Finite Group Databasebeta

← D3×#5186 #11863655

Subgroups — D3×#5186 #11863655

Order 1152.

1554 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×Q8C211yesmaximal, characteristic
2C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
3D3×#946C211yesmaximal, characteristic
4C2×D3×#216C211yesmaximal, characteristic, complemented
5#10592885C211yesmaximal, characteristic, complemented
6C3×#5186C211yesmaximal, characteristic, complemented
7#10591654C211yesmaximal, characteristic, complemented
8#10591653C211yesmaximal, characteristic, complemented
9#10591603C211yesmaximal, characteristic, complemented
10#10591594C211yesmaximal, characteristic, complemented
11D3×#835C211yesmaximal, characteristic, complemented
12#10590950C211yesmaximal, characteristic, complemented
13#10590949C211yesmaximal, characteristic, complemented
14D3×(C2×D3)⋊C8C211yesmaximal, characteristic
15D3×#816C211yesmaximal, characteristic, complemented
16C2×#5186—31nomaximal
17D3×#451—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic
22D32×Q8—24no—
23D32×Q8—24no—
24C2×C4×D32—21no—
25C2×C4×D32C2211yescharacteristic
26C2×#3797—21no—
27C2×#3797C2211yescharacteristic
28C2×D3×Dic6—21no—
29C2×D3×Dic6—21no—
30C2×D3×Dic6C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic
34C2×#3756C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#216C2211yescharacteristic, complemented
38C2×C3×#216C2211yescharacteristic, complemented
39C3×D3×Q16—24no—
40C2×C3×Dic12C2211yescharacteristic, complemented
41C2×C3×D3×C8C2211yescharacteristic
42D3×#216—24no—
43D3×(C2×D3)⋊C4—21no—
44D3×C4⋊Dic3C2211yescharacteristic
45#63888—21no—
46#63887—21no—
47D3×Dic3⋊C4—21no—
48#63871C2211yescharacteristic
49#63856C2211yescharacteristic
50C2×#3719C2211yescharacteristic, complemented
51C2×#3718C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63647C2211yescharacteristic
55#63643C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×#816C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#63557C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C22×D3×Q8—31no—
66C22×D3×Q8—31no—
67C22×C3×Q16—31no—
68C2×#946—31no—
69C22×#216—31no—
70C2×D3×Q16—31no—
71C2×D3×Q16D311yescharacteristic, complemented
72D3×C22⋊Q8—31no—
73C3×#451—31no—
74#5228—31no—
75C2×#835—31no—
76#5186—31no—
77#5186—31no—
78#5186—31no—
79#5186—31no—
80#5186—31no—
81#5186—31no—
82#5186—31no—
83#5186—31no—
84#5186—31no—
85#5186—61no—
86#5186D311yescharacteristic, direct product factor
87C2×(C2×D3)⋊C8—31no—
88C2×#816—31no—
89#5050—31no—
90#4809—31no—
91#4809—31no—
92D3×#103—31no—
93D3×#103—31no—
94#4739—31no—
95D3×C22⋊C8—31no—
96C22×D32D411yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99Q8×C3⋊D3—22no—
100Q8×C3⋊D3—22no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634—21no—
