Finite Group Databasebeta

← C2×#10594221 #11901525

Subgroups — C2×#10594221 #11901525

Order 1152.

2691 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×C3×#884C211yesmaximal, characteristic, complemented
4C2×#63979C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×Dic3×#67C211yesmaximal, characteristic, complemented
7C2×#63970C211yesmaximal, characteristic, complemented
8C2×#63916C211yesmaximal, characteristic, complemented
9C2×#63906C211yesmaximal, characteristic, complemented
10C2×#63891C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63885C211yesmaximal, characteristic, complemented
13C2×#63881C211yesmaximal, characteristic, complemented
14C2×#63846C211yesmaximal, characteristic, complemented
15C2×#63841C211yesmaximal, characteristic, complemented
16#10594221C2116yesmaximal, direct product factor
17C2×#5663—31nomaximal
18C2×#5619—31nomaximal
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×D3×Dic3C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
38C2×#3750C2211yescharacteristic
39#64092C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×C4⋊Dic3C2211yescharacteristic
44C2×C3×C4⋊Dic3C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C3×#886C2218yescomplemented
47C3×#884C2218yescomplemented
48#63979C2218yescomplemented
49#63978C2218yescomplemented
50Dic3×#67C2218yescomplemented
51#63970C2218yescomplemented
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63916C2218yescomplemented
62#63906C2218yescomplemented
63#63891C2218yescomplemented
64#63890C2218yescomplemented
65#63885C2218yescomplemented
66#63881C2218yescomplemented
67#63846C2218yescomplemented
68#63841C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#121—31no—
71C2×#940—31no—
72C2×#940—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#938—31no—
77C2×#938—31no—
78C2×D4×Dic3—31no—
79C2×#930—31no—
80C2×#930—31no—
81C2×C4×#67—31no—
82C2×#926—31no—
83#5663—316no—
84#5619—316no—
85C2×#895—31no—
86C2×#894—31no—
87C2×#893—31no—
88C2×#892—31no—
89C2×#890—31no—
90C2×#889—31no—
91C2×#886—31no—
92C2×#886—31no—
93C2×#886D311yescharacteristic, complemented
94C2×#884—31no—
95C2×#884—31no—
96C2×#884D311yescharacteristic, complemented
97C2×#883—31no—
98C2×#883—31no—
99C2×#883—31no—
100C2×#883—61no—
101C2×#67⋊C4—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C2×#638—42no—
110C2×#638C2314yes—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C2×C4×C3⋊D3—42no—
115C2×C4×C3⋊D3C2314yes—
116C2×C3×#67—24no—
117C2×C3×#67—42no—
118C2×C3×#67—42no—
119C2×C3×#67C2314yes—
120C2×C3×#67C2314yes—
121C2×C3×#67C2314yes—
122C22×C3×Dic3—42no—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2314yes—
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×D12—42no—
130C2×C3×D12C2314yes—
131C2×C3×C4×D3—24no—
132C2×C3×C4×D3C2314yes—
133C2×#626—24no—
134C2×#626—42no—
135C2×#626—42no—
136C2×#626C2314yes—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#625—42no—
140C2×#625—42no—
141C2×#625C2314yes—
142C2×#625C2314yes—
143C2×D3×Dic3—42no—
144C2×D3×Dic3—42no—
145C2×D3×Dic3C2314yes—
146C2×D3×Dic3C2314yes—
147C32×C22⋊C4C2314yes—
148#3757C2314yes—
149#3752C2314yes—
150C4⋊(C3⋊Dic3)C2314yes—
151#3750C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×C4⋊Dic3C2314yes—
156C3×C4⋊Dic3C2314yes—
157C3×Dic3⋊C4C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161#3722C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165Dic32C2314yes—
166Dic32C2314yes—
167C2×#540—91noSylow
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C23×C3×C4—31no—
173C23×C3×C4—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—61no—
184C22×#67C2×D311yescharacteristic
185C22×#67C2×D311yescharacteristic
186C22×#67C2×D311yescharacteristic
187C23×Dic3—31no—
188C23×Dic3—31no—
189C23×Dic3C2×D311yescharacteristic
190C22×D12—31no—
191C22×D12—31no—
192C22×D12—31no—
193C22×D12C2×D311yescharacteristic
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—31no—
198C22×C4×D3—61no—
199C22×C4×D3C2×D311yescharacteristic
200C3×#123—38no—
201C3×#121—38no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C22⋊C4—21no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4C2×D311yescharacteristic
210C2×C3×C22⋊C4C2×D311yescharacteristic
