Finite Group Databasebeta

← D3×#4758 #11859909

Subgroups — D3×#4758 #11859909

Order 1152.

1165 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D4×Dic3C211yesmaximal, characteristic
2C2×D3×#214C211yesmaximal, characteristic
3D3×#887C211yesmaximal, characteristic, complemented
4#10592457C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic
6C3×#4758C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590744C211yesmaximal, characteristic, complemented
10#10590742C211yesmaximal, characteristic, complemented
11D3×#816C211yesmaximal, characteristic, complemented
12D3×C8×Dic3C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16C4×D3×SD16—31nomaximal
17C2×#4758—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×D3×Dic3—21no—
20C2×D3×Dic6C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23#64096C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#887C2211yescharacteristic, complemented
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31D3×#217—21no—
32D3×#214C418yescomplemented
33#63898C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36D3×Dic3⋊C4—21no—
37C4×D3×Dic3—21no—
38C4×D3×Dic3C2211yescharacteristic
39#63844C2211yescharacteristic, complemented
40#63843C2211yescharacteristic, complemented
41#63838—21no—
42#63837—21no—
43C2×#3716C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63643C2211yescharacteristic, complemented
48C8×C3⋊Dic3C2211yescharacteristic, complemented
49#63635C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#808C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×D4×Dic3—31no—
63C22×#214—31no—
64C2×D3×SD16—31no—
65C4×D3×Q8—31no—
66C4×D3×D4—31no—
67C2×#887—31no—
68C3×C4×SD16—31no—
69C2×C3×#102—31no—
70Dic3×SD16—31no—
71C2×#816—31no—
72C2×C8×Dic3—31no—
73C4×#215—31no—
74C4×#214—31no—
75C2×#808—31no—
76D3×#106—31no—
77#4852—31no—
78D3×#103—31no—
79#4788—31no—
80D3×#102D311yescharacteristic
81#4758—31no—
82#4758—31no—
83#4758—31no—
84#4758—31no—
85#4758—31no—
86#4758—31no—
87#4758—31no—
88#4758—31no—
89#4758—61no—
90#4758D311yescharacteristic, direct product factor
91C4×#204—31no—
92C4×D3×C8—31no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4C2×C414yes—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—44no—
111C2×D3×Dic3D411yescharacteristic
112C2×D3×Dic3D411yescharacteristic
113D3×Dic6—22no—
114D3×Dic6C2×C414yescomplemented
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3757—21no—
118#3754C2×C414yescomplemented
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#214C2×C414yescomplemented
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D3×C8—22no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32D411yescharacteristic
143Dic32D411yescharacteristic
144#3716C2×C414yescomplemented
145#3715C2×C414yescomplemented
146D3×C3⋊C8C2×C414yescomplemented
147C2×C4×SD16—91noSylow
148C22×C3×D4—31no—
149C23×Dic3—61no—
150C2×D3×Q8—31no—
151C2×D3×D4C2×D311yescharacteristic
152C22×C4×D3—61no—
153C22×Dic6—31no—
154C2×C3×SD16—31no—
155C22×C3×C8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C2×C3×C4⋊C4—31no—
159C2×#217—61no—
160Q8×Dic3—31no—
161C2×#215—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—38no—
174C2×#214—31no—
175C2×#214—61no—
176C2×#214C2×D311yescharacteristic
177C4×#67—61no—
178C2×C4⋊Dic3—31no—
179C2×Dic3⋊C4—61no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—61no—
182C22×C3⋊C8—31no—
183D3×SD16—38no—
184C2×#204—31no—
185C2×D3×C8—31no—
186C2×D3×C8C2×D311yescharacteristic
187#893—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4C2×D311yescharacteristic
191#887—31no—
192#887—31no—
193#887—31no—