104C2×#634C2311yescharacteristic
105C3×D3×Q8—22no—
106C3×D3×Q8—22no—
107C3×D3×Q8—22no—
108C3×D3×Q8—22no—
109C3×D3×Q8—22no—
110C3×D3×Q8D414yes—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×#627—21no—
123C2×#627—21no—
124C2×#627—21no—
125C2×#624—21no—
126C2×#624D411yescharacteristic
127C2×D3×Dic3—21no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3D411yescharacteristic
131C2×D3×Dic3D411yescharacteristic
132C4×D32—28no—
133C4×D32—22no—
134C4×D32—22no—
135#3797—28no—
136#3797—22no—
137#3797—22no—
138D3×Dic6—28no—
139D3×Dic6—28no—
140D3×Dic6—22no—
141D3×Dic6—22no—
142D3×Dic6—22no—
143D3×Dic6D414yes—
144C32×Q16—22no—
145C2×C32×C8C2311yescharacteristic
146#3756—22no—
147#3752—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C3×#216—22no—
152C3×#216—22no—
153C3×#216—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×Dic12—22no—
160C3×D3×C8—22no—
161#3724—21no—
162Dic3⋊Dic3—21no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166#3719—22no—
167#3718—22no—
168D3×C3⋊C8—22no—
169C2×#451—91noSylow
170C22×C3×Q8—31no—
171C22×C3×Q8—31no—
172C22×C3×Q8—31no—
173C2×D3×Q8—31no—
174C2×D3×Q8—31no—
175C2×D3×Q8—31no—
176C2×D3×Q8—31no—
177C2×D3×Q8—31no—
178C2×D3×Q8—31no—
179C2×D3×Q8—61no—
180C2×D3×Q8—61no—
181C2×D3×Q8—61no—
182C2×D3×Q8—64no—
183C2×D3×Q8—61no—
184C2×D3×Q8—61no—
185C2×D3×Q8—64no—
186C2×D3×Q8—64no—
187C2×D3×Q8—64no—
188C2×D3×Q8C2×D311yescharacteristic
189C2×D3×Q8C2×D311yescharacteristic
190C2×D3×Q8C2×D311yescharacteristic
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—61no—
194C22×C4×D3—61no—
195C22×Dic6—31no—
196C22×Dic6—31no—
197C22×Dic6—61no—
198C22×Dic6—61no—
199C2×C3×Q16—21no—
200C2×C3×Q16—31no—
201C2×C3×Q16—31no—
202C2×C3×Q16—31no—
203C2×C3×Q16—31no—
204C2×C3×Q16—64no—
205C2×C3×Q16C2×D311yescharacteristic, complemented
206C2×C3×Q16C2×D311yescharacteristic, complemented
207C22×C3×C8—31no—
208C3×C22⋊Q8—31no—
209#946—31no—
210#946—31no—
211#946—31no—
212#946—31no—
213#946—61no—
214#946—61no—
215#946—61no—
216#946C2×D311yescharacteristic
217C2×#216—31no—
218C2×#216—31no—
219C2×#216—31no—
220C2×#216—31no—
221C2×#216—31no—
222C2×#216—61no—
223C2×#216—64no—
224C2×#216C2×D311yescharacteristic, complemented
225C2×#216C2×D311yescharacteristic, complemented
226C2×#216C2×D311yescharacteristic, complemented
227C2×(C2×D3)⋊C4—61no—
228C2×C4⋊Dic3—31no—
229#924—31no—
230C2×Dic3⋊C4—61no—
231C22×C3⋊C8—31no—
232D3×Q16—24no—
233D3×Q16—64no—
234C2×Dic12—31no—
235C2×Dic12C2×D311yescharacteristic, complemented
236C2×D3×C8—31no—
237C2×D3×C8C2×D311yescharacteristic
238#897—31no—
239#896—61no—
240D3×C4⋊C4—31no—
241D3×C4⋊C4—61no—
242D3×C22⋊C4—61no—
243#878—61no—
244C3×#103—31no—
245C3×#103—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—31no—
252#835—61no—
