Finite Group Databasebeta

← D3×#5825 #11901078

Subgroups — D3×#5825 #11901078

Order 1152.

3159 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3#10596296C211yesmaximal, characteristic, complemented
4C3×#5825C211yesmaximal, characteristic, complemented
5#10595356C212yesmaximal, complemented
6D3×#944C212yesmaximal, complemented
7#10595270C214yesmaximal, complemented
8#10595147C212yesmaximal, complemented
9D3×#936C212yesmaximal, complemented
10D3×#935C214yesmaximal, complemented
11D3×#926C211yesmaximal, characteristic, complemented
12#10594884C214yesmaximal, complemented
13D3×#924C214yesmaximal, complemented
14#10594856C211yesmaximal, characteristic, complemented
15#10594855C211yesmaximal, characteristic, complemented
16C2×#5825—31nomaximal
17D3×#536—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C22×#634C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×#237C2211yescharacteristic
24C2×C3×#237C2212yes—
25C2×C3×D3×D4C2212yes—
26C2×C3×D3×D4C2211yescharacteristic
27C2×C3×#235C2211yescharacteristic
28C2×C3×#235C2212yes—
29C22×C3×C4×D3C2212yes—
30C22×C3×C4×D3C2211yescharacteristic
31C22×C3×Dic6C2211yescharacteristic, complemented
32C22×#627C2212yescomplemented
33C22×D3×Dic3C2212yes—
34C2×D3×Dic6—28no—
35C2×D3×Dic6C2212yes—
36C2×D3×Dic6C2212yes—
37C2×D3×Dic6C2212yescomplemented
38C2×D3×Dic6C2212yescomplemented
39#64153C2212yescomplemented
40#64145C2212yescomplemented
41#64144C2214yescomplemented
42#64135C2211yescharacteristic, complemented
43#64133C2214yescomplemented
44C3×#944C2212yescomplemented
45C3×#936C2212yescomplemented
46C3×#935C2214yescomplemented
47C3×#926C2211yescharacteristic, complemented
48C3×#924C2214yescomplemented
49#63969C2218yescomplemented
50D3×#217C2218yes—
51D3×#217C2212yes—
52#63964C2218yescomplemented
53#63962C2214yescomplemented
54#63961C2214yescomplemented
55#63959C2218yescomplemented
56#63955C2212yescomplemented
57D3×C4⋊Dic3C2212yes—
58#63884C2218yescomplemented
59D3×Dic3⋊C4C2218yes—
60C4×D3×Dic3C2212yes—
61#63873C2212yescomplemented
62#63866C2212yescomplemented
63#63863C2212yescomplemented
64#63860C2212yescomplemented
65#63857C2214yescomplemented
66#63856C2214yescomplemented
67#63855C2212yescomplemented
68#63851C2218yescomplemented
69#63841C2212yescomplemented
70#63839C2218yescomplemented
71C22×C3×#41—31no—
72C2×D3×#41D311yescharacteristic
73C22×D3×Q8—31no—
74C23×Dic6—31no—
75C3×#536—31no—
76#5825—31no—
77#5825—31no—
78#5825—31no—
79#5825—32no—
80#5825—32no—
81#5825—34no—
82#5825—31no—
83#5825—34no—
