Finite Group Databasebeta

← C2×#10594238 #11901336

Subgroups — C2×#10594238 #11901336

Order 1152.

2833 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64087C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C2×#63976C211yesmaximal, characteristic, complemented
6C2×Dic3×#67C211yesmaximal, characteristic, complemented
7C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63913C211yesmaximal, characteristic, complemented
9C2×#63908C211yesmaximal, characteristic, complemented
10C2×#63905C211yesmaximal, characteristic, complemented
11C2×#63885C211yesmaximal, characteristic, complemented
12C2×#63884C211yesmaximal, characteristic, complemented
13C2×#63861C211yesmaximal, characteristic, complemented
14C2×#63860C211yesmaximal, characteristic, complemented
15C2×#63859C211yesmaximal, characteristic, complemented
16#10594238C2116yesmaximal, direct product factor
17C2×#5593—31nomaximal
18C2×#5560—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×#625C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C2×#3750C2211yescharacteristic, complemented
36C2×#3750C2211yescharacteristic, complemented
37#64087C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×C4×Dic3C2211yescharacteristic, complemented
43C3×#882C2218yescomplemented
44C3×#67⋊C4C2218yescomplemented
45#63980C2218yescomplemented
46#63976C2218yescomplemented
47Dic3×#67C2218yescomplemented
48C2×#3724C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2218yescomplemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63913C2218yescomplemented
62#63908C2218yescomplemented
63#63905C2218yescomplemented
64#63885C2218yescomplemented
65#63884C2218yescomplemented
66#63861C2218yescomplemented
67#63860C2218yescomplemented
68#63859C2218yescomplemented
69C2×C3×#120—31no—
70C2×C3×C4×D4—31no—
71C2×#953—31no—
72C22×#217—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#938—31no—
77C2×#937—31no—
78C2×#936—31no—
79C2×#935—31no—
80C2×D4×Dic3—31no—
81C2×#930—31no—
82C2×#929—31no—
83C2×C4×#67—31no—
84C22×(C2×D3)⋊C4—31no—
85#5593—316no—
86#5560—316no—
87C2×#898—31no—
88C2×#894—31no—
89C2×#885—31no—
90C2×#885—31no—
91C2×#884—31no—
92C2×#883—31no—
93C2×#882D311yescharacteristic, complemented
94C2×#67⋊C4D311yescharacteristic, complemented
95C2×#879—31no—
96C2×#879—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—61no—
100C2×#876—31no—
101C2×#875—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×D3C2311yescharacteristic
110C23×C3×D3C2314yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C3⋊Dic3—42no—
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2314yes—
119C2×#634—42no—
120C2×#634C2314yescomplemented
121C2×C3×#67—24no—
122C2×C3×#67—24no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C22×C3×Dic3—42no—
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2314yes—
131C2×C3×D12—42no—
132C2×C3×D12—42no—
133C2×C3×D12C2314yes—
134C2×C3×D12C2314yes—
135C2×C3×C4×D3—42no—
136C2×C3×C4×D3C2314yescomplemented
137C2×#625—42no—
138C2×#625—42no—
139C2×#625—42no—
140C2×#625C2314yes—
141C2×#625C2314yes—
142C2×#625C2314yescomplemented
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yescomplemented
145C32×C22⋊C4C2314yes—
146#3757C2314yes—
147C4⋊(C3⋊Dic3)C2314yescomplemented
148#3750C2314yescomplemented
149#3750C2314yescomplemented
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yescomplemented
153C3×Dic3⋊C4C2314yescomplemented
154C3×C4×Dic3C2314yescomplemented
155#3724C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yescomplemented
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C25×C3—31no—