253#835C2×D311yescharacteristic, complemented
254#830—31no—
255(C2×D3)⋊C8—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—61no—
261(C2×D3)⋊C8C2×D311yescharacteristic
262#816—31no—
263#816—31no—
264#816—31no—
265#816—31no—
266#816—31no—
267#816—61no—
268#816C2×D311yescharacteristic, complemented
269#810—31no—
270#810—31no—
271C22×C3⋊D3C2×D411yescharacteristic
272C22×C3×D3C2×D411yescharacteristic
273C22×C3×D3C2×D411yescharacteristic
274C2×D32—22no—
275C2×D32—22no—
276C2×D32Q1614yescomplemented
277C32×Q8—21no—
278C32×Q8—21no—
279C32×Q8—21no—
280C32×Q8C2×D412yes—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4C2411yescharacteristic
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3C2×D411yescharacteristic
287C4×C3⋊D3—24no—
288C4×C3⋊D3—21no—
289C4×C3⋊D3—21no—
290#634—24no—
291#634—21no—
292#634C2×D412yes—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3C2×D411yescharacteristic
298C2×C3×Dic3C2×D411yescharacteristic
299C3×C4×D3—24no—
300C3×C4×D3—24no—
301C3×C4×D3—21no—
302C3×C4×D3—21no—
303C3×C4×D3—42no—
304C3×C4×D3C2×D412yes—
305C3×C4×D3C2×D412yes—
306C3×Dic6—24no—
307C3×Dic6—21no—
308C3×Dic6—21no—
309C3×Dic6—24no—
310C3×Dic6—21no—
311C3×Dic6—21no—
312C3×Dic6—42no—
313C3×Dic6C2×D412yes—
314C3×Dic6C2×D412yes—
315#627—24no—
316#627—24no—
317#627—24no—
318#624—24no—
319#624—22no—
320D3×Dic3—24no—
321D3×Dic3—22no—
322D3×Dic3—24no—
323D3×Dic3—22no—
324D3×Dic3—42no—
325C32×C8—21no—
326C3⋊(C3⋊C8)—21no—
327C3×C3⋊C8—21no—
328C3×C3⋊C8—21no—
329C23×Q8—91no—
330C22×Q16—31no—
331C22×Q16—91no—
332C2×C22⋊Q8—91no—
333#451—31no—
334#451—91no—
335#451—91no—
336#451—91no—
337#451—91no—
338#451—91no—
339#451—91no—
340#451—91no—
341C2×#103—91no—
342C2×#103—91no—
343C2×C22⋊C8—91no—
344C23×D3—31no—
345C23×D3—31no—
346C2×C3×Q8—21no—
347C2×C3×Q8—21no—
348C2×C3×Q8—34no—
349C2×C3×Q8—31no—
350C2×C3×Q8—31no—
351C2×C3×Q8—31no—
352C2×C3×Q8—61no—
353C2×C3×Q8—61no—
354C2×C3×Q8—61no—
355C2×C3×Q8—62no—
356C2×C3×Q8—62no—
357C2×C3×Q8—62no—
358C2×C3×Q8—62no—
359C2×C3×Q8—62no—
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C22×C3×C4—61no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374D3×Q8—22no—
375D3×Q8—22no—
376D3×Q8—22no—
377D3×Q8—22no—
378D3×Q8—22no—
379D3×Q8—34no—
380D3×Q8—62no—
381D3×Q8—62no—
382D3×Q8—68no—
383D3×Q8—68no—
384D3×Q8—62no—
385D3×Q8—62no—
386D3×Q8—62no—
387D3×Q8—62no—
388D3×Q8—68no—
389D3×Q8—68no—
390D3×Q8—62no—
391D3×Q8—62no—
392D3×Q8—62no—
393D3×Q8—62no—
394D3×Q8—62no—
395D3×Q8—122no—
396D3×Q8—122no—
397D3×Q8#6714yes—
398C2×C4×D3—21no—
399C2×C4×D3—21no—
400C2×C4×D3—21no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—31no—
405C2×C4×D3—31no—
406C2×C4×D3—31no—
407C2×C4×D3—61no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—68no—
411C2×C4×D3—68no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3—61no—
