Finite Group Databasebeta

← D3×#4710 #11860062

Subgroups — D3×#4710 #11860062

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
1C2×D3×#204C211yesmaximal, characteristic
2C4×D3×D12C211yesmaximal, characteristic
3C4×D3×Dic6C211yesmaximal, characteristic, complemented
4#10592409C211yesmaximal, characteristic, complemented
5C3×#4710C211yesmaximal, characteristic, complemented
6C3×D3×#97C211yesmaximal, characteristic, complemented
7D3×#821C211yesmaximal, characteristic
8#10590795C211yesmaximal, characteristic, complemented
9#10590773C211yesmaximal, characteristic, complemented
10#10590766C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12D3×#818C211yesmaximal, characteristic, complemented
13D3×#816C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590360C211yesmaximal, characteristic, complemented
16D3×#440—31nomaximal
17C2×#4710—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C2×D3×Dic6C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C4×#634C2211yescharacteristic, complemented
24C2×C3×#204C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic, complemented
30D3×(C2×D3)⋊C4—21no—
31C4×#627—21no—
32C4×#626—21no—
33#63894C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63880—21no—
38D3×Dic3⋊C4—21no—
39C4×D3×Dic3—21no—
40#63844C2211yescharacteristic, complemented
41Dic3×Dic6C2211yescharacteristic, complemented
42#63837—21no—
43C2×#3717C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45D3×#204C418yescomplemented
46C32×#97C2211yescharacteristic, complemented
47#63648C2211yescharacteristic
48#63645C2211yescharacteristic, complemented
49#63643C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×#815C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63563C2211yescharacteristic
62C2×D3×SD16—31no—
63C22×#204—31no—
64C4×D3×Q8—31no—
65C4×D3×D4—31no—
66C2×C4×D12—31no—
67C2×C4×Dic6—31no—
68C3×#440—31no—
69C2×C3×#97—31no—
70#5164—31no—
71C2×#821—31no—
72C2×#818—31no—
73C2×#816—31no—
74#5026—31no—
75#5018—31no—
76#4889—31no—
77D3×#107—31no—
78#4817—31no—
79D3×#103—31no—
80D3×#102—31no—
81#4757—31no—
82#4710—31no—
83#4710—31no—
84#4710—31no—
85#4710—31no—
86#4710—31no—
87#4710—31no—
88#4710—31no—
89#4710—31no—
90#4710—61no—
91#4710D311yescharacteristic, direct product factor
92D3×#97D311yescharacteristic, complemented
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110D3×D12—22no—
111D3×D12C2×C414yes—
112C4×D32—44no—
113D3×Dic6—22no—
114D3×Dic6C2×C414yescomplemented
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C32×C42C2311yescharacteristic
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C4×C3⋊Dic3—21no—
123#3744C2×C414yescomplemented
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3D411yescharacteristic
130C3×C4×Dic3D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×#204C2×C414yescomplemented
135C3×D3×C8—22no—
136C3×D3×C8C2×C414yescomplemented
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144Dic32—21no—
145#3717C2×C414yescomplemented
146#3716C2×C414yescomplemented
147C2×#440—91noSylow
148C2×D3×Q8—31no—
149C2×D3×D4—31no—
150C22×D12—31no—
151C22×C4×D3—61no—
152C22×C4×D3—61no—
153C22×Dic6—31no—
154C2×C3×SD16—31no—
155C22×C3×C8—31no—
156C22×C3×C8—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C2×C3×C42—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162D4×Dic3—31no—
163C2×#214—31no—
164C4×#67—61no—
165C2×(C2×D3)⋊C4—61no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×Dic3⋊C4—61no—
169C2×C4×Dic3—61no—
170D3×SD16—38no—
171C2×#204—31no—
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—38no—
176C2×#204—61no—
177C2×#204C2×D311yescharacteristic
178C2×D3×C8C2×D311yescharacteristic
179C2×D3×C8C2×D311yescharacteristic
180#893—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—61no—
184#887—31no—
185#887—61no—
186#67⋊C4—61no—
187D3×C22⋊C4—61no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194C4×D12—61no—
195C4×D12C2×D311yescharacteristic
196C42×D3—61no—
197C42×D3C2×D311yescharacteristic
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—31no—
202C4×Dic6—61no—
203C4×Dic6—61no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C4×Dic6C2×D311yescharacteristic, complemented
207C3×#107—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#97—21no—
211C3×#97—31no—
212C3×#97—31no—
213C3×#97—31no—
214C3×#97C2×D311yescharacteristic, complemented
215C3×#97C2×D311yescharacteristic, complemented
216#835—31no—
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#818—31no—
