Finite Group Databasebeta

← C2×#10595003 #11900785

Subgroups — C2×#10595003 #11900785

Order 1152.

3669 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63979C211yesmaximal, characteristic, complemented
6C2×#63971C211yesmaximal, characteristic, complemented
7C2×#63970C211yesmaximal, characteristic, complemented
8C2×#63959C211yesmaximal, characteristic, complemented
9C2×#63907C211yesmaximal, characteristic, complemented
10#10595003C2116yesmaximal, direct product factor
11C2×C4×#626C211yesmaximal, characteristic, complemented
12C2×C4×#625C211yesmaximal, characteristic, complemented
13C2×#63886C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
16C2×#63839C211yesmaximal, characteristic, complemented
17C2×#5832—31nomaximal
18C2×#5548—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C2×C3×#235—28no—
26C2×C3×#235C2218yescomplemented
27C22×C3×D12C2211yescharacteristic
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×C4×D3C2211yescharacteristic
30C22×C3×C4×D3C2211yescharacteristic
31C22×C3×Dic6C2211yescharacteristic
32C22×#627C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic
35C22×#626C2211yescharacteristic
36C22×#625C2211yescharacteristic
37C22×#625C2211yescharacteristic
38C22×D3×Dic3C2211yescharacteristic
39C22×D3×Dic3C2211yescharacteristic
40C2×#3798—28no—
41C2×#3798C2218yescomplemented
42C2×#3757C2211yescharacteristic
43C4×#638C2218yescomplemented
44C2×#3752C2211yescharacteristic
45C2×#3750C2211yescharacteristic
46C2×C4×C3⋊Dic3C2211yescharacteristic
47C2×C3×#217C2211yescharacteristic
48C3×C4×#67C2218yescomplemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×C4×Dic3C2211yescharacteristic
52#63979C2218yescomplemented
53#63971C2218yescomplemented
54#63970C2218yescomplemented
55C2×#3724C2211yescharacteristic
56C2×Dic3⋊Dic3C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61#63959C2218yescomplemented
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64#63907C2218yescomplemented
65C4×#626C2218yescomplemented
66C4×#625C2218yescomplemented
67#63886C2218yescomplemented
68#63885C2218yescomplemented
69C4×D3×Dic3C2218yescomplemented
70#63839C2218yescomplemented
71C22×C3×#41—31no—
72C22×#235—31no—
73C22×#235—31no—
74C22×#235D311yescharacteristic, complemented
75C2×C3×C4×D4—31no—
76#5832—316no—
77C2×#947—31no—
78C2×#944—31no—
79C2×#940—31no—
80C2×#940—31no—
81C2×#939—31no—
82C2×#939—31no—
83C2×#939—31no—
84C2×#939—31no—
85C2×#938—31no—
86C2×#936—31no—
87C2×C4×#67—31no—
88C2×C4×#67—31no—
89C2×C4×#67—31no—
90C2×C4×#67—31no—
91C2×C4×#67—31no—
92C2×C4×#67—61no—
93C2×C4×#67D311yescharacteristic, complemented
94C22×C4×Dic3—31no—
95#5548—316no—
96C2×#895—31no—
97C2×#888—31no—
98C2×#885—31no—
99C2×#885—31no—
100C2×#884—31no—
101C2×#884—31no—
102C2×C4×D12—31no—
103C2×C42×D3—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4—24no—
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2314yes—
112C22×C32×C4C2311yescharacteristic
113C2×#638—24no—
114C2×#638C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C2×C4×C3⋊D3—24no—
119C2×C4×C3⋊D3C2314yes—
120C2×C3×#67—24no—
121C2×C3×#67—24no—
122C2×C3×#67—24no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C2×C3×#67C2314yes—
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C3×#235—232no—
132C2×C3×D12—24no—
133C2×C3×D12C2314yes—
134C2×C3×C4×D3—24no—
135C2×C3×C4×D3—24no—
136C2×C3×C4×D3D418yescomplemented
137C2×C3×C4×D3C2314yes—
