Finite Group Databasebeta

← #11872751

Subgroups — #11872751

Order 1152.

903 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic, complemented
2#10593986C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×#5014C211yesmaximal, characteristic, complemented
5#10591481C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic, complemented
8#10591409C211yesmaximal, characteristic, complemented
9#10590547C211yesmaximal, characteristic, complemented
10#10590545C211yesmaximal, characteristic, complemented
11#10590502C211yesmaximal, characteristic, complemented
12#10590425C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14C4×#3713C211yesmaximal, characteristic, complemented
15#10590265C211yesmaximal, characteristic, complemented
16#82542—31nomaximal
17#79874—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic, complemented
32C3×#872C2211yescharacteristic
33#63912—21no—
34#63911C2211yescharacteristic, complemented
35#63909C2211yescharacteristic
36#63908C2211yescharacteristic
37#63906—21no—
38#63869C2211yescharacteristic, complemented
39#63853—21no—
40#63850—21no—
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic
44#63636C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#809C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#803C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#518—31no—
62#5562—31no—
63#5545D311yescharacteristic, complemented
64#5535—31no—
65C3×#442—31no—
66#5217—31no—
67#5217—31no—
68#5156—31no—
69#5150—31no—
70#5015—31no—
71#5015—31no—
72#5014—31no—
73#5014D311yescharacteristic, complemented
74C4×#213—31no—
75C4×#213—31no—
76C4×#213—31no—
77C4×#213—31no—
78C4×#213—61no—
79#5009—31no—
80#5009—31no—
81#5003—31no—
82#5003—31no—
83#5000—31no—
84#4871—31no—
85#4866—31no—
86#4786—31no—
87#4779—31no—
88#4773—31no—
89#4763—31no—
90#4711—31no—
91#4709—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114#3753—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3714—22no—
140#3713—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×D8—31no—
145C3×C4×D4—21no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—61no—
151C3×C4×D4—61no—
152C3×C4×D4C2×D311yescharacteristic
153C3×C4×D4C2×D311yescharacteristic
154C3×#117—31no—
155C3×#117—31no—
156C2×C3×C22⋊C4—61no—
157C2×C3×C22⋊C4—61no—
158#940—31no—
159#938—31no—
160D4×Dic3C2×D311yescharacteristic
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—61no—
167C2×#213C2×D311yescharacteristic
168#930—31no—
169#930—31no—
170#930—61no—
171#929—61no—
172C4×#67—21no—
173C2×(C2×D3)⋊C4—21no—
174C2×D24—31no—
175#895—31no—
176#894—61no—
177#894—61no—
178#893C2×D311yescharacteristic
179#892C2×D311yescharacteristic
180#890—31no—
181#884—61no—
182#884—61no—
183#884—61no—
184#883—61no—
185#67⋊C4—21no—
186D3×C22⋊C4—21no—
187#874—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—61no—
191C4×D12C2×D311yescharacteristic
192C4×D12C2×D311yescharacteristic, complemented
193#872C2×D311yescharacteristic
194#870—31no—
195C3×#106—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#97—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#830—31no—
207#830—31no—
208#821—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#817—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—61no—
221#809C2×D311yescharacteristic, complemented
222#808—31no—
223#808C2×D311yescharacteristic, complemented
224#807—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—61no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803C2×D311yescharacteristic, complemented
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4×C3⋊D3—81no—
254C3×#67—24no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270#626—81no—
271#626—81no—
272#626—81no—
273#625—81no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—31no—
280#482—91no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—31no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—41no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C22×Dic3—21no—
318D3×D4—22no—
319D3×D4—22no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C3×D8—62no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—21no—
356C3×C42—31no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#217—21no—
361#217—61no—
362#213—22no—
363#213—62no—
364#213—62no—
365#213—64no—
366#213—62no—
367#213—62no—
368#213—62no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—121no—
379(C2×D3)⋊C4#6711yescharacteristic
380(C2×D3)⋊C4#6711yescharacteristic
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4#6711yescharacteristic
391Dic3⋊C4#6711yescharacteristic
392C4×Dic3—21no—
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402D24—62no—
403C22×C32—22no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3×D3—21no—
411C2×C3×D3—22no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—84no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C22×D4—31no—
432C2×D8—31no—
433C2×D8—91no—
434C2×D8—91no—
435C2×D8—91no—
436#127—91no—
437#125—91no—
438#123—181no—
439#123—181no—
440#121—91no—
441#121—91no—
442#121—181no—
443#121—181no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4—91no—
451C4×D4D3211yescharacteristic
452#117—31no—
453#117—31no—
454C2×C22⋊C4—61no—
455C2×C22⋊C4—61no—
456#107—91no—
457#107—91no—
458#106—31no—
459#106—91no—
460C4⋊C8—91no—
461C4⋊C8—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469#102—91no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472#97—31no—
473C4×C8—91no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3—41no—