194#887—31no—
195#887—61no—
196#887—61no—
197#887—61no—
198#887—61no—
199#887C2×D311yescharacteristic, complemented
200#67⋊C4—61no—
201D3×C22⋊C4—61no—
202C4×D12—31no—
203C42×D3—31no—
204C42×D3—61no—
205C4×Dic6—31no—
206C4×Dic6—61no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102C2×D311yescharacteristic
214C3×#102C2×D311yescharacteristic
215C3×C4×C8—31no—
216#835—31no—
217#832C2×D311yescharacteristic
218#821C2×D311yescharacteristic
219#817—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#816C2×D311yescharacteristic, complemented
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3—61no—
232C8×Dic3C2×D311yescharacteristic, complemented
233#810—31no—
234#809C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#808—31no—
238#808—31no—
239#808—31no—
240#808—61no—
241#808C2×D311yescharacteristic, complemented
242C4×C3⋊C8—31no—
243C23×C32—21no—
244C22×C3×D3—21no—
245C22×C3×D3—24no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3C2×D411yescharacteristic
249C32×D4—21no—
250C32×D4C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—42no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258#634—21no—
259#634C22×C412yescomplemented
260C3×#67—24no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12C22×C412yes—
270C3×C4×D3—42no—
271C3×C4×D3C22×C412yes—
272C3×C4×D3#4112yes—
273C3×Dic6—21no—
274C3×Dic6C22×C412yescomplemented
275#627—24no—
276D3×Dic3—24no—
277D3×Dic3—22no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281D3×Dic3SD1614yescomplemented
282C32×C8—21no—
283C3⋊(C3⋊C8)C22×C412yescomplemented
284C3×C3⋊C8—21no—
285C3×C3⋊C8C22×C412yescomplemented
286C22×SD16—91no—
287C2×C4×Q8—91no—
288C2×C4×D4—91no—
289C4×SD16—31no—
290C4×SD16—91no—
291C4×SD16—91no—
292C4×SD16—91no—
293C4×SD16—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296C4×SD16—91no—
297C2×#106—91no—
298C2×#103—91no—
299C2×#102—31no—
300C2×C4×C8—91no—
301C24×C3—61no—
302C23×D3—21no—
303C2×C3×Q8—31no—
304C2×C3×D4—21no—
305C2×C3×D4—34no—
306C2×C3×D4—31no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C22×Dic3—21no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325C22×Dic3—124no—
326D3×Q8—34no—
327D3×Q8—62no—
328D3×D4—22no—
329D3×D4C4×D314yes—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—124no—
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—34no—
343C2×Dic6—61no—
344C2×Dic6—62no—
345C2×Dic6—61no—
346C2×Dic6—61no—
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—34no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—62no—
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—61no—
363C3×C42—31no—
364C3×C42—61no—
365#217—21no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—121no—
371#215—34no—
372#214—34no—
373#214—34no—
374#214—34no—
375#214—34no—
376#214—64no—
377#214C4×D314yescomplemented
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—121no—
396C4×Dic3—21no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—121no—
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—34no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418#204—34no—
419D3×C8—22no—
420D3×C8—34no—
421C22×C32—22no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—48no—
429C2×C3×D3C4×D412yes—
430C2×C3×D3C2×SD1612yes—
431C2×C3×D3#13512yes—
432C32×C4—41no—
433C32×C4C23×C411yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—22no—
436C3⋊Dic3—21no—
437C3⋊Dic3—41no—
438C3⋊Dic3C2×SD1612yescomplemented
439C3×Dic3—22no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3C4×D412yes—
444C3×Dic3C2×SD1612yescomplemented
445C22×Q8—91no—
446C22×D4—31no—
447C23×C4—181no—
448C2×SD16—31no—
449C2×SD16—91no—
