Finite Group Databasebeta

← C2×#10595155 #11900771

Subgroups — C2×#10595155 #11900771

Order 1152.

3669 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64148C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6C2×#63979C211yesmaximal, characteristic, complemented
7C2×#63978C211yesmaximal, characteristic, complemented
8C2×Dic3×#67C211yesmaximal, characteristic, complemented
9C2×#63959C211yesmaximal, characteristic, complemented
10C22×Dic32C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595155C2116yesmaximal, direct product factor
13C2×#63907C211yesmaximal, characteristic, complemented
14C2×#63904C211yesmaximal, characteristic, complemented
15C2×#63879C211yesmaximal, characteristic, complemented
16C2×#63839C211yesmaximal, characteristic, complemented
17C2×#5832—31nomaximal
18C2×#5596—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C23×C3×Dic3C2211yescharacteristic
29C23×C3×Dic3C2211yescharacteristic
30C2×C3×#237—28no—
31C2×C3×#237C2218yescomplemented
32C22×C3×C4×D3C2211yescharacteristic
33C22×C3×Dic6C2211yescharacteristic
34C22×#627C2211yescharacteristic
35C22×#626C2211yescharacteristic
36C22×#626C2211yescharacteristic
37C22×#625C2211yescharacteristic
38C22×#624C2211yescharacteristic
39C2×#3804—28no—
40C2×#3804C2218yescomplemented
41C22×D3×Dic3C2211yescharacteristic
42C2×#3757C2211yescharacteristic
43#64148C2218yescomplemented
44C2×#3752C2211yescharacteristic
45C2×#3750C2211yescharacteristic
46C2×C3×#217C2211yescharacteristic
47C3×#939C2218yescomplemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50#63980C2218yescomplemented
51#63979C2218yescomplemented
52#63978C2218yescomplemented
53Dic3×#67C2218yescomplemented
54C2×#3724C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60#63959C2218yescomplemented
61C2×Dic32C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64C2×Dic32C2211yescharacteristic
65C2×Dic32C2218yescomplemented
66#63952C2218yescomplemented
67#63907C2218yescomplemented
68#63904C2218yescomplemented
69#63879C2218yescomplemented
70#63839C2218yescomplemented
71C22×C3×#41—31no—
72C22×#237—31no—
73C22×#237D311yescharacteristic, complemented
74C22×#235—31no—
75C2×C3×#121—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×#939—31no—
86C2×#939—61no—
87C2×#939D311yescharacteristic, complemented
88C2×#936—31no—
89C2×D4×Dic3—31no—
90C2×#930—31no—
91C2×C4×#67—31no—
92C2×C4×#67—31no—
93C2×C4×#67—31no—
94C2×C4×#67—31no—
95C22×C4×Dic3—31no—
96C22×C4×Dic3—31no—
97#5596—316no—
98C2×#893—31no—
99C2×#888—31no—
100C2×#885—31no—
101C2×#885—31no—
102C2×#67⋊C4—31no—
103C2×#67⋊C4—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C2×C32×D4—24no—
110C2×C32×D4C2314yes—
111C22×C32×C4C2311yescharacteristic
112C2×#638—24no—
113C2×#638—24no—
114C2×#638C2314yes—
115C2×#638C2314yes—
116C22×C3⋊Dic3—24no—
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2314yes—
120C22×C3⋊Dic3C2311yescharacteristic
121C2×C3×#67—24no—
122C2×C3×#67—24no—
123C2×C3×#67—24no—
124C2×C3×#67—24no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C22×C3×Dic3—24no—
130C22×C3×Dic3—24no—
131C22×C3×Dic3D418yescomplemented
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2314yes—
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2314yes—
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2314yes—
140C22×C3×Dic3C2311yescharacteristic
141C3×#237—232no—