138C2×C3×C4×D3C2314yes—
139C2×C3×C4×D3C2314yes—
140C2×C3×Dic6—24no—
141C2×C3×Dic6C2314yes—
142C2×#627—24no—
143C2×#627C2314yes—
144C2×#626—24no—
145C2×#626—24no—
146C2×#626—24no—
147C2×#626C2314yes—
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#625—24no—
151C2×#625—24no—
152C2×#625C2314yes—
153C2×#625C2314yes—
154C2×D3×Dic3—24no—
155C2×D3×Dic3—24no—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2314yes—
158#3798—232no—
159#3757C2314yes—
160#3752C2314yes—
161#3750C2314yes—
162C4×C3⋊Dic3C2314yes—
163C3×#217C2314yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×C4×Dic3C2314yes—
167#3724C2314yes—
168Dic3⋊Dic3C2314yes—
169#3722C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173Dic32C2314yes—
174Dic32C2314yes—
175C2×#532—91noSylow
176C2×C3×#41—38no—
177C2×C3×#41—68no—
178C22×C3×Q8—31no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C23×C3×C4—21no—
184C23×C3×C4—31no—
185C23×C3×C4—31no—
186C23×C3×C4—31no—
187C23×C3×C4C2×D311yescharacteristic
188C23×C3×C4C2×D311yescharacteristic
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—61no—
199C22×#67C2×D311yescharacteristic
200C22×#67C2×D311yescharacteristic
201C22×#67C2×D311yescharacteristic
202C23×Dic3—31no—
203C23×Dic3—31no—
204C2×#235—28no—
205C2×#235—38no—
206C2×#235—38no—
207C2×#235—68no—
208C2×#235—68no—
209C2×#235C2×D318yescomplemented
210C22×D12—31no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12C2×D311yescharacteristic
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—61no—
219C22×C4×D3C2×D311yescharacteristic
220C22×C4×D3C2×D311yescharacteristic
221C22×C4×D3C2×D311yescharacteristic
222C22×Dic6—31no—
223C22×Dic6—31no—
224C22×Dic6C2×D311yescharacteristic
225C3×C4×D4—38no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C42—31no—
230C2×#217—31no—
231C2×#217—31no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—31no—
235C2×#217—61no—
236C2×#217C2×D311yescharacteristic
237#947—38no—
238#944—38no—
239#940—38no—
240#940—38no—
241#939—38no—
242#939—38no—
243#939—38no—
244#939—38no—
245#938—38no—
246#936—38no—
247C4×#67—38no—
248C4×#67—38no—
249C4×#67—38no—
250C4×#67—38no—
251C4×#67—38no—
252C4×#67—68no—
253C4×#67C2×D318yescomplemented
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4C2×D311yescharacteristic
263C2×C4⋊Dic3—31no—
264C2×Dic3⋊C4—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—61no—
270C2×Dic3⋊C4C2×D311yescharacteristic
271C2×C4×Dic3—31no—
272C2×C4×Dic3—31no—
273C2×C4×Dic3—31no—
274C2×C4×Dic3—31no—
275C2×C4×Dic3—31no—
276C2×C4×Dic3—31no—
277C2×C4×Dic3—38no—
278C2×C4×Dic3—61no—
279C2×C4×Dic3C2×D311yescharacteristic
280#895—38no—
281#888—38no—
282#885—38no—
283#885—38no—
284#884—38no—
285#884—38no—
286C4×D12—38no—
287C42×D3—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32C2412yes—
292C23×C32C2411yescharacteristic
293C22×C3⋊D3—22no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3—22no—
296C22×C3⋊D3C2412yes—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3C2×D414yes—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C22×C3×D3C2412yes—
309C2×C32×C4—22no—
310C2×C32×C4—28no—
311C2×C32×C4C2×D414yes—
312C2×C32×C4C2412yes—
313C2×C32×C4C2412yes—
314#638—28no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3—22no—
317C2×C3⋊Dic3#4114yescomplemented
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
320C2×C3⋊Dic3C2412yes—
321C4×C3⋊D3—28no—
322C3×#67—28no—
323C3×#67—28no—