84#5825—61no—
85#5825D311yescharacteristic, direct product factor
86#5816—31no—
87C2×#944—32no—
88C2×#936—32no—
89C2×#935—34no—
90C2×#926—31no—
91C2×#924—34no—
92#5724—32no—
93D3×C4⋊Q8—32no—
94#5675—32no—
95D3×#124—32no—
96D3×#123—34no—
97#5648—34no—
98#5628—34no—
99D3×C22⋊Q8—34no—
100#5526—31no—
101D3×#117—31no—
102C23×C3×D3C2312yes—
103C23×C3×D3C2311yescharacteristic
104C32×#41—24no—
105C2×C32×Q8C2311yescharacteristic
106C2×C32×D4C2312yes—
107C2×C32×D4C2311yescharacteristic
108C22×C32×C4C2312yes—
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3C2312yes—
111C2×#634—24no—
112C2×#634C2312yes—
113C2×#634C2312yes—
114C2×C3×#67C2312yes—
115C2×C3×#67C2312yes—
116C2×C3×#67C2312yes—
117C22×C3×Dic3C2312yes—
118C22×C3×Dic3C2312yes—
119C22×C3×Dic3C2311yescharacteristic
120C3×#239—24no—
121C3×D3×Q8—24no—
122C3×#237—28no—
123C3×#237—24no—
124C3×D3×D4—28no—
125C3×D3×D4—24no—
126C3×#235—24no—
127C3×#235—28no—
128C2×C3×D12C2311yescharacteristic
129C2×C3×D12C2312yes—
130C2×C3×C4×D3—28no—
131C2×C3×C4×D3D418yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×Dic6—24no—
140C2×C3×Dic6C2312yes—
141C2×C3×Dic6C2312yes—
142C2×C3×Dic6C2312yes—
143C2×C3×Dic6C2311yescharacteristic
144C2×#627—28no—
145C2×#627C2314yes—
146C2×#627C2314yes—
147C2×D3×Dic3—28no—
148C2×D3×Dic3C2314yes—
149C2×D3×Dic3C2314yes—
150C2×D3×Dic3C2314yes—
151D3×Dic6—28no—
152D3×Dic6—28no—
153D3×Dic6—28no—
154D3×Dic6—28no—
155#3757C2318yes—
156#3757C2312yes—
157C4⋊(C3⋊Dic3)C2312yes—
158#3750C2318yes—
159C4×C3⋊Dic3C2312yes—
160C3×#217C2318yes—
161C3×#217C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×Dic3⋊C4C2318yes—
164C3×C4×Dic3C2312yes—
165#3724C2318yes—
166Dic3⋊Dic3C2318yes—
167Dic3⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2318yes—
170(C2×D3)⋊Dic3C2318yes—
171Dic32C2314yes—
172C2×#536—91noSylow
173C2×C3×#41—21no—
174C2×C3×#41—31no—
175C2×C3×#41—32no—
176C2×C3×#41—31no—
177C2×C3×#41—32no—
178C2×C3×#41—31no—
179C2×C3×#41—68no—
180C2×C3×#41C2×D311yescharacteristic
181C2×C3×#41C2×D311yescharacteristic
182C22×C3×Q8—31no—
183C22×C3×Q8—31no—
184C22×C3×D4—32no—
185C22×C3×D4—31no—
186C23×C3×C4—31no—
187C23×C3×C4—32no—
188C23×Dic3—32no—
189D3×#41—28no—
190C2×#239C2×D311yescharacteristic
191C2×D3×Q8—32no—
192C2×D3×Q8—32no—
193C2×D3×Q8—32no—
194C2×D3×Q8—32no—
195C2×D3×Q8—68no—
196C2×D3×Q8C2×D311yescharacteristic
197C2×#237C2×D312yes—
198C2×#237C2×D311yescharacteristic
199C2×D3×D4C2×D312yes—
200C2×D3×D4C2×D311yescharacteristic
201C2×#235C2×D311yescharacteristic
202C2×#235C2×D312yes—