416C2×C4×D3—61no—
417C2×C4×D3—61no—
418C2×C4×D3—62no—
419C2×C4×D3—62no—
420C2×C4×D3—61no—
421C2×C4×D3—121no—
422C2×C4×D3C22×D311yescharacteristic
423C2×C4×D3C22×D311yescharacteristic
424C2×Dic6—21no—
425C2×Dic6—21no—
426C2×Dic6—21no—
427C2×Dic6—31no—
428C2×Dic6—31no—
429C2×Dic6—34no—
430C2×Dic6—61no—
431C2×Dic6—62no—
432C2×Dic6—62no—
433C2×Dic6—68no—
434C2×Dic6—68no—
435C2×Dic6—61no—
436C2×Dic6—61no—
437C2×Dic6—61no—
438C2×Dic6—61no—
439C2×Dic6—61no—
440C2×Dic6—61no—
441C2×Dic6—61no—
442C2×Dic6—61no—
443C2×Dic6—62no—
444C2×Dic6—121no—
445C2×Dic6C22×D311yescharacteristic
446C2×Dic6C22×D311yescharacteristic
447C2×Dic6C22×D311yescharacteristic
448C3×Q16—22no—
449C3×Q16—22no—
450C3×Q16—42no—
451C3×Q16—62no—
452C3×Q16—62no—
453C3×Q16—62no—
454C3×Q16—62no—
455C2×C3×C8—21no—
456C2×C3×C8—31no—
457C2×C3×C8—31no—
458C2×C3×C8—62no—
459C2×C3×C8C22×D311yescharacteristic
460C2×C3×C8C22×D311yescharacteristic
461C3×C4⋊C4—31no—
462C3×C4⋊C4—61no—
463C3×C22⋊C4—61no—
464#217—61no—
465#216—22no—
466#216—22no—
467#216—22no—
468#216—62no—
469#216—62no—
470#216—62no—
471#216—62no—
472#216—62no—
473#216—122no—
474(C2×D3)⋊C4—21no—
475(C2×D3)⋊C4—61no—
476(C2×D3)⋊C4—61no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—121no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—61no—
484C4⋊Dic3—61no—
485C4⋊Dic3—61no—
486C4⋊Dic3C22×D311yescharacteristic
487Dic3⋊C4—21no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—121no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—61no—
498C2×C3⋊C8—62no—
499C2×C3⋊C8C22×D311yescharacteristic
500C2×C3⋊C8C22×D311yescharacteristic
501Dic12—22no—
502Dic12—62no—
503D3×C8—22no—
504D3×C8—62no—
505C22×C32C22×D411yescharacteristic
506C2×C3⋊D3—21no—
507C2×C3⋊D3—21no—
508C2×C3⋊D3C2×Q1612yescomplemented
509C2×C3×D3—21no—
510C2×C3×D3—21no—
511C2×C3×D3#12012yes—
512C2×C3×D3C2×Q1612yes—
513C2×C3×D3C2×Q1612yescomplemented
514C2×C3×D3#13712yes—
515D32—28no—
516C32×C4—22no—
517C32×C4—41no—
518C32×C4C22×D411yescharacteristic
519C32×C4C22×D411yescharacteristic
520C3⋊Dic3—21no—
521C3⋊Dic3—22no—
522C3⋊Dic3—41no—
523C3×Dic3—21no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—41no—
527C3×Dic3—41no—
528C3×Dic3#12012yes—
529C22×Q8—31no—
530C22×Q8—31no—
531C22×Q8—31no—
532C22×Q8—91no—
533C22×Q8—91no—
534C22×Q8—91no—
535C22×Q8—91no—
536C22×Q8—181no—
537C22×Q8—181no—
538C22×Q8—181no—
539C22×Q8—184no—
540C22×Q8—184no—
541C23×C4—91no—
542C23×C4—181no—
543C2×Q16—31no—
544C2×Q16—31no—
545C2×Q16—31no—
546C2×Q16—31no—
547C2×Q16—64no—
548C2×Q16—91no—
549C2×Q16—91no—
550C2×Q16—91no—
551C2×Q16—184no—
552C2×Q16D3211yescharacteristic, complemented
553C22×C8—31no—
554C22×C8—91no—
555C22⋊Q8—31no—
556C22⋊Q8—91no—
557C22⋊Q8—91no—
558C22⋊Q8—91no—
559C22⋊Q8—181no—