324C3×#67—28no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3C2×D414yes—
329C2×C3×Dic3#4114yescomplemented
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C3×D12—28no—
336C3×C4×D3—28no—
337C3×C4×D3—28no—
338C3×C4×D3C2×D4116yescomplemented
339C3×Dic6—28no—
340#627—28no—
341#626—28no—
342#626—28no—
343#626—28no—
344#625—28no—
345#625—28no—
346D3×Dic3—28no—
347D3×Dic3—28no—
348C22×#41—31no—
349C22×#41—91no—
350#532—916no—
351C2×C4⋊Q8—91no—
352C2×#127—91no—
353C2×#124—91no—
354C2×#124—91no—
355C2×#121—91no—
356C2×#121—91no—
357C2×#121—91no—
358C2×#121—91no—
359C2×C4×D4—31no—
360C2×C4×D4—91no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C22×C42—91no—
364C24×C3—21no—
365C24×C3—31no—
366C24×C3—31no—
367C24×C3—31no—
368C24×C3C22×D311yescharacteristic
369C24×C3C22×D311yescharacteristic
370C23×D3—31no—
371C23×D3—31no—
372C23×D3—61no—
373C23×D3C22×D311yescharacteristic
374C23×D3C22×D311yescharacteristic
375C23×D3C22×D311yescharacteristic
376C3×#41—632no—
377C2×C3×Q8—34no—
378C2×C3×Q8—64no—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—64no—
384C2×C3×D4—64no—
385C2×C3×D4—64no—
386C2×C3×D4—64no—
387C22×C3×C4—24no—
388C22×C3×C4—24no—
389C22×C3×C4—21no—
390C22×C3×C4—24no—
391C22×C3×C4—21no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—38no—
395C22×C3×C4—34no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—34no—
400C22×C3×C4—34no—
401C22×C3×C4—44no—
402C22×C3×C4—64no—
403C22×C3×C4—64no—
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C22×C3×C4C22×D314yes—
407C22×C3×C4C22×D314yes—
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C2×#67—24no—
411C2×#67—24no—
412C2×#67—24no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—34no—
421C2×#67—34no—
422C2×#67—64no—
423C2×#67—64no—
424C2×#67—64no—
425C2×#67—64no—
426C2×#67—64no—
427C2×#67—64no—
428C2×#67—64no—
429C2×#67—68no—
430C2×#67—64no—
431C2×#67—64no—
432C2×#67—64no—
433C2×#67C22×D314yes—
434C2×#67C22×D314yes—
435C2×#67C22×D314yes—
436C22×Dic3—31no—
437C22×Dic3—31no—
438C22×Dic3—31no—
439C22×Dic3—31no—
440C22×Dic3—31no—
441C22×Dic3—31no—
442C22×Dic3—34no—
443C22×Dic3—34no—
444C22×Dic3—61no—
445C22×Dic3—61no—
446C22×Dic3—61no—
447C22×Dic3—64no—
448C22×Dic3—64no—
449C22×Dic3C22×D311yescharacteristic
450C22×Dic3C22×D311yescharacteristic
451C22×Dic3C22×D311yescharacteristic
452C22×Dic3C22×D311yescharacteristic
453C22×Dic3C22×D311yescharacteristic
454#235—232no—
455#235—632no—
456#235—632no—
457C2×D12—24no—
458C2×D12—34no—
459C2×D12—34no—
460C2×D12—34no—
461C2×D12—64no—
462C2×D12—64no—
463C2×D12—64no—
464C2×D12C22×D314yes—
465C2×C4×D3—24no—
466C2×C4×D3—24no—
467C2×C4×D3—34no—
468C2×C4×D3—34no—
469C2×C4×D3—34no—
470C2×C4×D3—34no—
471C2×C4×D3—64no—
472C2×C4×D3—64no—
473C2×C4×D3—64no—
474C2×C4×D3—64no—
475C2×C4×D3—64no—
476C2×C4×D3—124no—
477C2×C4×D3#6718yescomplemented
478C2×C4×D3C22×D314yes—
479C2×C4×D3C22×D314yes—
480C2×C4×D3C22×D314yes—
481C2×Dic6—24no—
482C2×Dic6—34no—
483C2×Dic6—34no—
484C2×Dic6—64no—
485C2×Dic6—64no—
486C2×Dic6C22×D314yes—
487C3×C4⋊C4—34no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490C3×C42—34no—
491#217—34no—
492#217—34no—
493#217—34no—
494#217—34no—
495#217—34no—
496#217—64no—
497#217C22×D314yes—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—64no—
506(C2×D3)⋊C4C22×D314yes—
507C4⋊Dic3—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—64no—
514Dic3⋊C4C22×D314yes—
