Finite Group Databasebeta

← D3×#4890 #11868263

Subgroups — D3×#4890 #11868263

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#893C211yesmaximal, characteristic
2D3×#888C211yesmaximal, characteristic, complemented
3#10592589C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×D3×#107C211yesmaximal, characteristic, complemented
6D3×#821C211yesmaximal, characteristic
7#10590778C211yesmaximal, characteristic, complemented
8#10590764C211yesmaximal, characteristic, complemented
9D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic
11D3×#807C211yesmaximal, characteristic, complemented
12#10590555C211yesmaximal, characteristic, complemented
13#10590471C211yesmaximal, characteristic, complemented
14#10590464C211yesmaximal, characteristic, complemented
15#10590430C211yesmaximal, characteristic, complemented
16D3×#474—31nomaximal
17C2×#4890—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C2×D3×Dic6—21no—
21#64102C2211yescharacteristic
22#64097C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#888C2211yescharacteristic, complemented
28D3×(C2×D3)⋊C4—21no—
29#63919C2211yescharacteristic, complemented
30#63918C2211yescharacteristic, complemented
31#63904—21no—
32#63898C2211yescharacteristic
33#63894C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63881—21no—
36D3×Dic3⋊C4—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63840—21no—
39#63839—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#107C2211yescharacteristic, complemented
42#63648C2211yescharacteristic
43#63641C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63634C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic
47C3×#818C2211yescharacteristic, complemented
48C3×Dic3⋊C8C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63572C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61D3×C4⋊Q8—31no—
62C4×D3×D4—31no—
63C2×#893—31no—
64C2×#888—31no—
65C3×#474—31no—
66C2×C3×#107—31no—
67C2×#821—31no—
68C2×Dic3⋊C8—31no—
69#5087—31no—
70#5007—31no—
71C2×#809—31no—
72C2×#807—31no—
73#4890—31no—
74#4890—31no—
75#4890—31no—
76#4890—31no—
77#4890—31no—
78#4890—31no—
79#4890—31no—
80#4890—31no—
81#4890—31no—
82#4890—61no—
83#4890D311yescharacteristic, direct product factor
84D3×#107—31no—
85D3×#107D311yescharacteristic, complemented
86#4846—31no—
87D3×C4⋊C8—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4759—31no—
91#4759—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×#627—21no—
103C2×#627—21no—
104C2×#626—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3D411yescharacteristic
109C2×D3×Dic3D411yescharacteristic
110D3×D12—22no—
111D3×D12Q814yescomplemented
112C4×D32—44no—
113D3×Dic6—44no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—22no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32D411yescharacteristic
139Dic32D411yescharacteristic
140D3×C3⋊C8—22no—
141C2×#474—91noSylow
142C2×D3×Q8—61no—
143C2×D3×D4—31no—
144C22×D12—31no—
145C22×C4×D3—61no—
146C22×C4×D3—61no—
147C22×Dic6—61no—
148C22×C3×C8—31no—
149C3×C4⋊Q8—31no—
150C3×C4×D4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153#944—61no—
154D4×Dic3—31no—
155C4×#67—61no—
156C2×(C2×D3)⋊C4—61no—
157C2×C4⋊Dic3—31no—
158C2×Dic3⋊C4—61no—
159C2×C4×Dic3—31no—
160C22×C3⋊C8—31no—
161C2×D3×C8—31no—
162C2×D3×C8C2×D311yescharacteristic
163#893—31no—
164#893—31no—
165#893—31no—
166#893—31no—
167#893—61no—
168#893—61no—
169#893—61no—
170#893C2×D311yescharacteristic
171D3×C4⋊C4—31no—
172D3×C4⋊C4—61no—
173D3×C4⋊C4C2×D311yescharacteristic
174D3×C4⋊C4C2×D311yescharacteristic
175#888—31no—
176#888—31no—
177#888—31no—
178#888—31no—
179#888—31no—
180#888—61no—
181#888—61no—
182#888—61no—
183#888—61no—
184#888C2×D311yescharacteristic, complemented
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187C4×D12—31no—
188C42×D3—31no—
189#869—31no—
190C3×#107—21no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#107—31no—
194C3×#107—31no—
195C3×#107C2×D311yescharacteristic, complemented
196C3×#107C2×D311yescharacteristic, complemented
197C3×C4⋊C8—31no—
198C3×#102—31no—
199C3×#102—31no—
200#832—31no—
201#832—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—61no—
208#821C2×D311yescharacteristic
209#818—31no—
210#818C2×D311yescharacteristic, complemented
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—61no—
217Dic3⋊C8C2×D311yescharacteristic, complemented
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—61no—
224#809C2×D311yescharacteristic
225#807—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