142C2×C3×C4×D3—24no—
143C2×C3×C4×D3C2314yes—
144C2×C3×Dic6—24no—
145C2×C3×Dic6C2314yes—
146C2×#627—24no—
147C2×#627C2314yes—
148C2×#626—24no—
149C2×#626—24no—
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#625—24no—
153C2×#625C2314yes—
154C2×#624—24no—
155C2×#624C2314yes—
156#3804—232no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3C2314yes—
159#3757C2314yes—
160#3752C2314yes—
161#3750C2314yes—
162C3×#217C2314yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165#3724C2314yes—
166Dic3⋊Dic3C2314yes—
167#3722C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171Dic32C2314yes—
172Dic32C2314yes—
173Dic32C2314yes—
174Dic32C2314yes—
175C2×#532—91noSylow
176C2×C3×#41—38no—
177C2×C3×#41—68no—
178C22×C3×Q8—31no—
179C22×C3×D4—21no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C22×C3×D4—31no—
184C22×C3×D4C2×D311yescharacteristic
185C22×C3×D4C2×D311yescharacteristic
186C23×C3×C4—31no—
187C23×C3×C4—31no—
188C23×C3×C4—31no—
189C23×C3×C4—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×#67—61no—
200C22×#67C2×D311yescharacteristic
201C22×#67C2×D311yescharacteristic
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic
204C23×Dic3—31no—
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3—61no—
208C23×Dic3C2×D311yescharacteristic
209C23×Dic3C2×D311yescharacteristic
210C23×Dic3C2×D311yescharacteristic
211C2×#237—28no—
212C2×#237—38no—
213C2×#237—68no—
214C2×#237C2×D318yescomplemented
215C2×#235—38no—
216C2×#235—68no—
217C22×D12—31no—
218C22×D12—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3C2×D311yescharacteristic
223C22×Dic6—31no—
224C22×Dic6—31no—
225C22×Dic6C2×D311yescharacteristic
226C3×#121—38no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—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#939—38no—
246#939—68no—
247#939C2×D318yescomplemented
248#936—38no—
249D4×Dic3—38no—
250#930—38no—
251C4×#67—38no—
252C4×#67—38no—
253C4×#67—38no—
254C4×#67—38no—
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—31no—
262C2×(C2×D3)⋊C4—61no—
263C2×(C2×D3)⋊C4C2×D311yescharacteristic
264C2×C4⋊Dic3—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—61no—
271C2×Dic3⋊C4C2×D311yescharacteristic
272C2×C4×Dic3—31no—
273C2×C4×Dic3—31no—
274C2×C4×Dic3—31no—
275C2×C4×Dic3—31no—
276C2×C4×Dic3—31no—
277C2×C4×Dic3—31no—
278C2×C4×Dic3—31no—
279C2×C4×Dic3—31no—
280C2×C4×Dic3—38no—
281C2×C4×Dic3—38no—
282#893—38no—
283#888—38no—
284#885—38no—
285#885—38no—
286#67⋊C4—38no—
287#67⋊C4—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32C2×D414yes—
294C23×C32C2412yes—
295C23×C32C2412yes—
296C23×C32C2411yescharacteristic
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3C2412yes—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3C2412yes—
308C22×C3×D3C2412yes—
309C32×D4—28no—
310C2×C32×C4—22no—
311C2×C32×C4C2412yes—
312#638—28no—
313#638—28no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3—28no—
317C2×C3⋊Dic3#4114yescomplemented
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
320C2×C3⋊Dic3C2412yes—
321C3×#67—28no—
322C3×#67—28no—
323C3×#67—28no—
324C3×#67—28no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—28no—
329C2×C3×Dic3—28no—
330C2×C3×Dic3C2×D414yes—
331C2×C3×Dic3C2×D414yes—
332C2×C3×Dic3C2×D4116yescomplemented
333C2×C3×Dic3#4114yescomplemented
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C2×C3×Dic3C2412yes—