226#818—31no—
227#818—31no—
228#818—61no—
229#818C2×D311yescharacteristic, complemented
230#816—31no—
231#816—31no—
232#816—31no—
233#816—31no—
234#816—61no—
235#816C2×D311yescharacteristic, complemented
236#815C2×D311yescharacteristic, complemented
237#815C2×D311yescharacteristic, complemented
238#810—31no—
239#809—31no—
240#807—31no—
241#807—31no—
242#803C2×D311yescharacteristic, complemented
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—24no—
247C2×D32—42no—
248C2×D32—42no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)C22×C412yes—
257C4×C3⋊D3—42no—
258#634—21no—
259#634C22×C412yescomplemented
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—22no—
269C3×C4×D3—22no—
270C3×C4×D3—42no—
271C3×C4×D3C22×C412yes—
272C3×C4×D3#4112yes—
273C3×Dic6—21no—
274C3×Dic6C22×C412yescomplemented
275#627—24no—
276#626—24no—
277#624—42no—
278D3×Dic3—24no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281D3×Dic3—42no—
282C32×C8—21no—
283C32×C8C22×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—91no—
299C2×#102—91no—
300C2×#97—31no—
301C23×D3—61no—
302C23×D3—61no—
303C2×C3×Q8—31no—
304C2×C3×D4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314D3×Q8—34no—
315D3×Q8—62no—
316D3×D4—34no—
317D3×D4—62no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—34no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3—124no—
336C2×C4×D3—124no—
337C2×C4×D3D1211yescharacteristic
338C2×C4×D3D1211yescharacteristic
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—21no—
351C2×C3×C8—31no—
352C2×C3×C8—34no—
353C2×C3×C8—31no—
354C2×C3×C8—62no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—61no—
368C3×C42C22×D311yescharacteristic
369C3×C42C22×D311yescharacteristic
370#217—61no—
371#215—34no—
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—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400C4×Dic3—21no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—121no—
408C4×Dic3D1211yescharacteristic
409C4×Dic3D1211yescharacteristic
410C4×Dic3C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—34no—
414#204—34no—
415#204—34no—
416#204—34no—
417#204—64no—
418#204C4×D314yescomplemented
419D3×C8—22no—
420D3×C8C4×D314yescomplemented
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—21no—
433C32×C4—21no—
434C32×C4C23×C411yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—22no—
437C3⋊Dic3—41no—
438C3⋊Dic3—41no—
439C3×Dic3—22no—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3C4×D412yes—
445C22×Q8—91no—
446C22×D4—91no—
447C23×C4—181no—
448C2×SD16—31no—
449C2×SD16—98no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×SD16—91no—
453C22×C8—31no—
454C22×C8—31no—
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—91no—
468C2×C4⋊C4—91no—
469C2×C4⋊C4—181no—
470C2×C22⋊C4—181no—
471C2×C42—31no—
472C2×C42—181no—
473#107—31no—
474#107—91no—
475#107—91no—
476#107—91no—
477#103—31no—
478#103—91no—
479#103—91no—
480#103—91no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#97—31no—
486#97—31no—
487#97—31no—
488#97D3211yescharacteristic, complemented
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×D3C2×D1211yescharacteristic
502C3×Q8—32no—
503C3×Q8—61no—
504C3×D4—32no—
505C3×D4—61no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4C2×D1211yescharacteristic
521C2×C3×C4C2×D1211yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—64no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—64no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3—122no—
543C2×Dic3C2×D1211yescharacteristic
544C2×Dic3C2×D1211yescharacteristic
545C2×Dic3C2×D1211yescharacteristic
546D12—21no—
547D12—32no—
548D12—32no—
549D12—62no—
550D12—64no—
551D12—61no—
552D12—61no—
553D12—121no—
554D12C2×C4×D312yes—
555C4×D3—22no—
556C4×D3—22no—
557C4×D3—42no—
558C4×D3—64no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—122no—
566C4×D3—242no—
567C4×D3C2×C4×D312yes—
568C4×D3#23512yes—
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—22no—
582C3×C8—32no—
583C3×C8—41no—
584C3×C8—61no—
585C3×C8C2×C4×D312yescomplemented
586C3×C8C2×C4×D312yescomplemented
587C3⋊C8—21no—
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—31no—
597C2×Q8—94no—
598C2×Q8—91no—
599C2×Q8—181no—
600C2×Q8—182no—
601C2×D4—31no—
602C2×D4—94no—
603C2×D4—91no—
604C2×D4—182no—
605C2×D4—181no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—181no—
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—34no—
623C2×C8—31no—
624C2×C8—62no—
625C2×C8C2×D3211yescharacteristic