560C22⋊Q8—181no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—181no—
563C2×C22⋊C4—181no—
564#103—31no—
565#103—31no—
566#103—91no—
567#103—91no—
568#103—91no—
569#103—91no—
570#103—91no—
571#103—91no—
572C22⋊C8—31no—
573C22⋊C8—91no—
574C22⋊C8—91no—
575C22⋊C8—91no—
576C23×C3—31no—
577C23×C3—31no—
578C22×D3—31no—
579C22×D3—31no—
580C22×D3—34no—
581C22×D3—34no—
582C22×D3—61no—
583C22×D3—62no—
584C22×D3—62no—
585C22×D3—62no—
586C22×D3—62no—
587C22×D3D3×D411yescharacteristic
588C22×D3D3×D411yescharacteristic
589C3×Q8—21no—
590C3×Q8—21no—
591C3×Q8—21no—
592C3×Q8—21no—
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—22no—
596C3×Q8—32no—
597C3×Q8—32no—
598C3×Q8—41no—
599C3×Q8—41no—
600C3×Q8—41no—
601C3×Q8—64no—
602C3×Q8—64no—
603C3×Q8—61no—
604C3×Q8—61no—
605C3×Q8—61no—
606C3×Q8—61no—
607C3×Q8—122no—
608C3×Q8D3×D412yes—
609C3×Q8C2×#6712yes—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—31no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—31no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—64no—
622C2×C3×C4—64no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—122no—
630C2×C3×C4C23×D311yescharacteristic
631C2×C3×C4C23×D311yescharacteristic
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—31no—
637C2×Dic3—31no—
638C2×Dic3—61no—
639C2×Dic3—64no—
640C2×Dic3—62no—
641C2×Dic3—64no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—62no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—122no—
650C2×Dic3D3×D411yescharacteristic
651C2×Dic3D3×D411yescharacteristic
652C4×D3—24no—
653C4×D3—24no—
654C4×D3—21no—
655C4×D3—21no—
656C4×D3—42no—
657C4×D3—62no—
658C4×D3—64no—
659C4×D3—64no—
660C4×D3—64no—
661C4×D3—64no—
662C4×D3—62no—
663C4×D3—64no—
664C4×D3—62no—
665C4×D3—64no—
666C4×D3—61no—
667C4×D3—61no—
668C4×D3—61no—
669C4×D3—61no—
670C4×D3—62no—
671C4×D3—121no—
672C4×D3—121no—
673C4×D3—124no—
674C4×D3—122no—
675C4×D3D3×D412yes—
676C4×D3C2×#6712yes—
677Dic6—24no—
678Dic6—21no—
679Dic6—21no—
680Dic6—24no—
681Dic6—21no—
682Dic6—21no—
683Dic6—32no—
684Dic6—32no—
685Dic6—42no—
686Dic6—62no—
687Dic6—64no—
688Dic6—64no—
689Dic6—64no—
690Dic6—64no—
691Dic6—64no—
692Dic6—64no—
693Dic6—64no—
694Dic6—61no—
695Dic6—61no—
696Dic6—64no—
697Dic6—121no—
698Dic6—124no—
699Dic6D3×D412yes—
700Dic6C2×#6712yes—
701C3×C8—21no—
702C3×C8—21no—
703C3×C8—41no—
704C3×C8—61no—
705C3×C8—61no—
706C3⋊C8—21no—
707C3⋊C8—21no—
708C3⋊C8—61no—
709C3⋊C8—61no—
710C3⋊C8—121no—
711C2×C32C2×#12011yescharacteristic
712C2×C32C22×Q1611yescharacteristic
713C2×C32C2×#13711yescharacteristic
714C3⋊D3—22no—
715C3×D3—22no—
716C3×D3#45114yescomplemented
717C24—91no—
718C2×Q8—34no—
719C2×Q8—31no—
720C2×Q8—31no—
721C2×Q8—31no—
722C2×Q8—61no—
723C2×Q8—61no—
724C2×Q8—61no—
725C2×Q8—62no—
726C2×Q8—62no—
727C2×Q8—62no—
728C2×Q8—62no—
