Finite Group Databasebeta

← D3×#4817 #11860087

Subgroups — D3×#4817 #11860087

Order 1152.

1148 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×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic
3D3×#893C211yesmaximal, characteristic
4#10592516C211yesmaximal, characteristic, complemented
5C3×#4817C211yesmaximal, characteristic, complemented
6C3×D3×#103C211yesmaximal, characteristic, complemented
7#10591572C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic
10#10590795C211yesmaximal, characteristic, complemented
11#10590743C211yesmaximal, characteristic, complemented
12D3×#815C211yesmaximal, characteristic, complemented
13D3×#807C211yesmaximal, characteristic, complemented
14#10590484C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16D3×#440—31nomaximal
17C2×#4817—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23#64102C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29D3×#215C418yescomplemented
30D3×(C2×D3)⋊C4—21no—
31#63904—21no—
32#63898C2211yescharacteristic
33#63894C2211yescharacteristic
34D3×C4⋊Dic3—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63881—21no—
37C4×D3×Dic3—21no—
38C4×D3×Dic3C2211yescharacteristic
39#63843—21no—
40#63843C2211yescharacteristic, complemented
41Dic3×Dic6—21no—
42Dic3×Dic6C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C32×#103C2211yescharacteristic, complemented
47#63648C2211yescharacteristic
48#63642C2211yescharacteristic, complemented
49#63634C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62C2×Q8×Dic3—31no—
63C22×#215—31no—
64C2×D3×SD16—31no—
65C4×D3×Q8—31no—
66C4×D3×D4—31no—
67C2×#893—31no—
68C3×#440—31no—
69C2×C3×#103—31no—
70#5164—31no—
71C2×#821—31no—
72C2×#815—31no—
73#5026—31no—
74#5018—31no—
75C2×#807—31no—
76#4889—31no—
77D3×#107—31no—
78#4817—31no—
79#4817—31no—
80#4817—31no—
81#4817—31no—
82#4817—31no—
83#4817—31no—
84#4817—31no—
85#4817—31no—
86#4817—61no—
87#4817D311yescharacteristic, direct product factor
88D3×#103D311yescharacteristic, complemented
89D3×#102—31no—
90#4757—31no—
91#4710—31no—
92D3×#97—31no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8C2×C414yescomplemented
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3D411yescharacteristic
111C2×D3×Dic3D411yescharacteristic
112D3×D12—22no—
113D3×D12C2×C414yes—
114C4×D32—44no—
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3755C2×C414yescomplemented
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#215C2×C414yescomplemented
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D3×C8—22no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32D411yescharacteristic
143Dic32D411yescharacteristic
144#3717C2×C414yescomplemented
145#3715C2×C414yescomplemented
146D3×C3⋊C8C2×C414yescomplemented
147C2×#440—91noSylow
148C22×C3×Q8—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×D3×D4—31no—
151C22×D12—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C2×C3×SD16—31no—
155C22×C3×C8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C2×C3×C4⋊C4—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—61no—
164Q8×Dic3—61no—
165Q8×Dic3—61no—
166Q8×Dic3C2×D311yescharacteristic, complemented
167C2×#215—31no—
168C2×#215—31no—
169C2×#215—31no—
170C2×#215—38no—
171C2×#215—31no—
172C2×#215—61no—
173C2×#215C2×D311yescharacteristic
174D4×Dic3—31no—
175C2×#214—31no—
176C4×#67—61no—
177C2×(C2×D3)⋊C4—61no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—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—
188#893—31no—
189#893—31no—
190#893—31no—
191#893—61no—
192#893—61no—
193#893—61no—
194#893C2×D311yescharacteristic
195D3×C4⋊C4—31no—
196D3×C4⋊C4—61no—
197D3×C4⋊C4C2×D311yescharacteristic
198#887—31no—
199#887—61no—
200#67⋊C4—61no—
201D3×C22⋊C4—61no—
202C4×D12—31no—
203C42×D3—31no—
204C42×D3—61no—
205C4×Dic6—31no—
206C4×Dic6—61no—
207C3×#107—31no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103C2×D311yescharacteristic, complemented
213C3×#103C2×D311yescharacteristic, complemented
214C3×#102—31no—
215C3×#97—31no—
216#835C2×D311yescharacteristic, complemented
217#832—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821C2×D311yescharacteristic
224#818—31no—
225#816C2×D311yescharacteristic, complemented
226#815—31no—
227#815—31no—
228#815—31no—