203C22×C4×D3—32no—
204C22×C4×D3C2×D312yes—
205C22×C4×D3C2×D311yescharacteristic
206C22×Dic6—31no—
207C22×Dic6—31no—
208C22×Dic6—32no—
209C22×Dic6—32no—
210C22×Dic6—32no—
211C22×Dic6—32no—
212C22×Dic6—32no—
213C22×Dic6—32no—
214C22×Dic6—61no—
215C22×Dic6—68no—
216C22×Dic6C2×D311yescharacteristic, complemented
217C3×C4⋊Q8—32no—
218C3×#124—32no—
219C3×#123—34no—
220C3×C22⋊Q8—34no—
221C3×#117—31no—
222C2×#217—38no—
223C2×#217—32no—
224#947—32no—
225#946—34no—
226#944—32no—
227#944—32no—
228#944—32no—
229#944—32no—
230#944—38no—
231#944—32no—
232#944—62no—
233#944C2×D312yescomplemented
234#936—32no—
235#936—32no—
236#936—32no—
237#936—38no—
238#936—32no—
239#936—62no—
240#936C2×D312yescomplemented
241#935—34no—
242#935—34no—
243#935—34no—
244#935—34no—
245#935—38no—
246#935—38no—
247#935—64no—
248#935C2×D314yescomplemented
249#929—34no—
250#926—31no—
251#926—31no—
252#926—32no—
253#926—32no—
254#926—32no—
255#926—61no—
256#926C2×D311yescharacteristic, complemented
257C2×C4⋊Dic3—32no—
258#924—34no—
259#924—34no—
260#924—34no—
261#924—38no—
262#924—34no—
263#924—38no—
264#924—64no—
265#924C2×D314yescomplemented
266C2×Dic3⋊C4—38no—
267C2×C4×Dic3—32no—
268#897—34no—
269#896—38no—
270#894—38no—
271#892—32no—
272D3×C4⋊C4—38no—
273D3×C4⋊C4—32no—
274#888—38no—
275#886—34no—
276#885—38no—
277#883—38no—
278D3×C22⋊C4—32no—
279D3×C22⋊C4—38no—
280#878—38no—
281#877—32no—
282#875—32no—
283#872—32no—
284C42×D3—32no—
285#869—32no—
286C23×C32C2412yes—
287C23×C32C2411yescharacteristic
288C22×C3×D3—24no—
289C22×C3×D3—24no—
290C22×C3×D3—28no—
291C22×C3×D3C2×D414yes—
292C22×C3×D3C2412yes—
293C22×C3×D3C2411yescharacteristic
294C22×C3×D3C2411yescharacteristic
295C32×Q8—22no—
296C32×D4—24no—
297C32×D4—22no—
298C2×C32×C4—24no—
299C2×C32×C4C2×D414yes—
300C2×C32×C4C2412yes—
301C2×C32×C4C2411yescharacteristic
302C2×C32×C4C2411yescharacteristic
303C2×C3⋊Dic3—24no—
304C2×C3⋊Dic3C2414yes—
305C2×C3⋊Dic3C2414yes—
306#634—24no—
307#634—24no—
308C3×#67—24no—
309C3×#67—24no—
310C3×#67—24no—
311C2×C3×Dic3—24no—
312C2×C3×Dic3—24no—
313C2×C3×Dic3C2×D414yes—
314C2×C3×Dic3C2414yes—
315C2×C3×Dic3C2414yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2411yescharacteristic
318C2×C3×Dic3C2411yescharacteristic
319C3×D12—24no—
320C3×D12—22no—
321C3×C4×D3—24no—
322C3×C4×D3—24no—
323C3×C4×D3—24no—
324C3×C4×D3C2×D414yes—
325C3×C4×D3C2×D414yes—
326C3×C4×D3C2×D414yes—
327C3×C4×D3C2×D414yes—
328C3×Dic6—24no—
329C3×Dic6—24no—
330C3×Dic6—22no—
331C3×Dic6—24no—
332#627—28no—
333#627—28no—