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—61no—
217#940—38no—
218#940—38no—
219#939—38no—
220#939—38no—
221#939—38no—
222#938—38no—
223#938—38no—
224D4×Dic3—38no—
225#930—38no—
226#930—38no—
227C4×#67—38no—
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—61no—
236C2×(C2×D3)⋊C4C2×D311yescharacteristic
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239#926—38no—
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3—31no—
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3—61no—
246C2×C4⋊Dic3C2×D311yescharacteristic
247C2×C4⋊Dic3C2×D311yescharacteristic
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—61no—
254C2×Dic3⋊C4C2×D311yescharacteristic
255C2×C4×Dic3—31no—
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3—31no—
259#895—38no—
260#894—38no—
261#893—38no—
262#892—38no—
263#890—38no—
264#889—38no—
265#886—38no—
266#886—38no—
267#886C2×D318yescomplemented
268#884—38no—
269#884—38no—
270#884C2×D318yescomplemented
271#883—38no—
272#883—38no—
273#883—38no—
274#883—68no—
275#67⋊C4—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—22no—
294C22×C3×D3C2412yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×C32×C4—22no—
298C2×C32×C4—22no—
299C2×C32×C4C2412yes—
300C2×C32×C4C2412yes—
301#638—44no—
302C2×C3⋊Dic3—22no—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3—22no—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2412yes—
307C2×C3⋊Dic3C2412yes—
308C4×C3⋊D3—44no—
309C3×#67—28no—
310C3×#67—44no—
311C3×#67—44no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—44no—
317C2×C3×Dic3#4114yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C3×D12—44no—
324C3×C4×D3—28no—
325#626—28no—
326#626—44no—
327#626—44no—
328#625—44no—
329#625—44no—
330D3×Dic3—44no—
331D3×Dic3—44no—
332#540—916no—
333C2×#127—91no—
334C2×#125—91no—
335C2×#123—31no—
336C2×#123—91no—
337C2×#123—91no—
338C2×#123—91no—
339C2×#121—31no—
340C2×#121—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#121—91no—
345C2×C4×D4—91no—
346C2×C4×D4—91no—
347C2×#117—91no—
348C24×C3—21no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—61no—
357C23×D3C22×D311yescharacteristic
358C23×D3C22×D311yescharacteristic
359C23×D3C22×D311yescharacteristic
360C2×C3×D4—34no—
361C2×C3×D4—34no—
362C2×C3×D4—34no—
363C2×C3×D4—34no—
364C2×C3×D4—64no—
365C2×C3×D4—122no—
366C2×C3×D4—122no—
367C2×C3×D4—122no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—34no—
376C22×C3×C4—34no—
377C22×C3×C4—64no—
378C22×C3×C4—122no—
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C2×#67—24no—
384C2×#67—34no—
385C2×#67—34no—
386C2×#67—34no—
387C2×#67—34no—
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—42no—
394C2×#67—42no—
395C2×#67—64no—
396C2×#67—64no—
397C2×#67—122no—
398C2×#67—122no—
399C2×#67—122no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67—122no—
405C2×#67—124no—
406C2×#67C22×D314yes—
407C2×#67C22×D314yes—
408C2×#67C22×D314yes—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—34no—
416C22×Dic3—34no—
417C22×Dic3—42no—
418C22×Dic3—61no—
419C22×Dic3—61no—
420C22×Dic3—61no—
421C22×Dic3—122no—
422C22×Dic3—122no—
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D314yes—
428C22×Dic3C22×D311yescharacteristic
429C2×D12—34no—
430C2×D12—34no—
431C2×D12—34no—
432C2×D12—42no—
433C2×D12—64no—
434C2×D12—122no—
435C2×D12—122no—
436C2×D12C22×D314yes—
437C2×C4×D3—24no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—64no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—122no—
446C2×C4×D3—122no—
447C2×C4×D3—124no—
448C2×C4×D3C22×D314yes—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C22⋊C4—24no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4C22×D314yes—
457C3×C22⋊C4C22×D314yes—
458#217—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—64no—
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—64no—
472(C2×D3)⋊C4C22×D314yes—
473(C2×D3)⋊C4C22×D314yes—
474(C2×D3)⋊C4C22×D314yes—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—34no—
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—64no—
481C4⋊Dic3C22×D314yes—
482C4⋊Dic3C22×D314yes—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—64no—
489Dic3⋊C4C22×D314yes—
490C4×Dic3—34no—