169C24×D3C2×D311yescharacteristic
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C23×C3×C4—31no—
175C23×C3×C4—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67C2×D311yescharacteristic
183C22×#67C2×D311yescharacteristic
184C23×Dic3—31no—
185C23×Dic3—31no—
186C23×Dic3—31no—
187C23×Dic3—61no—
188C23×Dic3C2×D311yescharacteristic
189C22×D12C2×D311yescharacteristic
190C22×D12C2×D311yescharacteristic
191C22×C4×D3—31no—
192C22×C4×D3C2×D311yescharacteristic, complemented
193C22×Dic6—31no—
194C22×Dic6—31no—
195C22×Dic6—61no—
196C3×#120—38no—
197C3×C4×D4—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⋊C4C2×D311yescharacteristic
204C2×C3×C22⋊C4C2×D311yescharacteristic
205C2×C3×C42—31no—
206#953—38no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217—31no—
218C2×#217—38no—
219C2×#217—61no—
220#939—38no—
221#939—38no—
222#939—38no—
223#938—38no—
224#937—38no—
225#936—38no—
226#935—38no—
227D4×Dic3—38no—
228#930—38no—
229#929—38no—
230C4×#67—38no—
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—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—38no—
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×(C2×D3)⋊C4C2×D311yescharacteristic
243C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—61no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—61no—
256C2×Dic3⋊C4—61no—
257C2×Dic3⋊C4C2×D311yescharacteristic, complemented
258C2×C4×Dic3—31no—
259C2×C4×Dic3—31no—
260C2×C4×Dic3C2×D311yescharacteristic, complemented
261#898—38no—
262#894—38no—
263#885—38no—
264#885—38no—
265#884—38no—
266#883—38no—
267#882C2×D318yescomplemented
268#67⋊C4C2×D318yescomplemented
269#879—38no—
270#879—38no—
271#878—38no—
272#878—38no—
273#878—68no—
274#876—38no—
275#875—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32#4114yes—
279C23×C32C2412yes—
280C23×C32C2411yescharacteristic
281C22×C3×D3—28no—
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—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—44no—
295C22×C3×D3—44no—
296C22×C3×D3—416no—
297C22×C3×D3C2412yes—
298C22×C3×D3C2412yes—
299C22×C3×D3C2412yes—
300C22×C3×D3C2412yes—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304C2×C32×C4C2412yes—
305C2×C3⋊Dic3—22no—
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—
313C2×C3⋊Dic3C2412yes—
314#634—44no—
315C3×#67—28no—
316C3×#67—28no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—44no—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×D12—44no—
327C3×D12—44no—
328C3×C4×D3—44no—
329#625—44no—
330#625—44no—
331#625—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—91no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—31no—
345C2×#120—91no—
346C2×C4×D4—31no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—31no—
353C24×C3—31no—
354C24×C3—34no—
355C24×C3—64no—
356C24×C3—122no—
357C24×C3—122no—
358C24×C3C22×D311yescharacteristic
359C24×C3C22×D311yescharacteristic
360C23×D3—24no—
361C23×D3—42no—
362C23×D3—42no—
363C23×D3C22×D311yescharacteristic
364C23×D3C22×D311yescharacteristic
365C23×D3C22×D311yescharacteristic
366C23×D3C22×D311yescharacteristic
367C23×D3C22×D314yes—
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—34no—
372C2×C3×D4—64no—
373C2×C3×D4—64no—
374C2×C3×D4—122no—
375C2×C3×D4—122no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—34no—
383C22×C3×C4—34no—
384C22×C3×C4—122no—
385C22×C3×C4—122no—
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C2×#67—24no—
391C2×#67—24no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—122no—
399C2×#67—122no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67C22×D314yes—