515C4×Dic3—34no—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—64no—
522C4×Dic3C22×D314yes—
523C22×C32—22no—
524C22×C32—22no—
525C22×C32—22no—
526C22×C32—44no—
527C22×C32C22×D412yes—
528C22×C32C2×#4112yes—
529C22×C32C2×#4112yes—
530C22×C32C2511yescharacteristic
531C2×C3⋊D3—22no—
532C2×C3⋊D3—22no—
533C2×C3⋊D3—22no—
534C2×C3⋊D3—44no—
535C2×C3×D3—28no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—44no—
545C2×C3×D3—44no—
546C2×C3×D3C22×D414yes—
547C32×C4—22no—
548C32×C4C22×D414yes—
549C3⋊Dic3—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3C2×#4114yescomplemented
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3C22×D414yes—
556C3×Dic3C2×#4114yescomplemented
557C2×#41—38no—
558C2×#41—68no—
559C2×#41—98no—
560C2×#41—188no—
561C22×Q8—31no—
562C22×Q8—91no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4—91no—
573C23×C4—31no—
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—91no—
579C23×C4D3211yescharacteristic
580C4⋊Q8—98no—
581#127—98no—
582#124—98no—
583#124—98no—
584#121—98no—
585#121—98no—
586#121—98no—
587#121—98no—
588C4×D4—38no—
589C4×D4—98no—
590C4×D4—98no—
591C4×D4—98no—
592C2×C4⋊C4—31no—
593C2×C4⋊C4—91no—
594C2×C4⋊C4—91no—
595C2×C4⋊C4—91no—
596C2×C22⋊C4—31no—
597C2×C22⋊C4—31no—
598C2×C22⋊C4—91no—
599C2×C22⋊C4—91no—
600C2×C22⋊C4—91no—
601C2×C22⋊C4—91no—
602C2×C22⋊C4—91no—
603C2×C22⋊C4—91no—
604C2×C42—31no—
605C2×C42—98no—
606C2×C42—91no—
607C2×C42—91no—
608C2×C42—91no—
609C23×C3—24no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—21no—
617C23×C3—22no—
618C23×C3—34no—
619C23×C3—32no—
620C23×C3—32no—
621C23×C3—32no—
622C23×C3—42no—
623C23×C3—42no—
624C23×C3—62no—
625C23×C3—62no—
626C23×C3—62no—
627C23×C3—62no—
628C23×C3—62no—
629C23×C3—62no—
630C23×C3—62no—
631C23×C3—62no—
632C23×C3C23×D312yes—
633C23×C3C23×D312yes—
634C23×C3C23×D311yescharacteristic
635C23×C3C23×D311yescharacteristic
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—32no—
645C22×D3—32no—
646C22×D3—62no—
647C22×D3—64no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—62no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—122no—
655C22×D3—122no—
656C22×D3C2×#6714yes—
657C22×D3C23×D312yes—
658C22×D3C23×D312yes—
659C22×D3C23×D312yes—
660C3×Q8—68no—
661C3×D4—68no—
662C3×D4—68no—
663C3×D4—68no—
664C3×D4—68no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—28no—
668C2×C3×C4—28no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—24no—
672C2×C3×C4—34no—
673C2×C3×C4—34no—
674C2×C3×C4—32no—
675C2×C3×C4—32no—
676C2×C3×C4—316no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—48no—
681C2×C3×C4—42no—
682C2×C3×C4—62no—
683C2×C3×C4—62no—
684C2×C3×C4—62no—
685C2×C3×C4—68no—
686C2×C3×C4—68no—
687C2×C3×C4D3×D414yes—
688C2×C3×C4C2×#6714yes—
689C2×C3×C4C23×D312yes—
690C2×C3×C4C23×D312yes—
691C2×C3×C4C23×D312yes—
692C2×C3×C4C23×D312yes—
693#67—28no—
694#67—28no—
695#67—28no—
696#67—68no—
697#67—68no—
698#67—68no—
699#67—68no—
700#67—68no—
701#67—68no—
702#67—616no—
703#67—68no—
704#67—68no—
705#67—68no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—34no—
710C2×Dic3—34no—
711C2×Dic3—32no—
712C2×Dic3—32no—
713C2×Dic3—32no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—64no—
718C2×Dic3—62no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3—68no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—62no—
726C2×Dic3—68no—
727C2×Dic3—122no—
728C2×Dic3—122no—
729C2×Dic3#23514yescomplemented