229#815—31no—
230#815—31no—
231#815—61no—
232#815C2×D311yescharacteristic, complemented
233#810C2×D311yescharacteristic, complemented
234#809—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—31no—
239#807—31no—
240#807—61no—
241#807C2×D311yescharacteristic, complemented
242#803—31no—
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—24no—
247C2×D32—42no—
248C2×D32—42no—
249C32×Q8—21no—
250C32×Q8C22×C412yescomplemented
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)C22×C412yes—
259C4×C3⋊D3—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12C22×C412yes—
268C3×C4×D3—24no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3C22×C412yes—
272C3×C4×D3#4112yes—
273C3×Dic6—21no—
274C3×Dic6—24no—
275C3×Dic6C22×C412yescomplemented
276#626—24no—
277#624—42no—
278D3×Dic3—22no—
279D3×Dic3—22no—
280D3×Dic3—42no—
281D3×Dic3—42no—
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—
289#440—31no—
290#440—91no—
291#440—91no—
292#440—91no—
293#440—91no—
294#440—91no—
295#440—91no—
296#440—91no—
297C2×#107—91no—
298C2×#103—31no—
299C2×#102—91no—
300C2×#97—91no—
301C23×D3—61no—
302C23×D3—61no—
303C2×C3×Q8—21no—
304C2×C3×Q8—34no—
305C2×C3×Q8—31no—
306C2×C3×Q8—61no—
307C2×C3×Q8—62no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×D4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—61no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320D3×Q8—22no—
321D3×Q8C4×D314yescomplemented
322D3×D4—34no—
323D3×D4—62no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—34no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—121no—
343C2×C4×D3—124no—
344C2×C4×D3—124no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6—21no—
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—61no—
366#215—34no—
367#215—34no—
368#215—34no—
369#215—34no—
370#215—64no—
371#215C4×D314yescomplemented
372#214—34no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—121no—
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—121no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
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×C32C22×D411yescharacteristic
422C2×C3⋊D3—22no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3C4×D412yes—
429C2×C3×D3AGL(1,ℤ/8)12yes—
430C2×C3×D3#13712yes—
431D32—48no—
432C32×C4—22no—
433C32×C4—41no—
434C32×C4C23×C411yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—41no—
439C3×Dic3—22no—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3C4×D412yes—
445C22×Q8—31no—
446C22×D4—91no—
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#107—31no—
474#107—91no—
475#107—91no—
476#107—91no—
477#103—31no—
478#103—31no—
479#103—31no—
480#103D3211yescharacteristic, complemented
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#97—31no—
486#97—91no—
487#97—91no—
488#97—91no—
489C23×C3—31no—
490C23×C3—61no—
491C22×D3—21no—
492C22×D3—64no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—64no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3D3×D411yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—22no—
505C3×Q8—32no—
506C3×Q8—41no—
507C3×Q8—64no—
508C3×Q8—61no—
509C3×Q8C2×C4×D312yescomplemented
510C3×Q8C2×C4×D312yescomplemented
511C3×D4—32no—
512C3×D4—61no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—64no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—64no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—122no—
549C2×Dic3—122no—
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—21no—
554D12—32no—
555D12—32no—
556D12—62no—
557D12—64no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12C2×C4×D312yes—
562C4×D3—24no—
563C4×D3—42no—
564C4×D3—42no—
565C4×D3—62no—
566C4×D3—62no—
567C4×D3—122no—
568C4×D3—122no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—122no—
573C4×D3—242no—
574C4×D3C2×C4×D312yes—
575C4×D3#23712yes—
576Dic6—21no—
577Dic6—24no—
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×C32C2×C4×D411yescharacteristic
590C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
591C2×C32C2×#13711yescharacteristic
592C3⋊D3—42no—
593C3×D3—42no—
594C3×D3#44014yescomplemented
595C24—181no—
596C2×Q8—34no—
597C2×Q8—31no—
598C2×Q8—61no—
599C2×Q8—62no—
600C2×Q8C2×D3211yescharacteristic
601C2×D4—31no—
602C2×D4—94no—
603C2×D4—91no—
604C2×D4—182no—