491C4×Dic3—34no—
492C4×Dic3—34no—
493C4×Dic3—34no—
494C22×C32—22no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—44no—
498C22×C32C2×#4112yes—
499C22×C32H(5,𝔽2)12yes—
500C22×C32H(5,𝔽2)12yes—
501C22×C32C2511yescharacteristic
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—22no—
505C2×C3⋊D3—44no—
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—44no—
516C2×C3×D3—44no—
517C2×C3×D3—44no—
518C32×C4—22no—
519C32×C4—22no—
520C3⋊Dic3—22no—
521C3⋊Dic3—22no—
522C3⋊Dic3—22no—
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3C2×#4114yes—
528C22×D4—31no—
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—31no—
532C22×D4—91no—
533C22×D4—91no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C23×C4—31no—
539C23×C4—31no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543#127—98no—
544#125—98no—
545#123—38no—
546#123—98no—
547#123—98no—
548#123—98no—
549#121—38no—
550#121—98no—
551#121—98no—
552#121—98no—
553#121—98no—
554#121—98no—
555C4×D4—98no—
556C4×D4—98no—
557#117—98no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
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⋊C4D3211yescharacteristic
576C2×C42—91no—
577C2×C42—91no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—21no—
586C23×C3—32no—
587C23×C3—32no—
588C23×C3—32no—
589C23×C3—42no—
590C23×C3—42no—
591C23×C3—42no—
592C23×C3—62no—
593C23×C3—62no—
594C23×C3—62no—
595C23×C3—62no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3C23×D312yes—
602C23×C3C23×D312yes—
603C23×C3C23×D311yescharacteristic
604C23×C3C23×D311yescharacteristic
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—32no—
615C22×D3—32no—
616C22×D3—62no—
617C22×D3—64no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3C23×D312yes—
627C22×D3C23×D312yes—
628C22×D3C23×D312yes—
629C3×D4—68no—
630C3×D4—124no—
631C3×D4—124no—
632C3×D4—124no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—34no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—42no—
646C2×C3×C4—42no—
647C2×C3×C4—68no—
648C2×C3×C4—62no—
649C2×C3×C4—62no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—124no—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D312yes—
657#67—28no—
658#67—44no—
659#67—44no—
660#67—68no—
661#67—124no—
662#67—124no—
663#67—124no—
664#67—124no—
665#67—124no—
666#67—124no—
667#67—124no—
668#67—124no—
669#67—128no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—44no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—122no—
691C2×Dic3—122no—
692C2×Dic3—122no—
693C2×Dic3—124no—
694C2×Dic3—124no—
695C2×Dic3#23714yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701D12—44no—
702D12—68no—
703D12—124no—
704D12—124no—
705C4×D3—28no—
706C4×D3—124no—
707C4×D3—124no—
708C4×D3—124no—
709C4×D3—124no—
710C4×D3—128no—
711C2×C32—42no—
712C2×C32#54014yescomplemented
713C2×C32C22×#4111yescharacteristic
714C2×C32C2×H(5,𝔽2)11yescharacteristic
715C2×C32C2×H(5,𝔽2)11yescharacteristic
716C3⋊D3—42no—
717C3×D3—42no—
718C3×D3—42no—
719C3×D3—42no—
720C24—31no—
721C24—31no—
722C24—31no—
723C24—91no—
724C24C2×D3211yescharacteristic
725C2×D4—34no—
726C2×D4—34no—
727C2×D4—34no—
728C2×D4—34no—
729C2×D4—64no—
730C2×D4—94no—
731C2×D4—94no—
732C2×D4—94no—
733C2×D4—94no—
734C2×D4—94no—
735C2×D4—94no—
736C2×D4—122no—
737C2×D4—122no—
738C2×D4—122no—
739C2×D4—184no—
740C2×D4—362no—
741C2×D4—362no—
742C2×D4—362no—
743C2×D4—362no—
744C2×D4—362no—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—34no—
751C22×C4—34no—
752C22×C4—64no—
753C22×C4—94no—
754C22×C4—94no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—91no—
758C22×C4—94no—
759C22×C4—122no—
760C22×C4—362no—
761C22×C4—362no—
762C22×C4—362no—
763C22×C4C2×D3211yescharacteristic
764C22×C4C2×D3211yescharacteristic
765C4⋊C4—34no—
766C4⋊C4—34no—
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—94no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4C2×D3214yes—
783C42—94no—
784C42—94no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—21no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—44no—
799C22×C3—44no—
800C22×C3—62no—
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—84no—
810C22×C3—124no—
811C22×C3—124no—
812C22×C3—124no—
813C22×C3C2×#23712yes—