405C2×#67C22×D314yes—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—34no—
415C22×Dic3—34no—
416C22×Dic3—34no—
417C22×Dic3—42no—
418C22×Dic3—61no—
419C22×Dic3—64no—
420C22×Dic3—61no—
421C22×Dic3—61no—
422C22×Dic3—61no—
423C22×Dic3—122no—
424C22×Dic3—122no—
425C22×Dic3—122no—
426C22×Dic3—124no—
427C22×Dic3C22×D311yescharacteristic
428C22×Dic3C22×D311yescharacteristic
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D314yes—
432C2×D12—42no—
433C2×D12—42no—
434C2×D12C22×D314yes—
435C2×D12C22×D314yes—
436C2×C4×D3—34no—
437C2×C4×D3—42no—
438C2×C4×D3—122no—
439C2×C4×D3C22×D314yescomplemented
440C2×Dic6—34no—
441C2×Dic6—34no—
442C2×Dic6—64no—
443C2×Dic6—122no—
444C2×Dic6—122no—
445C2×Dic6—124no—
446C3×C4⋊C4—34no—
447C3×C22⋊C4—24no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4C22×D314yes—
452C3×C22⋊C4C22×D314yes—
453C3×C42—34no—
454#217—34no—
455#217—34no—
456#217—34no—
457#217—34no—
458#217—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—34no—
465#217—64no—
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—34no—
475(C2×D3)⋊C4C22×D314yes—
476(C2×D3)⋊C4C22×D314yes—
477(C2×D3)⋊C4C22×D314yescomplemented
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—64no—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—64no—
490Dic3⋊C4—64no—
491Dic3⋊C4C22×D314yescomplemented
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3C22×D314yescomplemented
495C22×C32—28no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32C2×#4114yes—
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—22no—
507C2×C3×D3—22no—
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—416no—
516C2×C3×D3—44no—
517C2×C3×D3—44no—
518C2×C3×D3—44no—
519C2×C3×D3—44no—
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—31no—
531C22×Q8—91no—
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—31no—
541C23×C4—91no—
542C23×C4—91no—
543#126—98no—
544#126—98no—
545#124—98no—
546#124—98no—
547#123—98no—
548#123—98no—
549C22⋊Q8—98no—
550#121—98no—
551#121—98no—
552#121—98no—
553#120—38no—
554#120—98no—
555C4×D4—38no—
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—91no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—98no—
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
578C2×C42—31no—
579C2×C42—91no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—21no—
586C23×C3—24no—
587C23×C3—32no—
588C23×C3—32no—
589C23×C3—32no—
590C23×C3—32no—
591C23×C3—42no—
592C23×C3—42no—
593C23×C3—62no—
594C23×C3—68no—
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×C3—62no—
604C23×C3—62no—
605C23×C3—62no—
606C23×C3—124no—
607C23×C3—124no—
608C23×C3—1216no—
609C23×C3#23514yes—
610C23×C3#23714yes—
611C23×C3C23×D312yes—
612C23×C3C23×D312yes—
613C23×C3C23×D311yescharacteristic
614C23×C3C23×D311yescharacteristic
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—28no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—44no—
629C22×D3—44no—
630C22×D3—416no—
631C22×D3C23×D312yes—
632C22×D3C23×D312yes—
633C22×D3C23×D312yes—
634C22×D3C23×D312yes—
635C3×D4—68no—
636C3×D4—68no—
637C3×D4—124no—
638C3×D4—124no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—42no—
650C2×C3×C4—42no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—62no—
655C2×C3×C4—124no—
656C2×C3×C4—124no—
657C2×C3×C4C23×D312yes—
658C2×C3×C4C23×D312yes—
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D312yes—
661#67—28no—
662#67—28no—
663#67—124no—
664#67—124no—
665#67—124no—
666#67—124no—
667#67—124no—