334D3×Dic3—28no—
335D3×Dic3—28no—
336D3×Dic3—28no—
337C22×#41—31no—
338C23×Q8—91no—
339#536—31no—
340#536—91no—
341#536—94no—
342#536—94no—
343#536—92no—
344#536—92no—
345#536—91no—
346#536—91no—
347C2×C4⋊Q8—92no—
348C2×#124—92no—
349C2×#123—94no—
350C2×C22⋊Q8—94no—
351C2×#117—91no—
352C24×C3—31no—
353C24×C3—32no—
354C23×D3C22×D312yes—
355C23×D3C22×D311yescharacteristic
356C3×#41—24no—
357C3×#41—24no—
358C3×#41—44no—
359C3×#41—68no—
360C3×#41—68no—
361C3×#41—64no—
362C3×#41—64no—
363C3×#41—64no—
364C2×C3×Q8—21no—
365C2×C3×Q8—32no—
366C2×C3×Q8—31no—
367C2×C3×Q8—32no—
368C2×C3×Q8—32no—
369C2×C3×Q8—64no—
370C2×C3×Q8—64no—
371C2×C3×Q8C22×D311yescharacteristic
372C2×C3×Q8C22×D311yescharacteristic
373C2×C3×D4—22no—
374C2×C3×D4—21no—
375C2×C3×D4—32no—
376C2×C3×D4—32no—
377C2×C3×D4—32no—
378C2×C3×D4—32no—
379C2×C3×D4—31no—
380C2×C3×D4—64no—
381C2×C3×D4—68no—
382C2×C3×D4C22×D312yes—
383C2×C3×D4C22×D312yes—
384C2×C3×D4C22×D311yescharacteristic
385C2×C3×D4C22×D311yescharacteristic
386C22×C3×C4—21no—
387C22×C3×C4—22no—
388C22×C3×C4—31no—
389C22×C3×C4—38no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—32no—
395C22×C3×C4—32no—
396C22×C3×C4—32no—
397C22×C3×C4—32no—
398C22×C3×C4—32no—
399C22×C3×C4—68no—
400C22×C3×C4C22×D312yes—
401C22×C3×C4C22×D312yes—
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C2×#67C22×D312yes—
405C2×#67C22×D312yes—
406C2×#67C22×D312yes—
407C22×Dic3—32no—
408C22×Dic3—32no—
409C22×Dic3—34no—
410C22×Dic3—34no—
411C22×Dic3—34no—
412C22×Dic3—62no—
413C22×Dic3—68no—
414C22×Dic3C22×D312yes—
415C22×Dic3C22×D312yes—
416C22×Dic3C22×D311yescharacteristic
417#239—24no—
418D3×Q8—24no—
419D3×Q8—68no—
420D3×Q8—68no—
421D3×Q8—68no—
422D3×Q8—68no—
423#237—28no—
424#237—24no—
425D3×D4—28no—
426D3×D4—24no—
427#235—24no—
428#235—28no—
429C2×D12C22×D311yescharacteristic
430C2×D12C22×D312yes—
431C2×C4×D3—28no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—68no—
436C2×C4×D3#6718yes—
437C2×C4×D3C22×D312yes—
438C2×C4×D3C22×D312yes—
439C2×C4×D3C22×D312yes—
440C2×C4×D3C22×D311yescharacteristic
441C2×C4×D3C22×D311yescharacteristic
442C2×C4×D3C22×D311yescharacteristic
443C2×C4×D3C22×D311yescharacteristic
444C2×Dic6—24no—
445C2×Dic6—32no—
446C2×Dic6—32no—
447C2×Dic6—32no—
448C2×Dic6—32no—
449C2×Dic6—34no—
450C2×Dic6—34no—
451C2×Dic6—34no—
452C2×Dic6—34no—
453C2×Dic6—62no—
454C2×Dic6—62no—
455C2×Dic6—68no—
456C2×Dic6—68no—
457C2×Dic6—68no—
458C2×Dic6—68no—
459C2×Dic6—68no—
460C2×Dic6—64no—
461C2×Dic6—64no—
462C2×Dic6—68no—
463C2×Dic6—124no—
