Finite Group Databasebeta

← D3×#4795 #11865656

Subgroups — D3×#4795 #11865656

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#944C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic
3C2×D3×Dic12C211yesmaximal, characteristic
4D3×#887C211yesmaximal, characteristic
5#10592494C211yesmaximal, characteristic, complemented
6C3×D3×#103C211yesmaximal, characteristic
7C3×#4795C211yesmaximal, characteristic, complemented
8#10591580C211yesmaximal, characteristic, complemented
9#10591575C211yesmaximal, characteristic, complemented
10#10590808C211yesmaximal, characteristic, complemented
11#10590798C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C8C211yesmaximal, characteristic
13D3×#810C211yesmaximal, characteristic
14#10590566C211yesmaximal, characteristic, complemented
15#10590561C211yesmaximal, characteristic, complemented
16D3×#462—31nomaximal
17C2×#4795—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64153C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C2×#3746C2211yescharacteristic
24#64096C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#887C2211yescharacteristic
31D3×#216—24no—
32D3×Dic3⋊C4—21no—
33D3×Dic3⋊C4—21no—
34D3×Dic3⋊C4—21no—
35C4×D3×Dic3—21no—
36C4×D3×Dic3C2211yescharacteristic
37#63873C2211yescharacteristic
38#63866C2211yescharacteristic
39#63844C2211yescharacteristic
40#63843C2211yescharacteristic
41#63839—21no—
42#63839—21no—
43#63838—21no—
44#63837—21no—
45C2×#3719C2211yescharacteristic
46C2×#3719C2211yescharacteristic
47C2×#3719C2211yescharacteristic
48C2×#3718C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×Dic12—24no—
51C32×#103C2211yescharacteristic
52#63641C2211yescharacteristic
53#63637C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59#63572C2211yescharacteristic
60Dic3⋊(C3⋊C8)C2211yescharacteristic
61#63567C2211yescharacteristic
62#63565C2211yescharacteristic
63C2×#944—31no—
64C22×#216—31no—
65C2×D3×Q16—31no—
66C2×D3×Q16—31no—
67C22×Dic12—31no—
68D3×C4⋊Q8—31no—
69C4×D3×Q8—31no—
70C2×#887—31no—
71C3×#462—31no—
72C2×C3×#103—31no—
73#5182—31no—
74#5182—31no—
75C2×Dic3⋊C8—31no—
76#5090—31no—
77#5031—31no—
78C2×#810—31no—
79#4849—31no—
80D3×C4⋊C8—31no—
81D3×#103—31no—
82D3×#103D311yescharacteristic
83#4795—31no—
84#4795—31no—
85#4795—31no—
86#4795—31no—
87#4795—31no—
88#4795—31no—
89#4795—31no—
90#4795—31no—
91#4795—31no—
92#4795—61no—
93#4795D311yescharacteristic, direct product factor
94C2×C32×Q8C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C3×D3×Q8—22no—
98C3×D3×Q8—22no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×#627—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3D411yescharacteristic
111C2×D3×Dic3D411yescharacteristic
112D3×Dic6—22no—
113D3×Dic6—22no—
114D3×Dic6—22no—
115D3×Dic6D414yes—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3756—22no—
119#3750—21no—
120#3750—21no—
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3746—22no—
126C3×#216—22no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
137C3×D3×C8—22no—
138#3724—21no—
139#3724—21no—
140#3724—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic32—21no—
145Dic32—21no—
146Dic32D411yescharacteristic
147Dic32D411yescharacteristic
148#3719—22no—
149#3719—22no—
150#3719—22no—
151#3718—22no—
152D3×C3⋊C8—22no—
153C2×#462—91noSylow
154C22×C3×Q8—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C22×Dic6—31no—
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×Q16—31no—
162C22×C3×C8—31no—
163C3×C4⋊Q8—31no—