668#67—124no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—44no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—64no—
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—122no—
696C2×Dic3—122no—
697C2×Dic3—122no—
698C2×Dic3—124no—
699C2×Dic3—124no—
700C2×Dic3—124no—
701C2×Dic3—128no—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706D12—44no—
707D12—44no—
708C4×D3—44no—
709C4×D3—124no—
710Dic6—124no—
711Dic6—124no—
712Dic6—128no—
713C2×C32—24no—
714C2×C32#53814yescomplemented
715C2×C32C22×#4111yescharacteristic
716C2×C32C2×H(5,𝔽2)11yescharacteristic
717C2×C32C2×H(5,𝔽2)11yescharacteristic
718C3×D3—42no—
719C3×D3—42no—
720C3×D3—42no—
721C3×D3—42no—
722C24—31no—
723C24—31no—
724C24—31no—
725C24—31no—
726C24—34no—
727C24—64no—
728C24—122no—
729C24—122no—
730C24C2×D3211yescharacteristic
731C2×Q8—94no—
732C2×Q8—362no—
733C2×D4—34no—
734C2×D4—34no—
735C2×D4—34no—
736C2×D4—34no—
737C2×D4—64no—
738C2×D4—64no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—94no—
742C2×D4—122no—
743C2×D4—122no—
744C2×D4—362no—
745C2×D4—362no—
746C2×D4—362no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—34no—
752C22×C4—34no—
753C22×C4—94no—
754C22×C4—91no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—91no—
758C22×C4—94no—
759C22×C4—122no—
760C22×C4—122no—
761C22×C4—362no—
762C22×C4—362no—
763C22×C4C2×D3211yescharacteristic
764C22×C4C2×D3211yescharacteristic
765C4⋊C4—34no—
766C4⋊C4—94no—
767C4⋊C4—94no—
768C4⋊C4—94no—
769C4⋊C4—94no—
770C4⋊C4—94no—
771C22⋊C4—34no—
772C22⋊C4—34no—
773C22⋊C4—34no—
774C22⋊C4—94no—
775C22⋊C4—94no—
776C22⋊C4—94no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4C2×D3214yes—
785C42—34no—
786C42—94no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—28no—
792C22×C3—28no—
793C22×C3—22no—
794C22×C3—24no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—21no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—48no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—1216no—
814C22×C3—124no—
815C22×C3—124no—
816C22×C3—124no—
817C22×C3—124no—
818C22×C3C2×#23514yes—
819C22×C3C2×#23512yes—
820C22×C3C2×#23714yes—
821C22×C3C2×#23712yes—
822C22×C3#100412yes—
823C22×C3#100412yes—
824C22×C3#100412yes—
825C22×C3#100912yes—
826C22×C3C24×D311yescharacteristic
827C22×C3C24×D311yescharacteristic
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—416no—
841C2×D3—44no—
842C2×D3—44no—
843C2×D3—44no—
844C2×D3—44no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—42no—
850C3×C4—42no—
851C3×C4—62no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—62no—
855Dic3—22no—
856Dic3—22no—
857Dic3—22no—
858Dic3—22no—
859Dic3—64no—
860Dic3—62no—
861Dic3—62no—
862Dic3—62no—
863Dic3—62no—
864Dic3—62no—
865Dic3—62no—
866Dic3—62no—
867Dic3—62no—
868Dic3—122no—
869Dic3—122no—
870Dic3—122no—
871C32C2×#53811yescharacteristic, complemented, Sylow
872C23—22no—
873C23—22no—
874C23—32no—
875C23—32no—
876C23—32no—
877C23—32no—
878C23—62no—
879C23—62no—
880C23—68no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—124no—
892C23—124no—
893C23—1216no—
894C23#379514yes—
895C23C22×D3212yes—
896C23C22×D3211yescharacteristic
897Q8—364no—
898D4—68no—
899D4—68no—
900D4—124no—
901D4—124no—
902D4—364no—
903D4—364no—
904D4—364no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—32no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—92no—
916C2×C4—92no—
917C2×C4—92no—
918C2×C4—92no—
919C2×C4—124no—
920C2×C4—124no—
921C2×C4—182no—
922C2×C4—182no—
923C2×C4—182no—
924C2×C4—182no—
925C2×C4—364no—
926C2×C4—364no—
927C2×C4C22×D3212yes—
928C2×C4C22×D3212yes—
929C2×C3—24no—
930C2×C3—24no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—24no—