729C2×Q8—62no—
730C2×Q8—94no—
731C2×Q8—91no—
732C2×Q8—181no—
733C2×Q8—181no—
734C2×Q8—181no—
735C2×Q8—182no—
736C2×Q8—181no—
737C2×Q8—182no—
738C2×Q8—182no—
739C2×Q8—188no—
740C2×Q8—188no—
741C2×Q8—182no—
742C2×Q8—182no—
743C2×Q8—182no—
744C2×Q8—188no—
745C2×Q8—182no—
746C2×Q8C2×D3211yescharacteristic
747C2×Q8C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—91no—
754C22×C4—91no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—181no—
758C22×C4—182no—
759C22×C4—182no—
760C22×C4—181no—
761C22×C4—188no—
762C22×C4—181no—
763C22×C4—181no—
764C22×C4—181no—
765Q16—22no—
766Q16—62no—
767Q16—62no—
768Q16—62no—
769Q16—62no—
770Q16—182no—
771Q16—182no—
772Q16—182no—
773C2×C8—31no—
774C2×C8—31no—
775C2×C8—62no—
776C2×C8—91no—
777C2×C8—182no—
778C2×C8C2×D3211yescharacteristic
779C4⋊C4—31no—
780C4⋊C4—61no—
781C4⋊C4—91no—
782C4⋊C4—181no—
783C4⋊C4—181no—
784C4⋊C4—181no—
785C4⋊C4—181no—
786C22⋊C4—61no—
787C22⋊C4—181no—
788C22⋊C4—181no—
789C22⋊C4—181no—
790C22×C3—21no—
791C22×C3—32no—
792C22×C3—32no—
793C22×C3—32no—
794C22×C3—32no—
795C22×C3—61no—
796C22×C3—61no—
797C22×C3C2×D3×D411yescharacteristic
798C22×C3C2×D3×D411yescharacteristic
799C2×D3—21no—
800C2×D3—21no—
801C2×D3—32no—
802C2×D3—32no—
803C2×D3—62no—
804C2×D3—68no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—68no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3D3×Q1612yes—
813C2×D3D3×Q1612yescomplemented
814C2×D3#91812yes—
815C2×D3#93712yes—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—32no—
821C3×C4—42no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—61no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—81no—
828C3×C4—121no—
829C3×C4—121no—
830C3×C4C2×D3×D411yescharacteristic
831C3×C4C2×D3×D411yescharacteristic
832C3×C4C2×D3×D411yescharacteristic
833C3×C4C22×#6711yescharacteristic
834Dic3—22no—
835Dic3—21no—
836Dic3—22no—
837Dic3—41no—
838Dic3—41no—
839Dic3—62no—
840Dic3—61no—
841Dic3—62no—
842Dic3—61no—
843Dic3—122no—
844Dic3—121no—
845Dic3—121no—
846Dic3—121no—
847Dic3—241no—
848Dic3#93712yes—
849C32C2×#45111yescharacteristic, complemented, Sylow
850C23—31no—
851C23—31no—
852C23—94no—
853C23—91no—
854C23—182no—
855C23—182no—
856Q8—21no—
857Q8—21no—
858Q8—21no—
859Q8—32no—
860Q8—32no—
861Q8—64no—
862Q8—64no—
863Q8—61no—
864Q8—61no—
865Q8—61no—
866Q8—61no—
867Q8—92no—
868Q8—122no—
869Q8—184no—
870Q8—184no—
871Q8—184no—
872Q8—184no—
873Q8—181no—
874Q8D3×#6712yes—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—31no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—31no—
881C2×C4—64no—
882C2×C4—64no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—91no—
890C2×C4—122no—
891C2×C4—184no—
892C2×C4—182no—
893C2×C4—182no—
894C2×C4—184no—
895C2×C4—182no—
896C2×C4—184no—