164C3×C4×Q8—31no—
165C2×C3×C4⋊C4—31no—
166Q8×Dic3—31no—
167#944—31no—
168#944—31no—
169#944—31no—
170#944—31no—
171#944—31no—
172#944—61no—
173#944—61no—
174#944—61no—
175#944C2×D311yescharacteristic
176C2×#216—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—61no—
184C2×#216—64no—
185C2×#216C2×D311yescharacteristic
186C2×Dic3⋊C4—61no—
187C2×Dic3⋊C4—61no—
188C2×Dic3⋊C4—61no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191C22×C3⋊C8—31no—
192D3×Q16—64no—
193D3×Q16—64no—
194C2×Dic12—31no—
195C2×Dic12—31no—
196C2×Dic12—31no—
197C2×Dic12—31no—
198C2×Dic12—31no—
199C2×Dic12—61no—
200C2×Dic12—64no—
201C2×Dic12C2×D311yescharacteristic
202C2×D3×C8—31no—
203C2×D3×C8C2×D311yescharacteristic
204D3×C4⋊C4—61no—
205D3×C4⋊C4—61no—
206D3×C4⋊C4—61no—
207D3×C4⋊C4C2×D311yescharacteristic
208#888—61no—
209#888—61no—
210#887—31no—
211#887—31no—
212#887—31no—
213#887—31no—
214#887—61no—
215#887—61no—
216#887—61no—
217#887—61no—
218#887C2×D311yescharacteristic
219C42×D3—31no—
220C42×D3—61no—
221#869—31no—
222C4×Dic6—31no—
223C4×Dic6—61no—
224C3×C4⋊C8—31no—
225C3×#103—21no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103C2×D311yescharacteristic
231C3×#103C2×D311yescharacteristic
232#835—31no—
233#835C2×D311yescharacteristic
234#816—31no—
235#816C2×D311yescharacteristic
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—61no—
242Dic3⋊C8C2×D311yescharacteristic
243#810—31no—
244#810—31no—
245#810—31no—
246#810—31no—
247#810—61no—
248#810C2×D311yescharacteristic
249#810C2×D311yescharacteristic
250C4⋊(C3⋊C8)—31no—
251C22×C3×D3C2×D411yescharacteristic
252C32×Q8—21no—
253C32×Q8—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261#634—21no—
262#634—21no—
263#634—21no—
264#634C2×D412yes—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×C4×D3—42no—
273C3×C4×D3—42no—
274C3×C4×D3C2×D412yes—
275C3×C4×D3#4112yes—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—42no—
282C3×Dic6C2×D412yes—
283#627—24no—
284#627—42no—
285D3×Dic3—24no—
286D3×Dic3—22no—
287D3×Dic3—42no—
288D3×Dic3Q1614yescomplemented
289C32×C8—21no—
290C3⋊(C3⋊C8)—21no—
291C3×C3⋊C8—21no—
292C3×C3⋊C8—21no—
293C22×Q16—91no—
294C22×Q16—91no—
295C2×C4⋊Q8—91no—
296C2×C4×Q8—91no—
297#462—31no—
298#462—91no—
299#462—91no—
300#462—91no—
301#462—91no—
302#462—91no—
303#462—91no—
304#462—91no—
305C2×C4⋊C8—91no—
306C2×#103—31no—
307C2×#103—91no—
308C2×C3×Q8—21no—
309C2×C3×Q8—31no—
310C2×C3×Q8—31no—
311C2×C3×Q8—31no—
312C2×C3×Q8—61no—
313C2×C3×Q8—62no—
314C2×C3×Q8—62no—
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×Q8C22×D311yescharacteristic
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324D3×Q8—22no—
325D3×Q8—22no—
326D3×Q8—34no—
327D3×Q8—62no—
328D3×Q8—62no—
329D3×Q8—62no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—21no—
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—34no—
341C2×Dic6—31no—
342C2×Dic6—31no—
343C2×Dic6—61no—
344C2×Dic6—61no—
345C2×Dic6—62no—
346C2×Dic6—62no—
347C2×Dic6—62no—
348C2×Dic6—61no—
349C2×Dic6—61no—
350C2×Dic6—61no—
351C2×Dic6—61no—
352C2×Dic6C22×D311yescharacteristic
353C2×Dic6C22×D311yescharacteristic
354C2×Dic6C22×D311yescharacteristic
355C3×Q16—62no—
356C3×Q16—62no—
357C2×C3×C8—21no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—62no—
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C3×C4⋊C4—21no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C42—31no—
372C3×C42—61no—
373#216—22no—
374#216—62no—
375#216—62no—
376#216—62no—
377#216—62no—
