22×C32—22no—
510C22×C32—44no—
511C22×C32H(5,𝔽2)12yes—
512C22×C32H(5,𝔽2)12yes—
513C22×C32H(5,𝔽2)12yes—
514C22×C32C2511yescharacteristic
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
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—416no—
531C2×C3×D3—44no—
532C2×C3×D3—44no—
533C2×C3×D3—44no—
534C2×C3×D3—44no—
535C2×C3×D3—44no—
536C32×C4—22no—
537C32×C4—22no—
538C3⋊Dic3—22no—
539C3⋊Dic3—22no—
540C3⋊Dic3—22no—
541C3⋊Dic3—22no—
542C3×Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C25—31no—
546C22×D4—31no—
547C22×D4—31no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—31no—
551C22×D4—31no—
552C22×D4—91no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C23×C4—31no—
559C23×C4—91no—
560C23×C4—91no—
561#127—98no—
562#126—98no—
563#126—98no—
564#123—98no—
565#123—98no—
566#123—98no—
567#121—38no—
568#121—98no—
569#121—98no—
570#121—98no—
571#121—98no—
572#121—98no—
573#120—38no—
574#120—98no—
575#120—98no—
576C2×C4⋊C4—31no—
577C2×C4⋊C4—91no—
578C2×C4⋊C4—91no—
579C2×C4⋊C4—91no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4—91no—
582C2×C22⋊C4—31no—
583C2×C22⋊C4—31no—
584C2×C22⋊C4—31no—
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⋊C4D3211yescharacteristic
594C2×C42—91no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—21no—
603C23×C3—32no—
604C23×C3—32no—
605C23×C3—32no—
606C23×C3—32no—
607C23×C3—32no—
608C23×C3—42no—
609C23×C3—42no—
610C23×C3—42no—
611C23×C3—62no—
612C23×C3—62no—
613C23×C3—62no—
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—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—44no—
650C22×D3—44no—
651C22×D3—44no—
652C22×D3—416no—
653C22×D3C23×D312yes—
654C22×D3C23×D312yes—
655C22×D3C23×D312yes—
656C22×D3C23×D312yes—
657C22×D3C23×D312yes—
658C3×D4—124no—
659C3×D4—124no—
660C3×D4—124no—
661C3×D4—124no—
662C3×D4—124no—
663C3×D4—124no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—42no—
674C2×C3×C4—42no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—124no—
679C2×C3×C4C23×D312yes—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D312yes—
683#67—44no—
684#67—44no—
685#67—44no—
686#67—124no—
687#67—124no—
688#67—124no—
689#67—124no—
690#67—124no—
691#67—124no—
692#67—124no—
693#67—124no—
694#67—124no—
695#67—124no—
696#67—124no—
697#67—124no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—32no—
705C2×Dic3—32no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—32no—
709C2×Dic3—62no—
710C2×Dic3—62no—
711C2×Dic3—62no—
712C2×Dic3—62no—
713C2×Dic3—62no—
714C2×Dic3—62no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3—122no—
722C2×Dic3—122no—
723C2×Dic3—122no—
724C2×Dic3—122no—
725C2×Dic3—124no—
726C2×Dic3—124no—
727C2×Dic3C23×D312yes—
728C2×Dic3C23×D312yes—
729C2×Dic3C23×D312yes—
730D12—44no—
731D12—44no—
732D12—44no—
733C4×D3—44no—
734C4×D3—124no—
735C4×D3—124no—
736C2×C32—42no—
737C2×C32#56014yescomplemented
738C2×C32C2×H(5,𝔽2)11yescharacteristic
739C2×C32C2×H(5,𝔽2)11yescharacteristic
740C2×C32C2×H(5,𝔽2)11yescharacteristic
741C3×D3—42no—
742C3×D3—42no—
743C3×D3—42no—
744C3×D3—42no—
745C3×D3—42no—
746C24—31no—
747C24—31no—
748C24—31no—
749C24—31no—
750C24—31no—
751C24—34no—
752C24—122no—
753C24—122no—
754C24—122no—
755C24C2×D3211yescharacteristic
756C2×D4—34no—
757C2×D4—34no—
758C2×D4—34no—
759C2×D4—34no—