730C2×Dic3C2×#6714yes—
731C2×Dic3C23×D312yes—
732C2×Dic3C23×D312yes—
733C2×Dic3C23×D312yes—
734C2×Dic3C23×D312yes—
735C2×Dic3C23×D312yes—
736D12—28no—
737D12—68no—
738D12—68no—
739D12—68no—
740C4×D3—28no—
741C4×D3—28no—
742C4×D3—68no—
743C4×D3—68no—
744C4×D3—68no—
745C4×D3—68no—
746C4×D3—128no—
747C4×D3C2×#67116yescomplemented
748Dic6—28no—
749Dic6—68no—
750Dic6—68no—
751C2×C32—42no—
752C2×C32#53214yescomplemented
753C2×C32C23×D411yescharacteristic
754C2×C32C22×#4111yescharacteristic
755C2×C32C22×#4111yescharacteristic
756C3⋊D3—42no—
757C3×D3—24no—
758C3×D3—42no—
759C3×D3—42no—
760C24—31no—
761C24—31no—
762C24—31no—
763C24—91no—
764C24C2×D3211yescharacteristic
765#41—632no—
766#41—1832no—
767C2×Q8—34no—
768C2×Q8—64no—
769C2×Q8—94no—
770C2×Q8—184no—
771C2×D4—34no—
772C2×D4—34no—
773C2×D4—34no—
774C2×D4—34no—
775C2×D4—64no—
776C2×D4—64no—
777C2×D4—64no—
778C2×D4—64no—
779C2×D4—94no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—94no—
784C2×D4—94no—
785C2×D4—184no—
786C2×D4—184no—
787C2×D4—184no—
788C2×D4—184no—
789C2×D4—184no—
790C2×D4—184no—
791C22×C4—24no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—34no—
795C22×C4—38no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—34no—
800C22×C4—34no—
801C22×C4—64no—
802C22×C4—64no—
803C22×C4—94no—
804C22×C4—94no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—94no—
809C22×C4—184no—
810C22×C4—184no—
811C22×C4—184no—
812C22×C4C2×D3211yescharacteristic
813C22×C4C2×D3214yes—
814C22×C4C2×D3211yescharacteristic
815C4⋊C4—34no—
816C4⋊C4—94no—
817C4⋊C4—94no—
818C4⋊C4—94no—
819C22⋊C4—34no—
820C22⋊C4—34no—
821C22⋊C4—94no—
822C22⋊C4—94no—
823C22⋊C4—94no—
824C22⋊C4—94no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C42—34no—
828C42—94no—
829C42—94no—
830C42—94no—
831C22×C3—24no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—34no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—48no—
846C22×C3—44no—
847C22×C3—44no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—68no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—124no—
858C22×C3—124no—
859C22×C3C2×#23512yes—
860C22×C3C2×D3×D412yes—
861C22×C3D3×#4112yes—
862C22×C3D3×#4112yes—
863C22×C3D3×#4112yes—
864C22×C3C22×#6712yes—
865C22×C3C24×D311yescharacteristic
866C22×C3C24×D311yescharacteristic
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—28no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—44no—
877C2×D3—44no—
878C2×D3—64no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—128no—
888C2×D3—124no—
889C2×D3—124no—
890C2×D3C22×#6714yes—
891C3×C4—22no—
892C3×C4—22no—
893C3×C4—24no—
894C3×C4—34no—
895C3×C4—34no—
896C3×C4—42no—
897C3×C4—62no—
898C3×C4—62no—
899C3×C4—62no—
900C3×C4C2×D3×D414yes—
901C3×C4C22×#6714yes—
902Dic3—22no—
903Dic3—22no—
904Dic3—22no—
905Dic3—34no—
906Dic3—34no—
907Dic3—64no—
908Dic3—62no—
909Dic3—62no—
910Dic3—62no—
911Dic3—62no—
912Dic3—122no—
913Dic3—122no—
914Dic3C2×#23514yescomplemented
915Dic3C22×#6714yes—
916C32C2×#53211yescharacteristic, complemented, Sylow
917C23—22no—
918C23—22no—
919C23—22no—
920C23—34no—
921C23—32no—
922C23—32no—
923C23—32no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—92no—
933C23—182no—
934C23—182no—
935C23—182no—
936C23C22×D3212yes—
937C23C22×D3211yescharacteristic
938Q8—68no—
939Q8—188no—
940D4—68no—
941D4—68no—
942D4—68no—
943D4—68no—
944D4—188no—
945D4—188no—
946D4—188no—
947D4—188no—