231#807C2×D311yescharacteristic, complemented
232#807C2×D311yescharacteristic, complemented
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C2×D32—24no—
239C2×D32—42no—
240C2×D32—42no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)C2×Q812yescomplemented
249C4×C3⋊D3—42no—
250#634—42no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12C2×Q812yescomplemented
259C3×C4×D3—42no—
260C3×C4×D3—42no—
261C3×C4×D3—42no—
262C3×C4×D3C2×Q812yes—
263C3×C4×D3#4112yes—
264C3×Dic6—42no—
265#627—42no—
266#627—42no—
267#626—24no—
268#624—42no—
269D3×Dic3—22no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272D3×Dic3D814yes—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C2×C4⋊Q8—91no—
278C2×C4×D4—91no—
279#474—31no—
280#474—91no—
281#474—91no—
282#474—91no—
283#474—91no—
284#474—91no—
285#474—91no—
286#474—91no—
287C2×#107—31no—
288C2×#107—91no—
289C2×C4⋊C8—91no—
290C2×#102—91no—
291C2×#102—91no—
292C23×D3—61no—
293C23×D3—61no—
294C2×C3×Q8—61no—
295C2×C3×D4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305D3×Q8—124no—
306D3×D4—34no—
307D3×D4—62no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—34no—
311C2×D12—61no—
312C2×D12—62no—
313C2×D12—61no—
314C2×D12C22×D311yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—121no—
327C2×C4×D3—124no—
328C2×C4×D3—124no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—21no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—121no—
338C2×Dic6—124no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—62no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—61no—
358C3×C42—31no—
359#217—61no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—62no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399D3×C8—22no—
400D3×C8—62no—
401C22×C32C22×D411yescharacteristic
402C2×C3⋊D3—22no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3×D3—22no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3C22⋊Q812yes—
409C2×C3×D3C2×D812yes—
410C2×C3×D3#13712yes—
411D32—48no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4C22×Q811yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—21no—
417C3⋊Dic3—41no—
418C3⋊Dic3C2×D812yes—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3C22⋊Q812yes—
424C3×Dic3C2×D812yes—
425C22×Q8—181no—
426C22×D4—91no—
427C23×C4—181no—
428C22×C8—31no—
429C22×C8—91no—
430C4⋊Q8—31no—
431C4⋊Q8—91no—
432C4⋊Q8—91no—
433C4⋊Q8—91no—
434C4⋊Q8—181no—
435C4⋊Q8—181no—
436C4×D4—31no—
437C4×D4—91no—
438C4×D4—91no—
439C4×D4—91no—
440C4×D4—181no—
441C4×D4—181no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—31no—
444C2×C4⋊C4—91no—
445C2×C4⋊C4—181no—
446C2×C22⋊C4—181no—
447C2×C42—91no—
448#107—31no—
449#107—31no—
450#107—31no—
451#107—31no—
452#107—91no—
453#107—91no—
454#107—91no—
455#107D3211yescharacteristic, complemented
456C4⋊C8—31no—
457C4⋊C8—91no—
458C4⋊C8—91no—
459C4⋊C8—91no—
460#102—31no—
461#102—31no—
462#102—91no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468C23×C3—31no—
469C23×C3—61no—
470C22×D3—21no—
471C22×D3—64no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—64no—
475C22×D3—121no—
476C22×D3—122no—
477C22×D3—122no—
478C22×D3—122no—
479C22×D3—122no—
480C22×D3D3×D411yescharacteristic
481C3×Q8—122no—
482C3×D4—32no—
483C3×D4—61no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—31no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—122no—
500C2×C3×C4—122no—
501C2×C3×C4—122no—
502C2×C3×C4C23×D311yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504#67—64no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—34no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—62no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3—122no—
520C2×Dic3—122no—
521C2×Dic3D3×D411yescharacteristic
522C2×Dic3D3×D411yescharacteristic
523C2×Dic3D3×D411yescharacteristic
524D12—21no—
525D12—32no—
526D12—32no—
527D12—62no—
528D12—64no—
529D12—61no—
530D12—61no—
531D12—121no—
532D12D3×Q812yescomplemented
533C4×D3—34no—
534C4×D3—42no—
535C4×D3—42no—
536C4×D3—42no—
537C4×D3—62no—
538C4×D3—122no—
539C4×D3—122no—
540C4×D3—122no—
541C4×D3—122no—
542C4×D3—122no—
543C4×D3—122no—
544C4×D3—242no—
545C4×D3#23512yes—
546C4×D3D3×Q812yes—
547Dic6—42no—
548Dic6—122no—
549Dic6—122no—
550Dic6—122no—
551Dic6—122no—
552Dic6—122no—
553Dic6—122no—
554Dic6—242no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C2×C32C2×C22⋊Q811yescharacteristic
566C2×C32C22×D811yescharacteristic
567C2×C32C2×#13711yescharacteristic
568C3⋊D3—42no—
569C3×D3—42no—
570C3×D3#47414yescomplemented
571C24—181no—