478C23×C3—64no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—241no—
482C23×C3—241no—
483C22×D3—21no—
484C22×D3—24no—
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—81no—
489C22×D3—81no—
490C22×D3—121no—
491C22×D3C2×#6711yescharacteristic
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—22no—
495C3×D4—32no—
496C3×D4—41no—
497C3×D4—64no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4#23512yes—
502C3×D4#23512yes—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—81no—
517C2×C3×C4—81no—
518C2×C3×C4—82no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4—241no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—24no—
530#67—241no—
531#67—241no—
532#67—241no—
533#67—241no—
534#67—241no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—81no—
540C2×Dic3—121no—
541C2×Dic3C2×#6711yescharacteristic
542C2×Dic3C2×#6711yescharacteristic
543C2×Dic3C2×#6711yescharacteristic
544D12—21no—
545D12—21no—
546D12—21no—
547D12—62no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—121no—
553D12—241no—
554D12—241no—
555D12—241no—
556D12#23512yes—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—81no—
560C4×D3—81no—
561C4×D3—81no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—242no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—62no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32—42no—
576C2×C32#52511yescharacteristic
577C2×C32#57611yescharacteristic
578C2×C32#57611yescharacteristic
579C3⋊D3—81no—
580C3×D3—41no—
581C3×D3—42no—
582C3×D3—81no—
583C24—61no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—62no—
588C2×D4—62no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—181no—
592C2×D4—181no—
593C2×D4—181no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—21no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—181no—
602D8—62no—
603D8—182no—
604D8—182no—
605D8—182no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—91no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—61no—
631C42C2×D3211yescharacteristic
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—62no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C22×#6711yescharacteristic
654C2×D3—21no—
655C2×D3—22no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—84no—
664C2×D3—122no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—241no—
672C2×D3—241no—
673C3×C4—22no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—81no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×#23511yescharacteristic
690C3×C4C2×#23511yescharacteristic
691C3×C4C2×#23511yescharacteristic
692C3×C4D3×#4111yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701C32#312211yescharacteristic, complemented, Sylow
702C23—21no—
703C23—31no—
704C23—64no—
705C23—61no—
706C23—61no—
707C23—181no—
708C23—241no—
709C23—241no—
710D4—21no—
711D4—32no—
712D4—64no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—181no—
717D4—181no—
718D4—721no—
719D4—721no—
720D4—721no—
721D4—721no—
722D4#379812yes—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—81no—
732C2×C4—181no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4—721no—
738C2×C4D3×#6711yescharacteristic
739C2×C4D3×#6711yescharacteristic
740C2×C4C22×D3211yescharacteristic
741C8—61no—
742C8—61no—
743C8—181no—
744C8—181no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—42no—
749C2×C3—42no—
750C2×C3—82no—
751C2×C3—121no—
752C2×C3—122no—
753C2×C3—241no—
754C2×C3#554711yescharacteristic
755C2×C3#577411yescharacteristic
756C2×C3#577411yescharacteristic
757C2×C3#579111yescharacteristic
758C2×C3#583511yescharacteristic
759C2×C3#583511yescharacteristic
760D3—41no—
761D3—42no—
762D3—81no—
763D3—242no—
764D3—241no—
765D3—241no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—62no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—244no—
779C22—361no—
780C22—361no—
781C22—361no—
782C22C2×D3×#6711yescharacteristic
783C4—21no—
784C4—21no—
785C4—41no—
786C4—61no—
787C4—61no—
788C4—61no—
789C4—121no—
790C4—121no—
791C4—361no—
792C4C2×#379811yescharacteristic
793C4D3×#23511yescharacteristic
794C3—21no—
795C3#7987411yescharacteristic, complemented
796C3#8254211yescharacteristic, complemented
797C2—42no—
798C2—121no—
799C2—122no—
800C2—241no—
801C2—721no—
802C2#1059500211yescharacteristic
803C2#1059509711yescharacteristic
804C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5545C2semidirect
2. #10593986C2semidirect
3. C4×#3753C2semidirect
4. C3×#5014C2semidirect
5. #10591481C2semidirect
6. #10591448C2semidirect
7. #10591447C2semidirect
8. #10591409C2semidirect
9. #10590547C2semidirect
10. #10590545C2semidirect
11. #10590502C2semidirect
12. #10590425C2semidirect
13. #10590346C2semidirect
14. C4×#3713C2semidirect
15. #10590265C2semidirect
21. C4×C4⋊(C3⋊D3)C22semidirect
31. C3×C4×D12C22semidirect
34. #63911C22semidirect
38. #63869C22semidirect
44. #63636C22semidirect
45. #63634C22semidirect
46. C4×C3⋊(C3⋊C8)C22semidirect
48. C3×#809C22semidirect
49. C3×#808C22semidirect
50. C3×#803C22semidirect
51. #63576C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
58. #63562C22semidirect
63. #5545D3semidirect
73. #5014D3semidirect
192. C4×D12C2×D3semidirect
221. #809C2×D3semidirect
223. #808C2×D3semidirect
231. #803C2×D3semidirect
701. C32#3122semidirect
795. C3#79874semidirect
796. C3#82542semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105939862
C4×#37532
C3×#50142
#105914812
#105914482
#105914472
#105914092
#105905472
#105905452
#105905022
#105904252
#105903462
C4×#37132
#105902652
#825423
#798743