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—31no—
643C42—31no—
644C42—61no—
645C42—181no—
646C42—181no—
647C42—181no—
648C42C2×D3211yescharacteristic
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—32no—
652C22×C3—32no—
653C22×C3—62no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3C22×D1211yescharacteristic
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×D3C4×D1212yes—
673C2×D3#90812yes—
674C2×D3#90912yes—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—32no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—62no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C22×C4×D311yescharacteristic
690C3×C4C22×C4×D311yescharacteristic
691C3×C4C2×#23511yescharacteristic
692C3×C4D3×#4111yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—22no—
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—62no—
700Dic3—122no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3—241no—
707Dic3C4×D1212yes—
708C32C2×#44011yescharacteristic, complemented, Sylow
709C23—31no—
710C23—61no—
711C23—184no—
712C23—181no—
713C23—362no—
714C23—362no—
715Q8—32no—
716Q8—61no—
717Q8—92no—
718Q8—184no—
719Q8—181no—
720D4—32no—
721D4—61no—
722D4—92no—
723D4—184no—
724D4—181no—
725C2×C4—31no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—122no—
736C2×C4—184no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—362no—
741C2×C4—362no—
742C2×C4—362no—
743C2×C4—362no—
744C2×C4—362no—
745C2×C4D3×D1211yescharacteristic
746C2×C4D3×D1211yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—21no—
749C8—32no—
750C8—61no—
751C8C4×D3212yescomplemented
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—34no—
756C2×C3—122no—
757C2×C3C2×C4×D1211yescharacteristic
758C2×C3C4×D3×D411yescharacteristic
759C2×C3C2×#90811yescharacteristic
760C2×C3C2×#90911yescharacteristic
761C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
762C2×C3D3×#13711yescharacteristic
763D3—42no—
764D3—122no—
765D3—122no—
766D3—242no—
767D3#471014yesdirect product factor
768C22—32no—
769C22—32no—
770C22—32no—
771C22—62no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—368no—
776C22—361no—
777C22—361no—
778C22C2×D3×D1211yescharacteristic
779C4—21no—
780C4—21no—
781C4—32no—
782C4—61no—
783C4—61no—
784C4—62no—
785C4—121no—
786C4—121no—
787C4—182no—
788C4—361no—
789C4—361no—
790C4C2×C4×D3211yescharacteristic
791C4D3×#23511yescharacteristic
792C3—21no—
793C3C2×#471011yescharacteristic, complemented
794C3D3×#44011yescharacteristic, complemented
795C2—34no—
796C2—122no—
797C2—362no—
798C2C4×D3×D1211yescharacteristic
799C2D3×#90811yescharacteristic
800C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. C4×D3×Dic6C2semidirect
4. #10592409C2semidirect
5. C3×#4710C2semidirect
6. C3×D3×#97C2semidirect
8. #10590795C2semidirect
9. #10590773C2semidirect
10. #10590766C2semidirect
11. #10590747C2semidirect
12. D3×#818C2semidirect
13. D3×#816C2semidirect
14. #10590362C2semidirect
15. #10590360C2semidirect
23. C4×#634C22semidirect
29. C3×C4×Dic6C22semidirect
40. #63844C22semidirect
41. Dic3×Dic6C22semidirect
45. D3×#204C4semidirect
46. C32×#97C22semidirect
48. #63645C22semidirect
49. #63643C22semidirect
51. C3×#818C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×#815C22semidirect
55. C3×#803C22semidirect
56. #63575C22semidirect
57. #63575C22semidirect
58. #63567C22semidirect
59. #63566C22semidirect
91. #4710D3direct (N × H)
92. D3×#97D3semidirect
114. D3×Dic6C2×C4semidirect
123. #3744C2×C4semidirect
134. C3×#204C2×C4semidirect
136. C3×D3×C8C2×C4semidirect
145. #3717C2×C4semidirect
146. #3716C2×C4semidirect
206. C4×Dic6C2×D3semidirect
214. C3×#97C2×D3semidirect
215. C3×#97C2×D3semidirect
229. #818C2×D3semidirect
235. #816C2×D3semidirect
236. #815C2×D3semidirect
237. #815C2×D3semidirect
242. #803C2×D3semidirect
259. #634C22×C4semidirect
274. C3×Dic6C22×C4semidirect
283. C32×C8C22×C4semidirect
285. C3×C3⋊C8C22×C4semidirect
418. #204C4×D3semidirect
420. D3×C8C4×D3semidirect
488. #97D32semidirect
578. Dic6C2×C4×D3semidirect
585. C3×C8C2×C4×D3semidirect
586. C3×C8C2×C4×D3semidirect
588. C3⋊C8C2×C4×D3semidirect
594. C3×D3#440semidirect
708. C32C2×#440semidirect
751. C8C4×D32semidirect
767. D3#4710direct (N × H)
793. C3C2×#4710semidirect
794. C3D3×#440semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2042
C4×D3×D122
C4×D3×Dic62
#105924092
C3×#47102
C3×D3×#972
D3×#8212
#105907952
#105907732
#105907662
#105907472
D3×#8182
D3×#8162
#105903622
#105903602
D3×#4403
C2×#47103