Finite Group Databasebeta

← #11872758

Subgroups — #11872758

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5719C211yesmaximal, characteristic, complemented
2#10593994C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5#10591515C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10591423C211yesmaximal, characteristic, complemented
10#10591422C211yesmaximal, characteristic, complemented
11#10591404C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10590308C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83435—31nomaximal
17#80317—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C32×#127C2211yescharacteristic, complemented
20C2×#3753C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#939—21no—
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×#935—21no—
28C3×#935—21no—
29C3×D4×Dic3C2211yescharacteristic, complemented
30C3×D4×Dic3C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×#872C2211yescharacteristic
35C3×#870C2211yescharacteristic, complemented
36#63921—21no—
37D3×(C2×D3)⋊C4—21no—
38#63904—21no—
39#63894C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41#63881—21no—
42#63841C2211yescharacteristic
43#63659C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#540—31no—
62#5719D311yescharacteristic, complemented
63#5545—31no—
64#5521—31no—
65C3×#459—31no—
66#5156—31no—
67#5156—31no—
68#5152—31no—
69Dic3×D8—31no—
70#5072—31no—
71#5072—31no—
72#5072—61no—
73#5072D311yescharacteristic, complemented
74#5066—31no—
75#5066—31no—
76#5036—31no—
77#5036—31no—
78#5035—31no—
79#5035—31no—
80#5014—31no—
81#5014—31no—
82C4×#213—31no—
83C4×#213—31no—
84#5009—31no—
85#5000—31no—
86#4847—31no—
87#4840—31no—
88#4785—31no—
89#4784—31no—
90#4779—31no—
91#4756—31no—
92C22×D32—21no—
93C2×C32×D4—21no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C32×C42C2311yescharacteristic
112#3753—22no—
113#3753—22no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#213—22no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#127—21no—
147C3×#127C2×D311yescharacteristic, complemented
148C3×#127C2×D311yescharacteristic, complemented
149C3×#125—31no—
150C3×#123—61no—
151C3×#123—61no—
152C3×#121—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#121—61no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160#939—21no—
161#939—21no—
162#938C2×D311yescharacteristic
163#938C2×D311yescharacteristic
164#935—21no—
165#935—21no—
166D4×Dic3—31no—
167D4×Dic3C2×D311yescharacteristic, complemented
168D4×Dic3C2×D311yescharacteristic, complemented
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—61no—
174C2×#213—61no—
175C2×#213C2×D311yescharacteristic
176C2×#213C2×D311yescharacteristic
177C4×#67—61no—
178C2×(C2×D3)⋊C4—61no—
179#926—31no—
180#893—31no—
181#893—61no—
182#893—61no—
183#892—31no—
184#67⋊C4—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194#872C2×D311yescharacteristic
195#870C2×D311yescharacteristic, complemented
196C3×C4⋊C8—31no—
197C3×#102—31no—
198C3×#102—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#832C2×D311yescharacteristic, complemented
208#832C2×D311yescharacteristic, complemented
209#830—31no—
210#830—31no—
211#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215#818—31no—
216#817—31no—
217#815—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32—21no—
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—81no—
248C32×D4—81no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—81no—
256C3×#67—81no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—81no—
271#626—24no—
272#624—81no—
273D3×Dic3—81no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—31no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—31no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—41no—
303C2×C3×D4—41no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—61no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320D3×D4—62no—
321D3×D4—62no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—62no—
326C2×D12—61no—
327C2×D12—62no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—121no—
336C2×C4×D3C22×D311yescharacteristic
337C3×D8—62no—
338C3×D8—62no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
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×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359#217—21no—
360#217—21no—
361#217—21no—
362#217—21no—
363#217—61no—
364#217—61no—
365#213—22no—
366#213—22no—
367#213—62no—
368#213—62no—
369#213—62no—
370#213—62no—
371#213—122no—
372#213—122no—
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—61no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4#6711yescharacteristic
382(C2×D3)⋊C4#6711yescharacteristic
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4#6711yescharacteristic
392Dic3⋊C4#6711yescharacteristic
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—22no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—22no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420D32—84no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C22×D4—91no—
433C2×D8—31no—
434C2×D8—31no—
435C2×D8—91no—
436C2×D8—91no—
437#127D3211yescharacteristic, complemented
438#125—31no—
439#123—61no—
440#123—61no—
441#121—31no—
442#121—31no—
443#121—61no—
444#121—61no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—31no—
454#117—91no—
455C2×C22⋊C4—181no—
456C2×C22⋊C4—181no—
457#107—91no—
458#107—91no—