464C2×Dic6C22×D311yescharacteristic
465C2×Dic6C22×D312yes—
466C2×Dic6C22×D312yes—
467C2×Dic6C22×D312yes—
468C3×C4⋊C4—38no—
469C3×C4⋊C4—32no—
470C3×C22⋊C4—32no—
471C3×C22⋊C4—38no—
472C3×C42—32no—
473#217—32no—
474#217—38no—
475#217—38no—
476#217—32no—
477#217—38no—
478#217—38no—
479#217—34no—
480#217—68no—
481#217—62no—
482#217C22×D318yes—
483#217C22×D312yes—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—38no—
486(C2×D3)⋊C4—38no—
487C4⋊Dic3—32no—
488C4⋊Dic3—32no—
489C4⋊Dic3—38no—
490C4⋊Dic3—34no—
491C4⋊Dic3—62no—
492C4⋊Dic3C22×D312yes—
493Dic3⋊C4—38no—
494Dic3⋊C4—38no—
495Dic3⋊C4—34no—
496Dic3⋊C4—38no—
497Dic3⋊C4—38no—
498Dic3⋊C4—38no—
499Dic3⋊C4—68no—
500Dic3⋊C4C22×D318yes—
501C4×Dic3—32no—
502C4×Dic3—32no—
503C4×Dic3—34no—
504C4×Dic3—34no—
505C4×Dic3—62no—
506C4×Dic3C22×D312yes—
507C22×C32—22no—
508C22×C32—22no—
509C22×C32—24no—
510C22×C32C22×D412yes—
511C22×C32C2511yescharacteristic
512C2×C3×D3—22no—
513C2×C3×D3—28no—
514C2×C3×D3—22no—
515C2×C3×D3—24no—
516C2×C3×D3—48no—
517C2×C3×D3C22×D412yes—
518C2×C3×D3C22×D412yes—
519C2×C3×D32−1+414yes—
520C32×C4—22no—
521C32×C4C22×D412yes—
522C32×C4C22×D412yes—
523C3⋊Dic3—24no—
524C3⋊Dic3—24no—
525C3×Dic3—24no—
526C3×Dic3—22no—
527C3×Dic3—24no—
528C3×Dic3C22×D412yes—
529C3×Dic3C22×D412yes—
530C2×#41—31no—
531C2×#41—32no—
532C2×#41—31no—
533C2×#41—32no—
534C2×#41—31no—
535C2×#41—68no—
536C2×#41D3211yescharacteristic
537C22×Q8—31no—
538C22×Q8—31no—
539C22×Q8—92no—
540C22×Q8—92no—
541C22×Q8—92no—
542C22×Q8—92no—
543C22×Q8—92no—
544C22×Q8—91no—
545C22×Q8—188no—
546C22×D4—32no—
547C22×D4—31no—
548C23×C4—31no—
549C23×C4—32no—
550C23×C4—92no—
551C4⋊Q8—32no—
552C4⋊Q8—92no—
553C4⋊Q8—98no—
554C4⋊Q8—92no—
555C4⋊Q8—92no—
556#124—32no—
557#124—92no—
558#124—98no—
559#124—92no—
560#124—92no—
561#123—34no—
562#123—98no—
563#123—94no—
564#123—98no—
565#123—94no—
566#123—94no—
567C22⋊Q8—34no—
568C22⋊Q8—98no—
569C22⋊Q8—98no—
570C22⋊Q8—94no—
571C22⋊Q8—94no—
572C22⋊Q8—94no—
573#117—31no—
574#117—92no—
575#117—92no—
576#117—92no—
577#117—91no—
578C2×C4⋊C4—92no—
579C2×C4⋊C4—98no—
580C2×C22⋊C4—92no—
581C2×C22⋊C4—98no—
582C2×C42—92no—
583C23×C3—21no—
584C23×C3—22no—
585C23×C3—31no—
586C23×C3—34no—
587C23×C3—31no—
588C23×C3—32no—
589C23×C3—64no—
590C23×C3—64no—
591C23×C3—68no—
592C23×C3C23×D312yes—
593C23×C3C23×D312yes—
594C23×C3C23×D311yescharacteristic
595C23×C3C23×D311yescharacteristic
596C22×D3—24no—
597C22×D3—28no—
598C22×D3—24no—
599C22×D3C2×#6714yes—
600C22×D3C23×D312yes—
601C22×D3C23×D311yescharacteristic