340C3×C4×D3—28no—
341C3×Dic6—28no—
342#627—28no—
343#626—28no—
344#626—28no—
345#625—28no—
346#624—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—31no—
356C2×#121—91no—
357C2×#121—91no—
358C2×#121—91no—
359C2×C4×D4—91no—
360C2×C4×D4—91no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C22×C42—91no—
364C24×C3—21no—
365C24×C3—21no—
366C24×C3—31no—
367C24×C3—31no—
368C24×C3C22×D311yescharacteristic
369C24×C3C22×D311yescharacteristic
370C24×C3C22×D311yescharacteristic
371C24×C3C22×D311yescharacteristic
372C23×D3—31no—
373C23×D3—31no—
374C23×D3—61no—
375C23×D3C22×D311yescharacteristic
376C23×D3C22×D311yescharacteristic
377C3×#41—632no—
378C2×C3×Q8—34no—
379C2×C3×Q8—64no—
380C2×C3×D4—24no—
381C2×C3×D4—24no—
382C2×C3×D4—24no—
383C2×C3×D4—34no—
384C2×C3×D4—34no—
385C2×C3×D4—34no—
386C2×C3×D4—34no—
387C2×C3×D4—44no—
388C2×C3×D4—64no—
389C2×C3×D4—64no—
390C2×C3×D4—64no—
391C2×C3×D4—64no—
392C2×C3×D4C22×D314yes—
393C2×C3×D4C22×D314yes—
394C22×C3×C4—21no—
395C22×C3×C4—38no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—34no—
400C22×C3×C4—31no—
401C22×C3×C4—34no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—34no—
405C22×C3×C4—34no—
406C22×C3×C4—64no—
407C22×C3×C4—64no—
408C22×C3×C4—64no—
409C22×C3×C4C22×D311yescharacteristic
410C22×C3×C4C22×D311yescharacteristic
411C2×#67—24no—
412C2×#67—24no—
413C2×#67—24no—
414C2×#67—24no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—34no—
421C2×#67—34no—
422C2×#67—34no—
423C2×#67—64no—
424C2×#67—64no—
425C2×#67—64no—
426C2×#67—64no—
427C2×#67—64no—
428C2×#67—64no—
429C2×#67—64no—
430C2×#67—64no—
431C2×#67—64no—
432C2×#67—64no—
433C2×#67—124no—
434C2×#67—124no—
435C2×#67C22×D314yes—
436C2×#67C22×D314yes—
437C2×#67C22×D314yes—
438C2×#67C22×D314yes—
439C22×Dic3—24no—
440C22×Dic3—24no—
441C22×Dic3—31no—
442C22×Dic3—31no—
443C22×Dic3—31no—
444C22×Dic3—31no—
445C22×Dic3—34no—
446C22×Dic3—34no—
447C22×Dic3—31no—
448C22×Dic3—31no—
449C22×Dic3—34no—
450C22×Dic3—61no—
451C22×Dic3—61no—
452C22×Dic3—61no—
453C22×Dic3—64no—
454C22×Dic3—64no—
455C22×Dic3—64no—
456C22×Dic3—64no—
457C22×Dic3—124no—
458C22×Dic3#6718yescomplemented
459C22×Dic3C22×D314yes—
460C22×Dic3C22×D311yescharacteristic
461C22×Dic3C22×D314yes—
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D311yescharacteristic
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D311yescharacteristic
466C22×Dic3C22×D311yescharacteristic
467C22×Dic3C22×D314yes—
468#237—232no—
469#237—632no—
470#235—632no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—64no—
474C2×D12—64no—
475C2×C4×D3—24no—
476C2×C4×D3—34no—
477C2×C4×D3—34no—
478C2×C4×D3—34no—
479C2×C4×D3—64no—
480C2×C4×D3—64no—
481C2×C4×D3—64no—
482C2×C4×D3C22×D314yes—
483C2×Dic6—24no—
484C2×Dic6—34no—
485C2×Dic6—34no—
486C2×Dic6—64no—
487C2×Dic6—64no—
488C2×Dic6C22×D314yes—
489C3×C4⋊C4—34no—
490C3×C22⋊C4—34no—
491C3×C22⋊C4—34no—
492#217—34no—
493#217—34no—
494#217—34no—
495#217—34no—
496#217—34no—
497#217—64no—
498#217C22×D314yes—
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—34no—
506(C2×D3)⋊C4—64no—
507(C2×D3)⋊C4C22×D314yes—
508C4⋊Dic3—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—64no—
515Dic3⋊C4C22×D314yes—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3—34no—
523C4×Dic3—34no—
524C22×C32—28no—
525C22×C32—22no—
526C22×C32—22no—
527C22×C32—22no—