378#216—62no—
379#216—62no—
380#216—62no—
381#216—122no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—121no—
406Dic3⋊C4—121no—
407Dic3⋊C4—121no—
408C4×Dic3—21no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—121no—
423C4×Dic3C22×D311yescharacteristic
424C2×C3⋊C8—31no—
425C2×C3⋊C8—31no—
426C2×C3⋊C8—61no—
427C2×C3⋊C8—62no—
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430Dic12—22no—
431Dic12—62no—
432Dic12—62no—
433Dic12—62no—
434Dic12—62no—
435Dic12—62no—
436Dic12—122no—
437D3×C8—22no—
438D3×C8—62no—
439C22×C32C22×D411yescharacteristic
440C2×C3×D3#12112yes—
441C2×C3×D3C2×Q1612yes—
442C2×C3×D3#13712yes—
443C32×C4—41no—
444C32×C4—41no—
445C32×C4C22×D411yescharacteristic
446C32×C4C2×#4111yescharacteristic
447C3⋊Dic3—22no—
448C3⋊Dic3—21no—
449C3⋊Dic3—41no—
450C3⋊Dic3C2×Q1612yescomplemented
451C3×Dic3—22no—
452C3×Dic3—21no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3#12112yes—
457C3×Dic3C2×Q1612yescomplemented
458C22×Q8—31no—
459C22×Q8—91no—
460C22×Q8—91no—
461C2×Q16—31no—
462C2×Q16—31no—
463C2×Q16—91no—
464C2×Q16—91no—
465C2×Q16—91no—
466C2×Q16—91no—
467C2×Q16—91no—
468C2×Q16—91no—
469C2×Q16—184no—
470C2×Q16—184no—
471C22×C8—31no—
472C22×C8—91no—
473C4⋊Q8—31no—
474C4⋊Q8—91no—
475C4⋊Q8—91no—
476C4⋊Q8—91no—
477C4⋊Q8—181no—
478C4⋊Q8—181no—
479C4×Q8—31no—
480C4×Q8—91no—
481C4×Q8—91no—
482C4×Q8—91no—
483C4×Q8—181no—
484C4×Q8—181no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—181no—
487C2×C4⋊C4—181no—
488C2×C4⋊C4—181no—
489C2×C42—91no—
490C2×C42—181no—
491C4⋊C8—31no—
492C4⋊C8—91no—
493C4⋊C8—91no—
494C4⋊C8—91no—
495#103—31no—
496#103—31no—
497#103—31no—
498#103—31no—
499#103—91no—
500#103—91no—
501#103—91no—
502#103D3211yescharacteristic
503C23×C3—31no—
504C22×D3D3×D411yescharacteristic
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—32no—
510C3×Q8—41no—
511C3×Q8—41no—
512C3×Q8—61no—
513C3×Q8—61no—
514C3×Q8—61no—
515C3×Q8—61no—
516C3×Q8—61no—
517C3×Q8—122no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—34no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—64no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—122no—
558C2×Dic3D3×D411yescharacteristic
559C2×Dic3D3×D411yescharacteristic
560C2×Dic3D3×D411yescharacteristic
561C4×D3—34no—
562C4×D3—42no—
563C4×D3—42no—
564C4×D3—64no—
565C4×D3—62no—
566C4×D3—122no—
567C4×D3#23512yes—
568C4×D3D3×D412yes—
569Dic6—21no—
570Dic6—21no—
571Dic6—21no—
572Dic6—21no—
573Dic6—21no—
574Dic6—32no—
575Dic6—32no—
576Dic6—42no—
577Dic6—62no—
578Dic6—64no—
579Dic6—61no—
580Dic6—61no—
581Dic6—64no—
582Dic6—61no—
583Dic6—61no—
584Dic6—61no—
585Dic6—61no—
586Dic6—121no—
587Dic6—121no—
588Dic6—121no—
589Dic6—122no—
590Dic6—122no—
591Dic6D3×D412yes—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—41no—
595C3×C8—61no—
596C3×C8—61no—
597C3⋊C8—21no—
598C3⋊C8—21no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—121no—
602C2×C32C2×#12111yescharacteristic
603C2×C32C22×Q1611yescharacteristic
604C2×C32C2×#13711yescharacteristic
605C3×D3#46214yescomplemented
606C2×Q8—31no—
607C2×Q8—31no—
608C2×Q8—31no—
609C2×Q8—61no—
610C2×Q8—62no—
611C2×Q8—62no—
612C2×Q8—94no—
613C2×Q8—91no—
614C2×Q8—91no—
615C2×Q8—181no—
616C2×Q8—181no—
617C2×Q8—182no—
618C2×Q8—182no—
619C2×Q8—182no—
620C2×Q8C2×D3211yescharacteristic
621C22×C4—31no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—91no—
625C22×C4—91no—
626C22×C4—181no—
627C22×C4—181no—
628Q16—62no—
629Q16—62no—
630Q16—182no—
631Q16—182no—
632Q16—182no—