948D4—188no—
949D4—188no—
950C2×C4—22no—
951C2×C4—28no—
952C2×C4—34no—
953C2×C4—34no—
954C2×C4—32no—
955C2×C4—32no—
956C2×C4—316no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—68no—
964C2×C4—68no—
965C2×C4—94no—
966C2×C4—92no—
967C2×C4—92no—
968C2×C4—92no—
969C2×C4—188no—
970C2×C4—188no—
971C2×C4—182no—
972C2×C4—182no—
973C2×C4—188no—
974C2×C4D3×#6714yes—
975C2×C4C22×D3212yes—
976C2×C4C22×D3212yes—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—24no—
981C2×C3—44no—
982C2×C3—42no—
983C2×C3—42no—
984C2×C3—64no—
985C2×C3—122no—
986C2×C3—122no—
987C2×C3#554814yescomplemented
988C2×C3#583214yescomplemented
989C2×C3C22×#23511yescharacteristic
990C2×C3C22×D3×D411yescharacteristic
991C2×C3C2×D3×#4111yescharacteristic
992C2×C3C2×D3×#4111yescharacteristic
993C2×C3C2×D3×#4111yescharacteristic
994C2×C3C23×#6711yescharacteristic
995D3—24no—
996D3—42no—
997D3—42no—
998D3—124no—
999D3—122no—
1000D3—122no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—34no—
1005C22—44no—
1006C22—62no—
1007C22—62no—
1008C22—68no—
1009C22—62no—
1010C22—62no—
1011C22—62no—
1012C22—62no—
1013C22—62no—
1014C22—62no—
1015C22—124no—
1016C22—124no—
1017C22—182no—
1018C22—182no—
1019C22—182no—
1020C22—364no—
1021C22D3×#23512yes—
1022C22#6430612yes—
1023C22C2×D3×#6712yes—
1024C22C23×D3211yescharacteristic
1025C4—22no—
1026C4—34no—
1027C4—34no—
1028C4—62no—
1029C4—62no—
1030C4—62no—
1031C4—94no—
1032C4—182no—
1033C4—182no—
1034C4C2×D3×#6714yes—
1035C3—21no—
1036C3C2×#554811yescharacteristic, complemented
1037C3C2×#583211yescharacteristic, complemented
1038C2—42no—
1039C2—64no—
1040C2—122no—
1041C2—122no—
1042C2—362no—
1043C2#1059500314yesdirect product factor
1044C2C2×D3×#23511yescharacteristic
1045C2C2×#6430611yescharacteristic
1046C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×#3798C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63979C2semidirect
6. C2×#63971C2semidirect
7. C2×#63970C2semidirect
8. C2×#63959C2semidirect
9. C2×#63907C2semidirect
10. #10595003C2direct (N × H)
11. C2×C4×#626C2semidirect
12. C2×C4×#625C2semidirect
13. C2×#63886C2semidirect
14. C2×#63885C2semidirect
15. C2×C4×D3×Dic3C2semidirect
16. C2×#63839C2semidirect
26. C2×C3×#235C22semidirect
41. C2×#3798C22semidirect
43. C4×#638C22semidirect
48. C3×C4×#67C22semidirect
52. #63979C22semidirect
53. #63971C22semidirect
54. #63970C22semidirect
61. #63959C22semidirect
64. #63907C22semidirect
65. C4×#626C22semidirect
66. C4×#625C22semidirect
67. #63886C22semidirect
68. #63885C22semidirect
69. C4×D3×Dic3C22semidirect
70. #63839C22semidirect
74. C22×#235D3semidirect
93. C2×C4×#67D3semidirect
136. C2×C3×C4×D3D4semidirect
209. C2×#235C2×D3semidirect
253. C4×#67C2×D3semidirect
317. C2×C3⋊Dic3#41semidirect
329. C2×C3×Dic3#41semidirect
338. C3×C4×D3C2×D4semidirect
477. C2×C4×D3#67semidirect
551. C3⋊Dic3C2×#41semidirect
556. C3×Dic3C2×#41semidirect
729. C2×Dic3#235semidirect
747. C4×D3C2×#67semidirect
752. C2×C32#532semidirect
914. Dic3C2×#235semidirect
916. C32C2×#532semidirect
987. C2×C3#5548semidirect
988. C2×C3#5832semidirect
1036. C3C2×#5548semidirect
1037. C3C2×#5832semidirect
1043. C2#10595003direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#37982
C2×C4×#6382
C2×C3×C4×#672
C2×#639792
C2×#639712
C2×#639702
C2×#639592
C2×#639072
#105950032
C2×C4×#6262
C2×C4×#6252
C2×#638862
C2×#638852
C2×C4×D3×Dic32
C2×#638392
C2×#58323
C2×#55483