602C22×D3C23×D311yescharacteristic
603C3×Q8—22no—
604C3×Q8—22no—
605C3×Q8—42no—
606C3×Q8—64no—
607C3×Q8—62no—
608C3×Q8—64no—
609C3×Q8—64no—
610C3×D4—24no—
611C3×D4—24no—
612C3×D4—22no—
613C3×D4—22no—
614C3×D4—42no—
615C3×D4—44no—
616C3×D4—64no—
617C3×D4—64no—
618C3×D4—64no—
619C3×D4—64no—
620C3×D4—62no—
621C2×C3×C4—24no—
622C2×C3×C4—24no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—22no—
626C2×C3×C4—24no—
627C2×C3×C4—34no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—34no—
631C2×C3×C4—34no—
632C2×C3×C4—34no—
633C2×C3×C4—34no—
634C2×C3×C4—34no—
635C2×C3×C4—32no—
636C2×C3×C4—34no—
637C2×C3×C4—44no—
638C2×C3×C4—64no—
639C2×C3×C4—64no—
640C2×C3×C4—64no—
641C2×C3×C4—64no—
642C2×C3×C4—64no—
643C2×C3×C4D3×D414yes—
644C2×C3×C4C2×#6714yes—
645C2×C3×C4C23×D312yes—
646C2×C3×C4C23×D312yes—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651#67—24no—
652#67—24no—
653#67—24no—
654C2×Dic3—24no—
655C2×Dic3—24no—
656C2×Dic3—34no—
657C2×Dic3—34no—
658C2×Dic3—34no—
659C2×Dic3—34no—
660C2×Dic3—64no—
661C2×Dic3—64no—
662C2×Dic3—68no—
663C2×Dic3—68no—
664C2×Dic3—68no—
665C2×Dic3—64no—
666C2×Dic3—64no—
667C2×Dic3—124no—
668C2×Dic3C2×#6714yes—
669C2×Dic3C23×D314yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D314yes—
672C2×Dic3C23×D311yescharacteristic
673C2×Dic3C23×D311yescharacteristic
674D12—24no—
675D12—22no—
676C4×D3—24no—
677C4×D3—24no—
678C4×D3—24no—
679C4×D3—68no—
680C4×D3—68no—
681C4×D3—68no—
682C4×D3C2×#6714yes—
683C4×D3C2×#6714yes—
684C4×D3C2×#6714yes—
685C4×D3C2×#6714yes—
686Dic6—24no—
687Dic6—24no—
688Dic6—22no—
689Dic6—24no—
690Dic6—68no—
691Dic6—68no—
692Dic6—64no—
693Dic6—64no—
694Dic6—64no—
695Dic6—64no—
696Dic6—68no—
697Dic6—68no—
698Dic6—124no—
699Dic6—124no—
700C2×C32—22no—
701C2×C32—42no—
702C2×C32C23×D411yescharacteristic
703C2×C32C2×2−1+412yes—
704C3×D3—22no—
705C3×D3—42no—
706C3×D3#53614yescomplemented
707C24—31no—
708C24—32no—
709#41—24no—
710#41—68no—
711#41—68no—
712#41—64no—
713#41—64no—
714#41—64no—
715C2×Q8—32no—
716C2×Q8—32no—
717C2×Q8—32no—
718C2×Q8—31no—
719C2×Q8—64no—
720C2×Q8—64no—
721C2×Q8—94no—
722C2×Q8—94no—
723C2×Q8—92no—
724C2×Q8—92no—
725C2×Q8—188no—
726C2×Q8—188no—
727C2×Q8—188no—
728C2×Q8—188no—
729C2×Q8—188no—
730C2×Q8—184no—
731C2×Q8C2×D3211yescharacteristic
732C2×D4—32no—
733C2×D4—32no—
734C2×D4—32no—
735C2×D4—32no—
736C2×D4—31no—
737C2×D4—64no—
738C2×D4—68no—
739C2×D4C2×D3212yes—
740C2×D4C2×D3211yescharacteristic
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—38no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—32no—