528C22×C32—22no—
529C22×C32—22no—
530C22×C32—44no—
531C22×C32C22×D414yes—
532C22×C32C22×D412yes—
533C22×C32C2×#4112yes—
534C22×C32C2×#4112yes—
535C22×C32C2511yescharacteristic
536C2×C3⋊D3—22no—
537C2×C3⋊D3—22no—
538C2×C3⋊D3—22no—
539C2×C3⋊D3—44no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—44no—
547C2×C3×D3—44no—
548C32×C4—22no—
549C3⋊Dic3—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3C2×#4114yescomplemented
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3C22×D414yes—
556C3×Dic3C22×D414yes—
557C3×Dic3C2×#4114yescomplemented
558C2×#41—38no—
559C2×#41—68no—
560C2×#41—98no—
561C2×#41—188no—
562C22×Q8—31no—
563C22×Q8—91no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4—91no—
573C22×D4D3211yescharacteristic
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—31no—
577C23×C4—31no—
578C23×C4—91no—
579C23×C4—91no—
580C23×C4—91no—
581C4⋊Q8—98no—
582#127—98no—
583#124—98no—
584#124—98no—
585#121—38no—
586#121—98no—
587#121—98no—
588#121—98no—
589C4×D4—98no—
590C4×D4—98no—
591C4×D4—98no—
592C4×D4—98no—
593C2×C4⋊C4—31no—
594C2×C4⋊C4—91no—
595C2×C4⋊C4—91no—
596C2×C4⋊C4—91no—
597C2×C22⋊C4—31no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—91no—
600C2×C22⋊C4—91no—
601C2×C22⋊C4—91no—
602C2×C22⋊C4—91no—
603C2×C22⋊C4—91no—
604C2×C22⋊C4—91no—
605C2×C42—91no—
606C2×C42—91no—
607C2×C42—91no—
608C2×C42—91no—
609C2×C42—98no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—21no—
623C23×C3—24no—
624C23×C3—32no—
625C23×C3—32no—
626C23×C3—42no—
627C23×C3—42no—
628C23×C3—42no—
629C23×C3—42no—
630C23×C3—42no—
631C23×C3—62no—
632C23×C3—62no—
633C23×C3—62no—
634C23×C3—62no—
635C23×C3—62no—
636C23×C3—62no—
637C23×C3D3×D414yes—
638C23×C3C2×#6714yes—
639C23×C3C23×D312yes—
640C23×C3C23×D312yes—
641C23×C3C23×D312yes—
642C23×C3C23×D312yes—
643C23×C3C23×D311yescharacteristic
644C23×C3C23×D311yescharacteristic
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—32no—
652C22×D3—32no—
653C22×D3—62no—
654C22×D3—62no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—62no—
658C22×D3—62no—
659C22×D3—62no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3C23×D312yes—
664C22×D3C23×D312yes—
665C3×Q8—68no—
666C3×D4—28no—
667C3×D4—28no—
668C3×D4—48no—
669C3×D4—68no—
670C3×D4—68no—
671C3×D4—68no—
672C3×D4—68no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—34no—
677C2×C3×C4—34no—
678C2×C3×C4—316no—
679C2×C3×C4—34no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—42no—
687C2×C3×C4—68no—
688C2×C3×C4—68no—
689C2×C3×C4—68no—
690C2×C3×C4—62no—
691C2×C3×C4—62no—
692C2×C3×C4—62no—
693C2×C3×C4C23×D312yes—
694C2×C3×C4C23×D312yes—
695#67—28no—
696#67—28no—
697#67—28no—
698#67—28no—
699#67—68no—
700#67—68no—
701#67—68no—
702#67—68no—
703#67—68no—
704#67—68no—
705#67—68no—
706#67—68no—
707#67—128no—
708#67—128no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—28no—
713C2×Dic3—28no—
714C2×Dic3—34no—
715C2×Dic3—34no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—32no—
722C2×Dic3—64no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—62no—
726C2×Dic3—68no—
727C2×Dic3—68no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—62no—
731C2×Dic3—62no—
732C2×Dic3—68no—
733C2×Dic3—128no—
734C2×Dic3—122no—
735C2×Dic3—122no—
736C2×Dic3#23714yescomplemented
737C2×Dic3C2×#6714yes—
738C2×Dic3C2×#6714yes—
739C2×Dic3C2×#67116yescomplemented
740C2×Dic3C23×D312yes—