459#106—91no—
460#106—91no—
461C4⋊C8—31no—
462C4⋊C8—91no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471C22⋊C8—91no—
472C22⋊C8—91no—
473#97—91no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—64no—
485C22×D3—64no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3C2×#6711yescharacteristic
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—32no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—41no—
507C3×D4—61no—
508C3×D4—81no—
509C3×D4—81no—
510C3×D4—81no—
511C3×D4—81no—
512C3×D4—82no—
513C3×D4—82no—
514C3×D4—241no—
515C3×D4—241no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—241no—
528C2×C3×C4—241no—
529C2×C3×C4—241no—
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—64no—
537#67—81no—
538#67—81no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—81no—
545C2×Dic3—81no—
546C2×Dic3—121no—
547C2×Dic3—241no—
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551D12—21no—
552D12—32no—
553D12—32no—
554D12—62no—
555D12—64no—
556D12—61no—
557D12—61no—
558D12—121no—
559D12#23712yes—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—81no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—242no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C3⋊C8—121no—
579C2×C32—81no—
580C2×C32—81no—
581C2×C32#52511yescharacteristic
582C2×C32#57611yescharacteristic
583C2×C32#57611yescharacteristic
584C3⋊D3—42no—
585C3×D3—41no—
586C3×D3—42no—
587C24—181no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—182no—
596C2×D4—182no—
597C2×D4C2×D3211yescharacteristic
598C2×D4C2×D3211yescharacteristic
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606D8—62no—
607D8—62no—
608D8—182no—
609D8—182no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—91no—
613C2×C8—91no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C22⋊C4—31no—
623C22⋊C4—31no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—31no—
634C42—181no—
635C42C2×D3211yescharacteristic
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—62no—
652C22×C3—61no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C22×#6711yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—244no—
679C2×D3—244no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4C2×#23711yescharacteristic
695C3×C4D3×#4111yescharacteristic
696C3×C4D3×#4111yescharacteristic
697C3×C4D3×#4111yescharacteristic
698Dic3—21no—
699Dic3—21no—
700Dic3—21no—
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#312211yescharacteristic, complemented, Sylow
708C23—21no—
709C23—21no—
710C23—31no—
711C23—61no—
712C23—184no—
713C23—181no—
714C23—721no—
715C23—721no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—32no—
721D4—61no—
722D4—81no—
723D4—81no—
724D4—92no—
725D4—184no—
726D4—181no—
727D4—241no—
728D4—241no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4D3×#6711yescharacteristic
745C2×C4D3×#6711yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—61no—
748C8—61no—
749C8—181no—
750C8—181no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—81no—
755C2×C3—81no—
756C2×C3—81no—
757C2×C3—81no—
758C2×C3—121no—
759C2×C3—122no—
760C2×C3—161no—
761C2×C3—161no—
762C2×C3#560611yescharacteristic
763C2×C3#575711yescharacteristic
764C2×C3#577411yescharacteristic
765C2×C3#582811yescharacteristic
766C2×C3#583511yescharacteristic
767C2×C3#583511yescharacteristic
768D3—42no—
769D3—41no—
770D3—122no—
771D3—122no—
772D3—242no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—62no—
783C22—121no—
784C22—121no—
785C22—182no—
786C22—361no—
787C22—361no—
788C22—724no—
789C22C2×D3×#6711yescharacteristic
790C4—21no—
791C4—21no—
792C4—61no—
793C4—61no—
794C4—61no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4—361no—
799C4D3×#23711yescharacteristic
800C4#6431211yescharacteristic
801C3—21no—
802C3#8031711yescharacteristic, complemented
803C3#8343511yescharacteristic, complemented
804C2—81no—
805C2—81no—
806C2—121no—
807C2—122no—
808C2—362no—
809C2#1059509611yescharacteristic
810C2#1059509711yescharacteristic
811C2#1059530111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5719C2semidirect
2. #10593994C2semidirect
3. #10592771C2semidirect
4. C3×#5072C2semidirect
5. #10591515C2semidirect
6. #10591515C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10591423C2semidirect
10. #10591422C2semidirect
11. #10591404C2semidirect
12. #10591400C2semidirect
13. #10590308C2semidirect
14. #10590270C2semidirect
15. #10590253C2semidirect
19. C32×#127C22semidirect
29. C3×D4×Dic3C22semidirect
30. C3×D4×Dic3C22semidirect
35. C3×#870C22semidirect
43. #63659C22semidirect
44. #63659C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
48. C3×C4⋊(C3⋊C8)C22semidirect
49. #63576C22semidirect
50. #63575C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5719D3semidirect
73. #5072D3semidirect
147. C3×#127C2×D3semidirect
148. C3×#127C2×D3semidirect
167. D4×Dic3C2×D3semidirect
168. D4×Dic3C2×D3semidirect
195. #870C2×D3semidirect
207. #832C2×D3semidirect
208. #832C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
437. #127D32semidirect
707. C32#3122semidirect
802. C3#80317semidirect
803. C3#83435semidirect

Maximal subgroups

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

subgroupindex
C3×#57192
#105939942
#105927712
C3×#50722
#105915152
#105914302
Dic3×#2132
#105914232
#105914222
#105914042
#105914002
#105903082
#105902702
#105902532
#834353
#803173