760C2×D4—34no—
761C2×D4—34no—
762C2×D4—94no—
763C2×D4—94no—
764C2×D4—94no—
765C2×D4—94no—
766C2×D4—94no—
767C2×D4—94no—
768C2×D4—122no—
769C2×D4—122no—
770C2×D4—122no—
771C2×D4—122no—
772C2×D4—122no—
773C2×D4—122no—
774C2×D4—362no—
775C2×D4—362no—
776C2×D4—362no—
777C2×D4—362no—
778C2×D4—362no—
779C2×D4—362no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—34no—
784C22×C4—94no—
785C22×C4—94no—
786C22×C4—91no—
787C22×C4—91no—
788C22×C4—91no—
789C22×C4—91no—
790C22×C4—122no—
791C22×C4—362no—
792C22×C4—362no—
793C22×C4C2×D3211yescharacteristic
794C22×C4C2×D3211yescharacteristic
795C4⋊C4—34no—
796C4⋊C4—94no—
797C4⋊C4—94no—
798C4⋊C4—94no—
799C4⋊C4—94no—
800C4⋊C4—94no—
801C22⋊C4—34no—
802C22⋊C4—34no—
803C22⋊C4—34no—
804C22⋊C4—94no—
805C22⋊C4—94no—
806C22⋊C4—94no—
807C22⋊C4—94no—
808C22⋊C4—94no—
809C22⋊C4—94no—
810C22⋊C4—94no—
811C22⋊C4—94no—
812C22⋊C4C2×D3214yes—
813C42—94no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—21no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—44no—
828C22×C3—44no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
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—84no—
845C22×C3—1216no—
846C22×C3—124no—
847C22×C3—124no—
848C22×C3—124no—
849C22×C3—124no—
850C22×C3—124no—
851C22×C3#100412yes—
852C22×C3#100412yes—
853C22×C3#100412yes—
854C22×C3#100412yes—
855C22×C3#100412yes—
856C22×C3#100912yes—
857C22×C3C24×D311yescharacteristic
858C22×C3C24×D311yescharacteristic
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—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—416no—
875C2×D3—44no—
876C2×D3—44no—
877C2×D3—44no—
878C2×D3—44no—
879C2×D3—44no—
880C3×C4—22no—
881C3×C4—22no—
882C3×C4—22no—
883C3×C4—22no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—62no—
887C3×C4—62no—
888C3×C4—62no—
889Dic3—22no—
890Dic3—22no—
891Dic3—22no—
892Dic3—62no—
893Dic3—62no—
894Dic3—62no—
895Dic3—62no—
896Dic3—62no—
897Dic3—62no—
898Dic3—62no—
899Dic3—62no—
900Dic3—122no—
901Dic3—122no—
902Dic3—122no—
903Dic3—122no—
904C32C2×#56011yescharacteristic, complemented, Sylow
905C23—22no—
906C23—22no—
907C23—22no—
908C23—32no—
909C23—32no—
910C23—32no—
911C23—32no—
912C23—32no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—124no—
929C23—124no—
930C23—124no—
931C23—1216no—
932C23C22×D3212yes—
933C23C22×D3211yescharacteristic
934D4—124no—
935D4—124no—
936D4—124no—
937D4—124no—
938D4—124no—
939D4—124no—
940D4—364no—
941D4—364no—
942D4—364no—
943D4—364no—
944D4—364no—
945D4—364no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—32no—
949C2×C4—32no—
950C2×C4—32no—
951C2×C4—62no—
952C2×C4—62no—
953C2×C4—62no—
954C2×C4—92no—
955C2×C4—92no—
956C2×C4—92no—
957C2×C4—92no—
958C2×C4—124no—
959C2×C4—182no—
960C2×C4—182no—
961C2×C4—182no—
962C2×C4—182no—
963C2×C4—364no—
964C2×C4—364no—
965C2×C4C22×D3212yes—
966C2×C4C22×D3212yes—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—24no—
971C2×C3—42no—
972C2×C3—42no—
973C2×C3—82no—
974C2×C3—122no—
975C2×C3—122no—
976C2×C3—122no—
977C2×C3—122no—
978C2×C3—122no—
979C2×C3#559514yescomplemented
980C2×C3#562014yescomplemented
981C2×C3C2×#100411yescharacteristic
982C2×C3C2×#100411yescharacteristic
983C2×C3C2×#100411yescharacteristic
984C2×C3C2×#100411yescharacteristic
985C2×C3C2×#100411yescharacteristic
986C2×C3C2×#100911yescharacteristic