741C2×Dic3C23×D312yes—
742C2×Dic3C23×D312yes—
743C2×Dic3C23×D312yes—
744C2×Dic3C23×D312yes—
745C2×Dic3C23×D312yes—
746D12—68no—
747D12—68no—
748C4×D3—28no—
749C4×D3—68no—
750C4×D3—68no—
751C4×D3—68no—
752Dic6—28no—
753Dic6—68no—
754Dic6—68no—
755C2×C32—24no—
756C2×C32—42no—
757C2×C32#53214yescomplemented
758C2×C32C23×D411yescharacteristic
759C2×C32C22×#4111yescharacteristic
760C2×C32C22×#4111yescharacteristic
761C3⋊D3—42no—
762C3×D3—42no—
763C3×D3—42no—
764C24—31no—
765C24—31no—
766C24—91no—
767C24C2×D3211yescharacteristic
768C24C2×D3211yescharacteristic
769#41—632no—
770#41—1832no—
771C2×Q8—34no—
772C2×Q8—64no—
773C2×Q8—94no—
774C2×Q8—184no—
775C2×D4—24no—
776C2×D4—34no—
777C2×D4—34no—
778C2×D4—34no—
779C2×D4—34no—
780C2×D4—64no—
781C2×D4—64no—
782C2×D4—64no—
783C2×D4—64no—
784C2×D4—94no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—94no—
788C2×D4—94no—
789C2×D4—184no—
790C2×D4—184no—
791C2×D4—184no—
792C2×D4—184no—
793C2×D4—184no—
794C2×D4C2×D3214yes—
795C22×C4—34no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—38no—
800C22×C4—34no—
801C22×C4—34no—
802C22×C4—31no—
803C22×C4—31no—
804C22×C4—31no—
805C22×C4—34no—
806C22×C4—64no—
807C22×C4—64no—
808C22×C4—64no—
809C22×C4—94no—
810C22×C4—94no—
811C22×C4—91no—
812C22×C4—94no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—184no—
816C22×C4—184no—
817C22×C4—184no—
818C22×C4C2×D3211yescharacteristic
819C4⋊C4—34no—
820C4⋊C4—94no—
821C4⋊C4—94no—
822C4⋊C4—94no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—94no—
830C22⋊C4—94no—
831C42—94no—
832C42—94no—
833C42—94no—
834C42—94no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—28no—
840C22×C3—28no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—24no—
851C22×C3—21no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—48no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—44no—
859C22×C3—44no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—84no—
867C22×C3—124no—
868C22×C3—124no—
869C22×C3C2×D3×D414yes—
870C22×C3C2×D3×D412yes—
871C22×C3C2×#23712yes—
872C22×C3D3×#4112yes—
873C22×C3D3×#4112yes—
874C22×C3D3×#4112yes—
875C22×C3C22×#6714yes—
876C22×C3C22×#6712yes—
877C22×C3C24×D311yescharacteristic
878C22×C3C24×D311yescharacteristic
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—44no—
886C2×D3—44no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—122no—
894C2×D3—122no—
895C2×D3—122no—
896C2×D3—124no—
897C2×D3—124no—
898C2×D3—244no—
899C3×C4—22no—
900C3×C4—22no—
901C3×C4—34no—
902C3×C4—34no—
903C3×C4—34no—
904C3×C4—42no—
905C3×C4—62no—
906C3×C4—62no—
907C3×C4—62no—
908Dic3—22no—
909Dic3—22no—
910Dic3—22no—
911Dic3—34no—
912Dic3—34no—
913Dic3—64no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—122no—
919Dic3—122no—
920Dic3C2×#23714yescomplemented
921Dic3C22×#6714yes—
922Dic3C22×#6714yes—
923C32C2×#53211yescharacteristic, complemented, Sylow
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—32no—
930C23—32no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—92no—
938C23—182no—
939C23—182no—
940C23—182no—
941C23D3×#6714yes—
942C23C22×D3212yes—
943C23C22×D3212yes—
944C23C22×D3211yescharacteristic
945Q8—68no—
946Q8—188no—
947D4—28no—
948D4—68no—
949D4—68no—
950D4—68no—
951D4—68no—
952D4—188no—
953D4—188no—
954D4—188no—
955D4—188no—
956D4—188no—
957C2×C4—22no—
958C2×C4—34no—
959C2×C4—34no—