935C2×C3—44no—
936C2×C3—122no—
937C2×C3—122no—
938C2×C3—122no—
939C2×C3—122no—
940C2×C3#556014yescomplemented
941C2×C3#559314yescomplemented
942C2×C3C22×#23511yescharacteristic
943C2×C3C22×#23711yescharacteristic
944C2×C3C2×#100411yescharacteristic
945C2×C3C2×#100411yescharacteristic
946C2×C3C2×#100411yescharacteristic
947C2×C3C2×#100911yescharacteristic
948D3—42no—
949D3—42no—
950D3—42no—
951D3—42no—
952C22—22no—
953C22—22no—
954C22—28no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—1216no—
968C22—124no—
969C22—124no—
970C22—124no—
971C22—124no—
972C22C2×#379514yes—
973C22C2×#379512yes—
974C22#6431312yes—
975C22#6431412yes—
976C22C23×D3211yescharacteristic
977C4—22no—
978C4—22no—
979C4—62no—
980C4—62no—
981C4—62no—
982C4—62no—
983C4—182no—
984C4—182no—
985C4—182no—
986C4—182no—
987C3—21no—
988C3C2×#556011yescharacteristic, complemented
989C3C2×#559311yescharacteristic, complemented
990C2—24no—
991C2—122no—
992C2—122no—
993C2—122no—
994C2—122no—
995C2#1059423814yesdirect product factor
996C2C22×#379511yescharacteristic
997C2C2×#6431311yescharacteristic
998C2C2×#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×#64087C2semidirect
2. C2×C3×#882C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C2×#63980C2semidirect
5. C2×#63976C2semidirect
6. C2×Dic3×#67C2semidirect
7. C22×(C2×D3)⋊Dic3C2semidirect
8. C2×#63913C2semidirect
9. C2×#63908C2semidirect
10. C2×#63905C2semidirect
11. C2×#63885C2semidirect
12. C2×#63884C2semidirect
13. C2×#63861C2semidirect
14. C2×#63860C2semidirect
15. C2×#63859C2semidirect
16. #10594238C2direct (N × H)
21. C22×#634C22semidirect
27. C22×C3×C4×D3C22semidirect
30. C22×#625C22semidirect
31. C22×D3×Dic3C22semidirect
34. C2×C4⋊(C3⋊Dic3)C22semidirect
35. C2×#3750C22semidirect
36. C2×#3750C22semidirect
37. #64087C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C2×C3×C4×Dic3C22semidirect
43. C3×#882C22semidirect
44. C3×#67⋊C4C22semidirect
45. #63980C22semidirect
46. #63976C22semidirect
47. Dic3×#67C22semidirect
48. C2×#3724C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×Dic32C22semidirect
61. #63913C22semidirect
62. #63908C22semidirect
63. #63905C22semidirect
64. #63885C22semidirect
65. #63884C22semidirect
66. #63861C22semidirect
67. #63860C22semidirect
68. #63859C22semidirect
93. C2×#882D3semidirect
94. C2×#67⋊C4D3semidirect
120. C2×#634C23semidirect
136. C2×C3×C4×D3C23semidirect
142. C2×#625C23semidirect
144. C2×D3×Dic3C23semidirect
147. C4⋊(C3⋊Dic3)C23semidirect
148. #3750C23semidirect
149. #3750C23semidirect
152. C3×(C2×D3)⋊C4C23semidirect
153. C3×Dic3⋊C4C23semidirect
154. C3×C4×Dic3C23semidirect
155. #3724C23semidirect
156. Dic3⋊Dic3C23semidirect
163. (C2×D3)⋊Dic3C23semidirect
164. (C2×D3)⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
192. C22×C4×D3C2×D3semidirect
243. C2×(C2×D3)⋊C4C2×D3semidirect
257. C2×Dic3⋊C4C2×D3semidirect
260. C2×C4×Dic3C2×D3semidirect
267. #882C2×D3semidirect
268. #67⋊C4C2×D3semidirect
439. C2×C4×D3C22×D3semidirect
477. (C2×D3)⋊C4C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
494. C4×Dic3C22×D3semidirect
714. C2×C32#538semidirect
871. C32C2×#538semidirect
940. C2×C3#5560semidirect
941. C2×C3#5593semidirect
988. C3C2×#5560semidirect
989. C3C2×#5593semidirect
995. C2#10594238direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640872
C2×C3×#8822
C2×C3×#67⋊C42
C2×#639802
C2×#639762
C2×Dic3×#672
C22×(C2×D3)⋊Dic32
C2×#639132
C2×#639082
C2×#639052
C2×#638852
C2×#638842
C2×#638612
C2×#638602
C2×#638592
#105942382
C2×#55933
C2×#55603