987D3—42no—
988D3—42no—
989D3—42no—
990D3—42no—
991D3—42no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—44no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—62no—
1011C22—1216no—
1012C22—124no—
1013C22—124no—
1014C22—124no—
1015C22—124no—
1016C22—124no—
1017C22#6430712yes—
1018C22#6431312yes—
1019C22#6431312yes—
1020C22C23×D3211yescharacteristic
1021C4—22no—
1022C4—22no—
1023C4—62no—
1024C4—62no—
1025C4—62no—
1026C4—182no—
1027C4—182no—
1028C4—182no—
1029C4—182no—
1030C3—21no—
1031C3C2×#559511yescharacteristic, complemented
1032C3C2×#562011yescharacteristic, complemented
1033C2—42no—
1034C2—122no—
1035C2—122no—
1036C2—122no—
1037C2—122no—
1038C2—122no—
1039C2#1059423414yesdirect product factor
1040C2C2×#6430711yescharacteristic
1041C2C2×#6431311yescharacteristic
1042C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#560
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×#64088C2semidirect
2. C2×C3×#884C2semidirect
3. C2×C3×#882C2semidirect
4. C2×#63976C2semidirect
5. C2×#63976C2semidirect
6. C2×#63970C2semidirect
7. C2×#63970C2semidirect
8. C2×#63914C2semidirect
9. C2×#63908C2semidirect
10. C2×#63905C2semidirect
11. C2×#63891C2semidirect
12. C2×#63885C2semidirect
13. C2×#63885C2semidirect
14. C2×#63884C2semidirect
15. C2×#63862C2semidirect
16. #10594234C2direct (N × H)
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
31. C22×#625C22semidirect
32. C22×#625C22semidirect
33. C22×D3×Dic3C22semidirect
34. C22×D3×Dic3C22semidirect
38. C2×C4⋊(C3⋊Dic3)C22semidirect
39. C2×#3750C22semidirect
40. C2×#3750C22semidirect
41. C2×C4×C3⋊Dic3C22semidirect
42. #64088C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C3×#884C22semidirect
48. C3×#882C22semidirect
49. #63976C22semidirect
50. #63976C22semidirect
51. #63970C22semidirect
52. #63970C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63914C22semidirect
62. #63908C22semidirect
63. #63905C22semidirect
64. #63891C22semidirect
65. #63885C22semidirect
66. #63885C22semidirect
67. #63884C22semidirect
68. #63862C22semidirect
94. C2×#884D3semidirect
97. C2×#882D3semidirect
132. C2×C3×D12C23semidirect
134. C2×C3×C4×D3C23semidirect
145. C2×#625C23semidirect
146. C2×#625C23semidirect
149. C2×D3×Dic3C23semidirect
150. C2×D3×Dic3C23semidirect
154. C4⋊(C3⋊Dic3)C23semidirect
155. #3750C23semidirect
156. #3750C23semidirect
157. C4×C3⋊Dic3C23semidirect
160. C3×(C2×D3)⋊C4C23semidirect
161. C3×Dic3⋊C4C23semidirect
162. Dic3⋊Dic3C23semidirect
163. Dic3⋊Dic3C23semidirect
168. (C2×D3)⋊Dic3C23semidirect
169. (C2×D3)⋊Dic3C23semidirect
199. C22×D12C2×D3semidirect
202. C22×C4×D3C2×D3semidirect
248. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×Dic3⋊C4C2×D3semidirect
271. #884C2×D3semidirect
274. #882C2×D3semidirect
455. C2×D12C22×D3semidirect
461. C2×C4×D3C22×D3semidirect
489. (C2×D3)⋊C4C22×D3semidirect
503. Dic3⋊C4C22×D3semidirect
737. C2×C32#560semidirect
904. C32C2×#560semidirect
979. C2×C3#5595semidirect
980. C2×C3#5620semidirect
1031. C3C2×#5595semidirect
1032. C3C2×#5620semidirect
1039. C2#10594234direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640882
C2×C3×#8842
C2×C3×#8822
C2×#639762
C2×#639702
C2×#639142
C2×#639082
C2×#639052
C2×#638912
C2×#638852
C2×#638842
C2×#638622
#105942342
C2×#56203
C2×#55953