572C2×Q8—61no—
573C2×Q8—181no—
574C2×Q8—181no—
575C2×Q8—181no—
576C2×Q8—364no—
577C2×D4—31no—
578C2×D4—94no—
579C2×D4—91no—
580C2×D4—182no—
581C2×D4—181no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—91no—
587C22×C4—91no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—364no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—62no—
596C2×C8—91no—
597C2×C8—182no—
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—31no—
617C42—91no—
618C42—91no—
619C42—91no—
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—32no—
623C22×C3—32no—
624C22×C3—62no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—22no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—122no—
635C2×D3—128no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—128no—
641C2×D3—241no—
642C2×D3—241no—
643C2×D3#89612yes—
644C2×D3D3×D812yes—
645C2×D3#91812yes—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—32no—
649C3×C4—32no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—81no—
656C3×C4—81no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4C2×#23511yescharacteristic
661C3×C4C2×D3×Q811yescharacteristic
662C3×C4C2×D3×Q811yescharacteristic
663C3×C4D3×#4111yescharacteristic
664Dic3—21no—
665Dic3—32no—
666Dic3—32no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—62no—
671Dic3—61no—
672Dic3—61no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—241no—
677Dic3#89612yes—
678Dic3D3×D812yes—
679C32C2×#47411yescharacteristic, complemented, Sylow
680C23—31no—
681C23—61no—
682C23—184no—
683C23—181no—
684C23—362no—
685C23—362no—
686Q8—122no—
687Q8—362no—
688Q8—362no—
689Q8—362no—
690D4—32no—
691D4—61no—
692D4—92no—
693D4—184no—
694D4—181no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—94no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—182no—
712C2×C4—181no—
713C2×C4—362no—
714C2×C4—362no—
715C2×C4—362no—
716C2×C4—362no—
717C2×C4C22×D3211yescharacteristic
718C8—21no—
719C8—61no—
720C8—61no—
721C8—181no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—34no—
726C2×C3—122no—
727C2×C3C2×#89611yescharacteristic
728C2×C3D3×C22⋊Q811yescharacteristic
729C2×C3C2×D3×D811yescharacteristic
730C2×C3C2×D3×D811yescharacteristic
731C2×C3C2×#91811yescharacteristic
732C2×C3D3×#13711yescharacteristic
733D3—42no—
734D3—122no—
735D3—122no—
736D3—242no—
737D3#489014yesdirect product factor
738C22—32no—
739C22—32no—
740C22—32no—
741C22—62no—
742C22—121no—
743C22—121no—
744C22—182no—
745C22—368no—
746C22—361no—
747C22—361no—
748C22D32×D411yescharacteristic
749C4—32no—
750C4—32no—
751C4—41no—
752C4—41no—
753C4—61no—
754C4—92no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—181no—
759C4—361no—
760C4D3×#23511yescharacteristic
761C4D32×Q811yescharacteristic
762C3—21no—
763C3C2×#489011yescharacteristic, complemented
764C3D3×#47411yescharacteristic, complemented
765C2—34no—
766C2—122no—
767C2—362no—
768C2D3×#89611yescharacteristic
769C2D32×D811yescharacteristic
770C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#107D32
hypocenterC32C2×#474
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. D3×#888C2semidirect
3. #10592589C2semidirect
4. C3×#4890C2semidirect
5. C3×D3×#107C2semidirect
7. #10590778C2semidirect
8. #10590764C2semidirect
9. D3×Dic3⋊C8C2semidirect
11. D3×#807C2semidirect
12. #10590555C2semidirect
13. #10590471C2semidirect
14. #10590464C2semidirect
15. #10590430C2semidirect
22. #64097C22semidirect
27. C3×#888C22semidirect
29. #63919C22semidirect
30. #63918C22semidirect
41. C32×#107C22semidirect
43. #63641C22semidirect
45. #63634C22semidirect
47. C3×#818C22semidirect
48. C3×Dic3⋊C8C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63572C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
83. #4890D3direct (N × H)
85. D3×#107D3semidirect
111. D3×D12Q8semidirect
184. #888C2×D3semidirect
195. C3×#107C2×D3semidirect
196. C3×#107C2×D3semidirect
210. #818C2×D3semidirect
217. Dic3⋊C8C2×D3semidirect
231. #807C2×D3semidirect
232. #807C2×D3semidirect
233. #807C2×D3semidirect
248. C4⋊(C3⋊D3)C2×Q8semidirect
258. C3×D12C2×Q8semidirect
455. #107D32semidirect
532. D12D3×Q8semidirect
570. C3×D3#474semidirect
679. C32C2×#474semidirect
737. D3#4890direct (N × H)
763. C3C2×#4890semidirect
764. C3D3×#474semidirect

Maximal subgroups

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

subgroupindex
D3×#8932
D3×#8882
#105925892
C3×#48902
C3×D3×#1072
D3×#8212
#105907782
#105907642
D3×Dic3⋊C82
D3×#8092
D3×#8072
#105905552
#105904712
#105904642
#105904302
D3×#4743
C2×#48903