751C22×C4—32no—
752C22×C4—68no—
753C22×C4—94no—
754C22×C4—94no—
755C22×C4—94no—
756C22×C4—92no—
757C22×C4—188no—
758C22×C4C2×D3212yes—
759C22×C4C2×D3211yescharacteristic
760C4⋊C4—32no—
761C4⋊C4—38no—
762C4⋊C4—94no—
763C4⋊C4—98no—
764C4⋊C4—98no—
765C4⋊C4—92no—
766C4⋊C4—98no—
767C22⋊C4—32no—
768C22⋊C4—38no—
769C22⋊C4—94no—
770C22⋊C4—98no—
771C22⋊C4—98no—
772C22⋊C4—92no—
773C22⋊C4—98no—
774C42—32no—
775C42—94no—
776C42—92no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—24no—
781C22×C3—24no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—21no—
785C22×C3—32no—
786C22×C3—34no—
787C22×C3—32no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—44no—
791C22×C3—68no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—64no—
795C22×C3—128no—
796C22×C3C2×D3×D412yes—
797C22×C3C22×#6712yes—
798C22×C3C24×D311yescharacteristic
799C22×C3C24×D311yescharacteristic
800C2×D3—22no—
801C2×D3—28no—
802C2×D3—24no—
803C2×D3—22no—
804C2×D3—48no—
805C2×D3#101014yes—
806C2×D3C22×#6712yes—
807C2×D3C22×#6712yes—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—32no—
813C3×C4—32no—
814C3×C4—42no—
815C3×C4—62no—
816C3×C4—64no—
817C3×C4—64no—
818C3×C4C2×D3×D412yes—
819C3×C4C2×D3×D412yes—
820C3×C4C22×#6712yes—
821C3×C4C22×#6712yes—
822Dic3—24no—
823Dic3—24no—
824Dic3—22no—
825Dic3—64no—
826Dic3—64no—
827Dic3—64no—
828Dic3—64no—
829Dic3—124no—
830Dic3—124no—
831Dic3C22×#6712yes—
832Dic3C22×#6712yes—
833C32C2×#53611yescharacteristic, complemented, Sylow
834C23—31no—
835C23—34no—
836C23—31no—
837C23—32no—
838C23—64no—
839C23—64no—
840C23—68no—
841C23C22×D3212yes—
842C23C22×D3211yescharacteristic
843Q8—22no—
844Q8—64no—
845Q8—64no—
846Q8—64no—
847Q8—62no—
848Q8—188no—
849Q8—188no—
850Q8—184no—
851Q8—184no—
852D4—24no—
853D4—22no—
854D4—64no—
855D4—64no—
856D4—64no—
857D4—64no—
858D4—62no—
859C2×C4—24no—
860C2×C4—34no—
861C2×C4—31no—
862C2×C4—31no—
863C2×C4—34no—
864C2×C4—34no—
865C2×C4—34no—
866C2×C4—34no—
867C2×C4—34no—
868C2×C4—34no—
869C2×C4—32no—
870C2×C4—64no—
871C2×C4—64no—
872C2×C4—64no—
873C2×C4—64no—
874C2×C4—64no—
875C2×C4—94no—
876C2×C4—94no—
877C2×C4—188no—
878C2×C4—188no—
879C2×C4—188no—
880C2×C4—184no—
881C2×C4D3×#6714yes—
882C2×C4C22×D3212yes—
883C2×C4C22×D3211yescharacteristic
884C2×C4C22×D3211yescharacteristic
885C2×C3—22no—
886C2×C3—22no—
887C2×C3—22no—
888C2×C3—21no—
889C2×C3—34no—
890C2×C3—42no—
891C2×C3—42no—
892C2×C3—42no—
893C2×C3—62no—
894C2×C3—82no—
895C2×C3—122no—
896C2×C3C22×D3×D411yescharacteristic