450C2×SD16—98no—
451C2×SD16—91no—
452C2×SD16—91no—
453C22×C8—31no—
454C22×C8—91no—
455C4×Q8—31no—
456C4×Q8—91no—
457C4×Q8—91no—
458C4×Q8—91no—
459C4×Q8—181no—
460C4×Q8—181no—
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—181no—
466C4×D4—181no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—91no—
469C2×C4⋊C4—181no—
470C2×C22⋊C4—181no—
471C2×C42—91no—
472C2×C42—181no—
473#106—31no—
474#106—91no—
475#106—91no—
476#106—91no—
477#103—31no—
478#103—91no—
479#103—91no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102D3211yescharacteristic
485C4×C8—31no—
486C4×C8—91no—
487C4×C8—91no—
488C4×C8—91no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—41no—
493C23×C3—64no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C22×D3—21no—
498C22×D3—24no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3D3×D411yescharacteristic
502C3×Q8—32no—
503C3×Q8—61no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—64no—
510C3×D4—61no—
511C3×D4C2×C4×D312yes—
512C3×D4C2×C4×D312yes—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—24no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—34no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—42no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—64no—
542C2×Dic3—62no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—122no—
554C2×Dic3—242no—
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557C2×Dic3D3×D411yescharacteristic
558D12—21no—
559D12C2×C4×D312yes—
560C4×D3—34no—
561C4×D3—42no—
562C4×D3—64no—
563C4×D3—62no—
564C4×D3—122no—
565C4×D3—122no—
566C4×D3—122no—
567C4×D3C2×C4×D312yes—
568C4×D3#23712yes—
569Dic6—21no—
570Dic6—32no—
571Dic6—32no—
572Dic6—62no—
573Dic6—64no—
574Dic6—61no—
575Dic6—61no—
576Dic6—64no—
577Dic6—121no—
578Dic6C2×C4×D312yescomplemented
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—32no—
582C3×C8—41no—
583C3×C8—61no—
584C3⋊C8—21no—
585C3⋊C8—32no—
586C3⋊C8—32no—
587C3⋊C8—62no—
588C3⋊C8C2×C4×D312yescomplemented
589C2×C32—42no—
590C2×C32C2×C4×D411yescharacteristic
591C2×C32C22×SD1611yescharacteristic
592C2×C32C2×#13511yescharacteristic
593C3×D3—42no—
594C3×D3C4×SD1614yescomplemented
595C24—61no—
596C2×Q8—31no—
597C2×Q8—94no—
598C2×Q8—91no—
599C2×Q8—181no—
600C2×Q8—182no—
601C2×D4—34no—
602C2×D4—31no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4C2×D3211yescharacteristic
606C22×C4—31no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—364no—
617SD16—34no—
618SD16—94no—
619SD16—94no—
620SD16—94no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—62no—
624C2×C8—94no—
625C2×C8—91no—
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—61no—
643C42—91no—
644C42—91no—
645C42—91no—
646C42—181no—
647C42—181no—
648C42—181no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—32no—
654C22×C3—32no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—62no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—128no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C2×D3×D411yescharacteristic
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—48no—
672C2×D3#67⋊C412yes—
673C2×D3#91212yes—
674C2×D3D3×SD1612yes—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—32no—
678C3×C4—32no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—62no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C22×C4×D311yescharacteristic
687C3×C4C22×C4×D311yescharacteristic
688C3×C4C2×#23711yescharacteristic
689C3×C4D3×#4111yescharacteristic
690Dic3—21no—
691Dic3—22no—
692Dic3—32no—
693Dic3—32no—
694Dic3—41no—
695Dic3—41no—
696Dic3—62no—
697Dic3—62no—
698Dic3—61no—
699Dic3—61no—