960C2×C4—34no—
961C2×C4—316no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—32no—
966C2×C4—32no—
967C2×C4—32no—
968C2×C4—68no—
969C2×C4—68no—
970C2×C4—68no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—94no—
975C2×C4—92no—
976C2×C4—92no—
977C2×C4—92no—
978C2×C4—188no—
979C2×C4—188no—
980C2×C4—188no—
981C2×C4—182no—
982C2×C4—182no—
983C2×C4C22×D3212yes—
984C2×C3—24no—
985C2×C3—24no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—24no—
989C2×C3—21no—
990C2×C3—44no—
991C2×C3—42no—
992C2×C3—42no—
993C2×C3—82no—
994C2×C3—122no—
995C2×C3—122no—
996C2×C3#559614yescomplemented
997C2×C3#583214yescomplemented
998C2×C3C22×D3×D411yescharacteristic
999C2×C3C22×#23711yescharacteristic
1000C2×C3C2×D3×#4111yescharacteristic
1001C2×C3C2×D3×#4111yescharacteristic
1002C2×C3C2×D3×#4111yescharacteristic
1003C2×C3C23×#6711yescharacteristic
1004D3—42no—
1005D3—42no—
1006D3—122no—
1007D3—122no—
1008D3—242no—
1009C22—22no—
1010C22—22no—
1011C22—28no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—44no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—124no—
1023C22—124no—
1024C22—182no—
1025C22—182no—
1026C22—182no—
1027C22—364no—
1028C22D3×#23712yes—
1029C22#6431212yes—
1030C22C2×D3×#6714yes—
1031C22C2×D3×#6712yes—
1032C22C23×D3211yescharacteristic
1033C4—22no—
1034C4—34no—
1035C4—34no—
1036C4—34no—
1037C4—62no—
1038C4—62no—
1039C4—62no—
1040C4—94no—
1041C4—182no—
1042C4—182no—
1043C3—21no—
1044C3C2×#559611yescharacteristic, complemented
1045C3C2×#583211yescharacteristic, complemented
1046C2—24no—
1047C2—42no—
1048C2—122no—
1049C2—122no—
1050C2—362no—
1051C2#1059515514yesdirect product factor
1052C2C2×D3×#23711yescharacteristic
1053C2C2×#6431211yescharacteristic
1054C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×#3804C2semidirect
3. C2×#64148C2semidirect
4. C2×C3×#939C2semidirect
5. C2×#63980C2semidirect
6. C2×#63979C2semidirect
7. C2×#63978C2semidirect
8. C2×Dic3×#67C2semidirect
9. C2×#63959C2semidirect
10. C22×Dic32C2semidirect
11. C2×#63952C2semidirect
12. #10595155C2direct (N × H)
13. C2×#63907C2semidirect
14. C2×#63904C2semidirect
15. C2×#63879C2semidirect
16. C2×#63839C2semidirect
31. C2×C3×#237C22semidirect
40. C2×#3804C22semidirect
43. #64148C22semidirect
47. C3×#939C22semidirect
50. #63980C22semidirect
51. #63979C22semidirect
52. #63978C22semidirect
53. Dic3×#67C22semidirect
60. #63959C22semidirect
65. C2×Dic32C22semidirect
66. #63952C22semidirect
67. #63907C22semidirect
68. #63904C22semidirect
69. #63879C22semidirect
70. #63839C22semidirect
73. C22×#237D3semidirect
87. C2×#939D3semidirect
131. C22×C3×Dic3D4semidirect
214. C2×#237C2×D3semidirect
247. #939C2×D3semidirect
317. C2×C3⋊Dic3#41semidirect
332. C2×C3×Dic3C2×D4semidirect
333. C2×C3×Dic3#41semidirect
458. C22×Dic3#67semidirect
551. C3⋊Dic3C2×#41semidirect
557. C3×Dic3C2×#41semidirect
736. C2×Dic3#237semidirect
739. C2×Dic3C2×#67semidirect
757. C2×C32#532semidirect
920. Dic3C2×#237semidirect
923. C32C2×#532semidirect
996. C2×C3#5596semidirect
997. C2×C3#5832semidirect
1044. C3C2×#5596semidirect
1045. C3C2×#5832semidirect
1051. C2#10595155direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×#38042
C2×#641482
C2×C3×#9392
C2×#639802
C2×#639792
C2×#639782
C2×Dic3×#672
C2×#639592
C22×Dic322
C2×#639522
#105951552
C2×#639072
C2×#639042
C2×#638792
C2×#638392
C2×#58323
C2×#55963