897C2×C3C2×#101012yes—
898C2×C3D3×2−1+412yes—
899C2×C3C23×#6711yescharacteristic
900D3—22no—
901D3—42no—
902D3#582514yesdirect product factor
903C22—22no—
904C22—24no—
905C22—22no—
906C22—34no—
907C22—32no—
908C22—32no—
909C22—68no—
910C22—62no—
911C22—64no—
912C22—62no—
913C22—128no—
914C22C2×D3×#6712yes—
915C22C23×D3211yescharacteristic
916C4—22no—
917C4—32no—
918C4—32no—
919C4—64no—
920C4—62no—
921C4—64no—
922C4—184no—
923C4—184no—
924C4C2×D3×#6712yes—
925C4C2×D3×#6712yes—
926C3—21no—
927C3D3×#53611yescharacteristic, complemented
928C3C2×#582511yescharacteristic, complemented
929C2—22no—
930C2—34no—
931C2—42no—
932C2—62no—
933C2—122no—
934C2D3×#101012yes—
935C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
prime radicalC2×C3×D3×#41C2
hypercenterC2×#41D32
hypocenterC32C2×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic6C2semidirect
3. #10596296C2semidirect
4. C3×#5825C2semidirect
5. #10595356C2semidirect
6. D3×#944C2semidirect
7. #10595270C2semidirect
8. #10595147C2semidirect
9. D3×#936C2semidirect
10. D3×#935C2semidirect
11. D3×#926C2semidirect
12. #10594884C2semidirect
13. D3×#924C2semidirect
14. #10594856C2semidirect
15. #10594855C2semidirect
19. C22×#634C22semidirect
31. C22×C3×Dic6C22semidirect
32. C22×#627C22semidirect
37. C2×D3×Dic6C22semidirect
38. C2×D3×Dic6C22semidirect
39. #64153C22semidirect
40. #64145C22semidirect
41. #64144C22semidirect
42. #64135C22semidirect
43. #64133C22semidirect
44. C3×#944C22semidirect
45. C3×#936C22semidirect
46. C3×#935C22semidirect
47. C3×#926C22semidirect
48. C3×#924C22semidirect
49. #63969C22semidirect
52. #63964C22semidirect
53. #63962C22semidirect
54. #63961C22semidirect
55. #63959C22semidirect
56. #63955C22semidirect
58. #63884C22semidirect
61. #63873C22semidirect
62. #63866C22semidirect
63. #63863C22semidirect
64. #63860C22semidirect
65. #63857C22semidirect
66. #63856C22semidirect
67. #63855C22semidirect
68. #63851C22semidirect
69. #63841C22semidirect
70. #63839C22semidirect
85. #5825D3direct (N × H)
216. C22×Dic6C2×D3semidirect
233. #944C2×D3semidirect
240. #936C2×D3semidirect
248. #935C2×D3semidirect
256. #926C2×D3semidirect
265. #924C2×D3semidirect
706. C3×D3#536semidirect
833. C32C2×#536semidirect
902. D3#5825direct (N × H)
927. C3D3×#536semidirect
928. C3C2×#5825semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C22×D3×Dic62
#105962962
C3×#58252
#105953562
D3×#9442
#105952702
#105951472
D3×#9362
D3×#9352
D3×#9262
#105948842
D3×#9242
#105948562
#105948552
C2×#58253
D3×#5363