633Q16—182no—
634Q16—182no—
635Q16—182no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—62no—
639C2×C8—91no—
640C2×C8—182no—
641C2×C8C2×D3211yescharacteristic
642C4⋊C4—31no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4C2×D3211yescharacteristic
657C42—31no—
658C42—61no—
659C42—91no—
660C42—91no—
661C42—91no—
662C42—181no—
663C42—181no—
664C42—181no—
665C22×C3—21no—
666C22×C3—32no—
667C22×C3—32no—
668C22×C3—32no—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C2×D3#88412yes—
672C2×D3#91512yes—
673C2×D3D3×Q1612yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—32no—
677C3×C4—32no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—62no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×#23511yescharacteristic
690C3×C4C2×D3×D411yescharacteristic
691C3×C4C2×D3×D411yescharacteristic
692C3×C4D3×#4111yescharacteristic
693Dic3—21no—
694Dic3—22no—
695Dic3—32no—
696Dic3—32no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—62no—
701Dic3—62no—
702Dic3—61no—
703Dic3—61no—
704Dic3—62no—
705Dic3—122no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—241no—
710Dic3#88412yes—
711Dic3D3×Q1612yescomplemented
712C32C2×#46211yescharacteristic, complemented, Sylow
713C23—31no—
714Q8—21no—
715Q8—21no—
716Q8—32no—
717Q8—61no—
718Q8—61no—
719Q8—61no—
720Q8—61no—
721Q8—61no—
722Q8—92no—
723Q8—122no—
724Q8—184no—
725Q8—181no—
726Q8—181no—
727Q8—181no—
728Q8—362no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—31no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—94no—
741C2×C4—91no—
742C2×C4—91no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—182no—
746C2×C4—184no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—362no—
750C2×C4C22×D3211yescharacteristic
751C8—21no—
752C8—61no—
753C8—61no—
754C8—181no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—34no—
759C2×C3C2×#88411yescharacteristic
760C2×C3D3×#12111yescharacteristic
761C2×C3C2×#91511yescharacteristic
762C2×C3C2×D3×Q1611yescharacteristic
763C2×C3C2×D3×Q1611yescharacteristic
764C2×C3D3×#13711yescharacteristic
765D3#479514yesdirect product factor
766C22—32no—
767C22—32no—
768C22—32no—
769C22D32×D411yescharacteristic
770C4—32no—
771C4—32no—
772C4—41no—
773C4—41no—
774C4—61no—
775C4—62no—
776C4—92no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4—182no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4D32×D411yescharacteristic
785C3—21no—
786C3C2×#479511yescharacteristic, complemented
787C3D3×#46211yescharacteristic, complemented
788C2—34no—
789C2D3×#88411yescharacteristic
790C2D3×#91511yescharacteristic
791C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#103D32
hypocenterC32C2×#462
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
5. #10592494C2semidirect
7. C3×#4795C2semidirect
8. #10591580C2semidirect
9. #10591575C2semidirect
10. #10590808C2semidirect
11. #10590798C2semidirect
14. #10590566C2semidirect
15. #10590561C2semidirect
93. #4795D3direct (N × H)
288. D3×Dic3Q16semidirect
450. C3⋊Dic3C2×Q16semidirect
457. C3×Dic3C2×Q16semidirect
605. C3×D3#462semidirect
711. Dic3D3×Q16semidirect
712. C32C2×#462semidirect
765. D3#4795direct (N × H)
786. C3C2×#4795semidirect
787. C3D3×#462semidirect

Maximal subgroups

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

subgroupindex
D3×#9442
C2×D3×#2162
C2×D3×Dic122
D3×#8872
#105924942
C3×D3×#1032
C3×#47952
#105915802
#105915752
#105908082
#105907982
D3×Dic3⋊C82
D3×#8102
#105905662
#105905612
D3×#4623
C2×#47953