897C2×C4—184no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—362no—
903C2×C4C22×D3211yescharacteristic
904C8—21no—
905C8—61no—
906C8—61no—
907C8—181no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—34no—
912C2×C3—62no—
913C2×C3D3×#12011yescharacteristic
914C2×C3C2×D3×Q1611yescharacteristic
915C2×C3C2×D3×Q1611yescharacteristic
916C2×C3C2×#91811yescharacteristic
917C2×C3D3×#13711yescharacteristic
918C2×C3C2×#93711yescharacteristic
919D3—22no—
920D3—62no—
921D3—62no—
922D3—122no—
923D3#518614yesdirect product factor
924C22—32no—
925C22—32no—
926C22—32no—
927C22—32no—
928C22—61no—
929C22—61no—
930C22—92no—
931C22—188no—
932C22—181no—
933C22—181no—
934C22D32×D411yescharacteristic
935C4—22no—
936C4—32no—
937C4—41no—
938C4—61no—
939C4—62no—
940C4—62no—
941C4—121no—
942C4—121no—
943C4—181no—
944C4—182no—
945C4—361no—
946C4D32×D411yescharacteristic
947C4C2×D3×#6711yescharacteristic
948C3—21no—
949C3D3×#45111yescharacteristic, complemented
950C3C2×#518611yescharacteristic, complemented
951C2—34no—
952C2—62no—
953C2—182no—
954C2D32×Q1611yescharacteristic
955C2D3×#91811yescharacteristic
956C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenterC2×Q16D32
hypocenterC32C2×#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Q16C2semidirect
4. C2×D3×#216C2semidirect
5. #10592885C2semidirect
6. C3×#5186C2semidirect
7. #10591654C2semidirect
8. #10591653C2semidirect
9. #10591603C2semidirect
10. #10591594C2semidirect
11. D3×#835C2semidirect
12. #10590950C2semidirect
13. #10590949C2semidirect
15. D3×#816C2semidirect
32. C2×C32×Q16C22semidirect
34. C2×#3756C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#216C22semidirect
38. C2×C3×#216C22semidirect
40. C2×C3×Dic12C22semidirect
50. C2×#3719C22semidirect
51. C2×#3718C22semidirect
53. #63662C22semidirect
55. #63643C22semidirect
56. C3×#835C22semidirect
58. C3×#816C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63566C22semidirect
62. #63565C22semidirect
71. C2×D3×Q16D3semidirect
86. #5186D3direct (N × H)
205. C2×C3×Q16C2×D3semidirect
206. C2×C3×Q16C2×D3semidirect
224. C2×#216C2×D3semidirect
225. C2×#216C2×D3semidirect
226. C2×#216C2×D3semidirect
235. C2×Dic12C2×D3semidirect
253. #835C2×D3semidirect
268. #816C2×D3semidirect
276. C2×D32Q16semidirect
508. C2×C3⋊D3C2×Q16semidirect
513. C2×C3×D3C2×Q16semidirect
552. C2×Q16D32semidirect
716. C3×D3#451semidirect
813. C2×D3D3×Q16semidirect
849. C32C2×#451semidirect
923. D3#5186direct (N × H)
949. C3D3×#451semidirect
950. C3C2×#5186semidirect

Maximal subgroups

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

subgroupindex
C2×D32×Q82
C2×C3×D3×Q162
D3×#9462
C2×D3×#2162
#105928852
C3×#51862
#105916542
#105916532
#105916032
#105915942
D3×#8352
#105909502
#105909492
D3×(C2×D3)⋊C82
D3×#8162
C2×#51863
D3×#4513