605C2×D4—181no—
606C22×C4—31no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—91no—
611C22×C4—91no—
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—21no—
650C22×C3—32no—
651C22×C3—32no—
652C22×C3—32no—
653C22×C3—62no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—22no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—122no—
664C2×D3—128no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—128no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3#67⋊C412yes—
673C2×D3#91412yes—
674C2×D3#91812yes—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—32no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—62no—
686C3×C4—81no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C22×C4×D311yescharacteristic
690C3×C4C22×C4×D311yescharacteristic
691C3×C4C2×#23711yescharacteristic
692C3×C4D3×#4111yescharacteristic
693Dic3—22no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707Dic3#67⋊C412yes—
708C32C2×#44011yescharacteristic, complemented, Sylow
709C23—31no—
710C23—61no—
711C23—184no—
712C23—181no—
713C23—362no—
714C23—362no—
715Q8—21no—
716Q8—32no—
717Q8—64no—
718Q8—61no—
719Q8C4×D3212yescomplemented
720D4—32no—
721D4—61no—
722D4—92no—
723D4—184no—
724D4—181no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—64no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—182no—
741C2×C4—182no—
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—122no—
757C2×C3C2×#67⋊C411yescharacteristic
758C2×C3C4×D3×D411yescharacteristic
759C2×C3C2×#91411yescharacteristic
760C2×C3C2×#91811yescharacteristic
761C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
762C2×C3D3×#13711yescharacteristic
763D3—42no—
764D3—122no—
765D3—122no—
766D3—242no—
767D3#481714yesdirect product factor
768C22—32no—
769C22—32no—
770C22—32no—
771C22—62no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—368no—
776C22—361no—
777C22—361no—
778C22D32×D411yescharacteristic
779C4—22no—
780C4—32no—
781C4—41no—
782C4—61no—
783C4—61no—
784C4—62no—
785C4—121no—
786C4—121no—
787C4—181no—
788C4—181no—
789C4—361no—
790C4C2×C4×D3211yescharacteristic
791C4D3×#23711yescharacteristic
792C3—21no—
793C3C2×#481711yescharacteristic, complemented
794C3D3×#44011yescharacteristic, complemented
795C2—34no—
796C2—122no—
797C2—362no—
798C2D3×#67⋊C411yescharacteristic
799C2D3×#91411yescharacteristic
800C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. D3×Q8×Dic3C2semidirect
4. #10592516C2semidirect
5. C3×#4817C2semidirect
6. C3×D3×#103C2semidirect
7. #10591572C2semidirect
8. #10591540C2semidirect
10. #10590795C2semidirect
11. #10590743C2semidirect
12. D3×#815C2semidirect
13. D3×#807C2semidirect
14. #10590484C2semidirect
15. #10590478C2semidirect
21. Q8×C3⋊Dic3C22semidirect
24. C3×Q8×Dic3C22semidirect
29. D3×#215C4semidirect
40. #63843C22semidirect
42. Dic3×Dic6C22semidirect
46. C32×#103C22semidirect
48. #63642C22semidirect
49. #63634C22semidirect
50. C3×#835C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×#810C22semidirect
55. C3×#807C22semidirect
56. #63576C22semidirect
57. #63575C22semidirect
60. #63555C22semidirect
61. #63554C22semidirect
87. #4817D3direct (N × H)
88. D3×#103D3semidirect
98. C3×D3×Q8C2×C4semidirect
117. #3755C2×C4semidirect
124. C3×#215C2×C4semidirect
144. #3717C2×C4semidirect
145. #3715C2×C4semidirect
146. D3×C3⋊C8C2×C4semidirect
166. Q8×Dic3C2×D3semidirect
212. C3×#103C2×D3semidirect
213. C3×#103C2×D3semidirect
216. #835C2×D3semidirect
225. #816C2×D3semidirect
232. #815C2×D3semidirect
233. #810C2×D3semidirect
241. #807C2×D3semidirect
250. C32×Q8C22×C4semidirect
275. C3×Dic6C22×C4semidirect
283. C3⋊(C3⋊C8)C22×C4semidirect
285. C3×C3⋊C8C22×C4semidirect
321. D3×Q8C4×D3semidirect
371. #215C4×D3semidirect
480. #103D32semidirect
509. C3×Q8C2×C4×D3semidirect
510. C3×Q8C2×C4×D3semidirect
578. Dic6C2×C4×D3semidirect
588. C3⋊C8C2×C4×D3semidirect
594. C3×D3#440semidirect
708. C32C2×#440semidirect
719. Q8C4×D32semidirect
767. D3#4817direct (N × H)
793. C3C2×#4817semidirect
794. C3D3×#440semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×Dic32
C2×D3×#2152
D3×#8932
#105925162
C3×#48172
C3×D3×#1032
#105915722
#105915402
D3×#8212
#105907952
#105907432
D3×#8152
D3×#8072
#105904842
#105904782
D3×#4403
C2×#48173