814C22×C3#100412yes—
815C22×C3#100412yes—
816C22×C3D3×#4112yes—
817C22×C3#100912yes—
818C22×C3#100912yes—
819C22×C3C24×D311yescharacteristic
820C22×C3C24×D311yescharacteristic
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—44no—
831C2×D3—44no—
832C2×D3—44no—
833C2×D3—64no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—128no—
843C2×D3—124no—
844C2×D3—124no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—34no—
850C3×C4—42no—
851C3×C4—42no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—62no—
855C3×C4—62no—
856Dic3—22no—
857Dic3—22no—
858Dic3—22no—
859Dic3—22no—
860Dic3—62no—
861Dic3—62no—
862Dic3—62no—
863Dic3—62no—
864Dic3—62no—
865Dic3—62no—
866Dic3—122no—
867Dic3—122no—
868Dic3—122no—
869Dic3C2×#23714yes—
870C32C2×#54011yescharacteristic, complemented, Sylow
871C23—22no—
872C23—22no—
873C23—22no—
874C23—32no—
875C23—32no—
876C23—32no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—92no—
887C23—182no—
888C23—182no—
889C23—182no—
890C23C22×D3212yes—
891C23C22×D3211yescharacteristic
892D4—68no—
893D4—124no—
894D4—124no—
895D4—124no—
896D4—188no—
897D4—364no—
898D4—364no—
899D4—364no—
900D4—364no—
901D4—364no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—34no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—68no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—92no—
916C2×C4—92no—
917C2×C4—92no—
918C2×C4—124no—
919C2×C4—182no—
920C2×C4—182no—
921C2×C4—182no—
922C2×C4—364no—
923C2×C4—364no—
924C2×C4—364no—
925C2×C4C22×D3212yes—
926C2×C4C22×D3212yes—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—24no—
931C2×C3—42no—
932C2×C3—42no—
933C2×C3—82no—
934C2×C3—122no—
935C2×C3—122no—
936C2×C3—122no—
937C2×C3#561914yescomplemented
938C2×C3#566314yescomplemented
939C2×C3C22×#23711yescharacteristic
940C2×C3C2×#100411yescharacteristic
941C2×C3C2×#100411yescharacteristic
942C2×C3C2×D3×#4111yescharacteristic
943C2×C3C2×#100911yescharacteristic
944C2×C3C2×#100911yescharacteristic
945D3—42no—
946D3—42no—
947D3—42no—
948D3—124no—
949D3—122no—
950D3—122no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—44no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—124no—
965C22—124no—
966C22—124no—
967C22—182no—
968C22—182no—
969C22—182no—
970C22—364no—
971C22#6430712yes—
972C22D3×#23712yes—
973C22#6431412yes—
974C22C23×D3211yescharacteristic
975C4—22no—
976C4—22no—
977C4—34no—
978C4—62no—
979C4—62no—
980C4—62no—
981C4—62no—
982C4—182no—
983C4—182no—
984C4—182no—
985C3—21no—
986C3C2×#561911yescharacteristic, complemented
987C3C2×#566311yescharacteristic, complemented
988C2—42no—
989C2—122no—
990C2—122no—
991C2—122no—
992C2—362no—
993C2#1059422114yesdirect product factor
994C2C2×#6430711yescharacteristic
995C2C2×D3×#23711yescharacteristic
996C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#540
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×#64092C2semidirect
2. C2×C3×#886C2semidirect
3. C2×C3×#884C2semidirect
4. C2×#63979C2semidirect
5. C2×#63978C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×#63970C2semidirect
8. C2×#63916C2semidirect
9. C2×#63906C2semidirect
10. C2×#63891C2semidirect
11. C2×#63890C2semidirect
12. C2×#63885C2semidirect
13. C2×#63881C2semidirect
14. C2×#63846C2semidirect
15. C2×#63841C2semidirect
16. #10594221C2direct (N × H)
39. #64092C22semidirect
46. C3×#886C22semidirect
47. C3×#884C22semidirect
48. #63979C22semidirect
49. #63978C22semidirect
50. Dic3×#67C22semidirect
51. #63970C22semidirect
61. #63916C22semidirect
62. #63906C22semidirect
63. #63891C22semidirect
64. #63890C22semidirect
65. #63885C22semidirect
66. #63881C22semidirect
67. #63846C22semidirect
68. #63841C22semidirect
93. C2×#886D3semidirect
96. C2×#884D3semidirect
267. #886C2×D3semidirect
270. #884C2×D3semidirect
712. C2×C32#540semidirect
870. C32C2×#540semidirect
937. C2×C3#5619semidirect
938. C2×C3#5663semidirect
986. C3C2×#5619semidirect
987. C3C2×#5663semidirect
993. C2#10594221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640922
C2×C3×#8862
C2×C3×#8842
C2×#639792
C2×#639782
C2×Dic3×#672
C2×#639702
C2×#639162
C2×#639062
C2×#638912
C2×#638902
C2×#638852
C2×#638812
C2×#638462
C2×#638412
#105942212
C2×#56633
C2×#56193