700Dic3—62no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3#67⋊C412yes—
707Dic3D3×SD1612yescomplemented
708C32C2×C4×SD1611yescharacteristic, complemented, Sylow
709C23—21no—
710C23—31no—
711C23—64no—
712C23—61no—
713C23—122no—
714C23—122no—
715Q8—32no—
716Q8—61no—
717Q8—92no—
718Q8—184no—
719Q8—181no—
720D4—21no—
721D4—32no—
722D4—64no—
723D4—61no—
724D4C4×D3212yes—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—31no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—94no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—182no—
740C2×C4—184no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—362no—
744C2×C4—362no—
745C2×C4—362no—
746C2×C4—362no—
747C2×C4C22×D3211yescharacteristic
748C8—21no—
749C8—32no—
750C8—61no—
751C8—92no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—34no—
756C2×C3—42no—
757C2×C3—42no—
758C2×C3—82no—
759C2×C3—122no—
760C2×C3C2×#67⋊C411yescharacteristic
761C2×C3C4×D3×D411yescharacteristic
762C2×C3C2×#91211yescharacteristic
763C2×C3C2×D3×SD1611yescharacteristic
764C2×C3C2×D3×SD1611yescharacteristic
765C2×C3D3×#13511yescharacteristic
766D3—42no—
767D3#475814yesdirect product factor
768C22—22no—
769C22—32no—
770C22—32no—
771C22—32no—
772C22—41no—
773C22—41no—
774C22—62no—
775C22—128no—
776C22—121no—
777C22—121no—
778C22D32×D411yescharacteristic
779C4—32no—
780C4—32no—
781C4—41no—
782C4—61no—
783C4—62no—
784C4—92no—
785C4—121no—
786C4—121no—
787C4—181no—
788C4—182no—
789C4—361no—
790C4C2×C4×D3211yescharacteristic
791C4D3×#23711yescharacteristic
792C3—21no—
793C3C2×#475811yescharacteristic, complemented
794C3C4×D3×SD1611yescharacteristic, complemented
795C2—34no—
796C2—42no—
797C2—122no—
798C2D3×#67⋊C411yescharacteristic
799C2D3×#91211yescharacteristic
800C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32C2×C4×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
3. D3×#887C2semidirect
4. #10592457C2semidirect
6. C3×#4758C2semidirect
7. #10591445C2semidirect
8. #10591401C2semidirect
9. #10590744C2semidirect
10. #10590742C2semidirect
11. D3×#816C2semidirect
12. D3×C8×Dic3C2semidirect
13. D3×#808C2semidirect
14. #10590460C2semidirect
15. #10590453C2semidirect
23. #64096C22semidirect
28. C3×#887C22semidirect
32. D3×#214C4semidirect
39. #63844C22semidirect
40. #63843C22semidirect
47. #63643C22semidirect
48. C8×C3⋊Dic3C22semidirect
49. #63635C22semidirect
52. C3×#816C22semidirect
53. C3×C8×Dic3C22semidirect
55. C3×#808C22semidirect
56. #63574C22semidirect
57. #63573C22semidirect
58. #63567C22semidirect
59. #63566C22semidirect
60. #63553C22semidirect
61. Dic3×C3⋊C8C22semidirect
90. #4758D3direct (N × H)
114. D3×Dic6C2×C4semidirect
118. #3754C2×C4semidirect
125. C3×#214C2×C4semidirect
144. #3716C2×C4semidirect
145. #3715C2×C4semidirect
146. D3×C3⋊C8C2×C4semidirect
199. #887C2×D3semidirect
225. #816C2×D3semidirect
232. C8×Dic3C2×D3semidirect
241. #808C2×D3semidirect
259. #634C22×C4semidirect
274. C3×Dic6C22×C4semidirect
281. D3×Dic3SD16semidirect
283. C3⋊(C3⋊C8)C22×C4semidirect
285. C3×C3⋊C8C22×C4semidirect
377. #214C4×D3semidirect
438. C3⋊Dic3C2×SD16semidirect
444. C3×Dic3C2×SD16semidirect
578. Dic6C2×C4×D3semidirect
588. C3⋊C8C2×C4×D3semidirect
594. C3×D3C4×SD16semidirect
707. Dic3D3×SD16semidirect
708. C32C2×C4×SD16semidirect
767. D3#4758direct (N × H)
793. C3C2×#4758semidirect
794. C3C4×D3×SD16semidirect

Maximal subgroups

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

subgroupindex
D3×D4×Dic32
C2×D3×#2142
D3×#8872
#105924572
C3×D3×#1022
C3×#47582
#105914452
#105914012
#105907442
#105907422
D3×#8162
D3×C8×Dic32
D3×#8082
#105904602
#105904532
C4×D3×SD163
C2×#47583