Finite Group Databasebeta

← #11872731

Subgroups — #11872731

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic, complemented
2#10594985C211yesmaximal, characteristic, complemented
3#10592916C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic, complemented
5#10591481C211yesmaximal, characteristic, complemented
6#10591481C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10591411C211yesmaximal, characteristic, complemented
10#10591409C211yesmaximal, characteristic, complemented
11#10591404C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10591136C211yesmaximal, characteristic, complemented
14#10591090C211yesmaximal, characteristic, complemented
15#10591056C211yesmaximal, characteristic, complemented
16#82542—31nomaximal
17#79993—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3753C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×C3×#217—21no—
23C2×C3×#217—21no—
24C3×D4×Dic3—21no—
25C3×D4×Dic3—21no—
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#930C2211yescharacteristic
33C3×#926C2211yescharacteristic
34C3×#926C2211yescharacteristic
35#63971—21no—
36#63958—21no—
37#63911C2211yescharacteristic, complemented
38#63894C2211yescharacteristic, complemented
39Dic3×D12C2211yescharacteristic, complemented
40#63890—21no—
41#63869C2211yescharacteristic, complemented
42#63854—21no—
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63657C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63576C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5798D311yescharacteristic, complemented
63#5619—31no—
64#5535—31no—
65C3×#447—31no—
66#5217—31no—
67#5217—31no—
68#5217—61no—
69#5217D311yescharacteristic, complemented
70#5152—31no—
71#5150—31no—
72#5150—31no—
73Dic3×D8—31no—
74#5035—31no—
75#5015—31no—
76#5015—31no—
77#5014—31no—
78#5014—31no—
79C4×#213—31no—
80C4×#213—31no—
81#5009—31no—
82#5009—31no—
83#5003—31no—
84#5003—31no—
85#5000—31no—
86#4785—31no—
87#4766—31no—
88#4763—31no—
89#4756—31no—
90#4737—31no—
91#4720—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C2×C3×D12C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3753—22no—
112#3753—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×#217D411yescharacteristic
124C3×#213—22no—
125C3×#213—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141#3122—91noSylow
142C22×C3×D4—21no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C2×D311yescharacteristic
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C3×#121—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—61no—
153C3×C4×D4—61no—
154C3×#117—31no—
155C3×#117—31no—
156C2×C3×C22⋊C4—61no—
157C2×C3×C22⋊C4—61no—
158C2×#217—21no—
159C2×#217—21no—
160#940—31no—
161#939—61no—
162#938—61no—
163D4×Dic3—21no—
164D4×Dic3—21no—
165D4×Dic3—31no—
166D4×Dic3C2×D311yescharacteristic
167D4×Dic3C2×D311yescharacteristic
168D4×Dic3C2×D311yescharacteristic
169D4×Dic3C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—61no—
175C2×#213—61no—
176C2×#213C2×D311yescharacteristic
177C2×#213C2×D311yescharacteristic
178#930—31no—
179#930—31no—
180#930—61no—
181#930C2×D311yescharacteristic
182#926C2×D311yescharacteristic
183#926C2×D311yescharacteristic
184#894—61no—
185#894—61no—
186#893—31no—
187#890—31no—
188#886—61no—
189#884—61no—
190#884—61no—
191#883—61no—
192#874—31no—
193C4×D12—31no—
194C4×D12—31no—
195#870—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C22⋊C8—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
208#832C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211#830—61no—
212#830C2×D311yescharacteristic
213#821—31no—
214#821—31no—
215#818—31no—
216#817—31no—
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—24no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—81no—
239C23×C32—81no—
240C23×C32C2×D411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3×D3—21no—
243C32×D4—24no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252#638—81no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270#626—81no—
271#626—81no—
272#624—81no—
273D3×Dic3—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—31no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C24×C3—21no—
294C24×C3—21no—
295C24×C3—41no—
296C2×C3×D4—22no—
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4—22no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—41no—
306C2×C3×D4—42no—
307C2×C3×D4—42no—
308C2×C3×D4—61no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—21no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—121no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—61no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C3×D8—62no—
341C3×D8—62no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360#217—21no—
361#217—21no—
362#217—21no—
363#217—21no—
364#217—21no—
365#217—61no—
366#217#6711yescharacteristic
367#217#6711yescharacteristic
368#213—22no—
369#213—22no—
370#213—62no—
371#213—62no—
372#213—62no—
373#213—62no—
374#213—122no—
375#213—122no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—121no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3#6711yescharacteristic
388C4⋊Dic3#6711yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—21no—
396C4×Dic3C22×D311yescharacteristic
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—21no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—84no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C32×C4—21no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3⋊Dic3—41no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C22×D4D3211yescharacteristic
435C2×D8—31no—
436C2×D8—31no—
437C2×D8—91no—
438C2×D8—91no—
439#127—91no—
440#125—91no—
441#123—181no—
442#123—181no—
443#121—31no—
444#121—91no—
445#121—181no—
446#121—181no—
447C4×D4—31no—
448C4×D4—31no—
449C4×D4—31no—
450C4×D4—31no—
451C4×D4—61no—
452C4×D4—61no—
453C4×D4—91no—
454C4×D4—91no—
455#117—31no—
456#117—31no—
457C2×C22⋊C4—61no—
458C2×C22⋊C4—61no—
459#107—91no—
460#107—91no—
461#106—91no—
462#106—91no—
463C4⋊C8—91no—
464C4⋊C8—91no—
465#102—31no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472#102—91no—
473C22⋊C8—31no—
474C22⋊C8—91no—
475#97—91no—
476C4×C8—91no—
477C23×C3—24no—
478C23×C3—24no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—44no—
487C23×C3—61no—
488C23×C3—81no—
489C23×C3—81no—
490C23×C3—81no—
491C23×C3—81no—
492C23×C3—82no—
493C23×C3—82no—
494C23×C3D3×D411yescharacteristic
495C23×C3C2×#6711yescharacteristic
496C22×D3—21no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—121no—
500C3×D4—24no—
501C3×D4—24no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—44no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—241no—
514C3×D4#23512yes—
515C3×D4#23512yes—
516C3×D4#23712yes—
517C3×D4#23712yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
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—241no—
534C2×C3×C4—241no—
535C2×C3×C4—241no—
536C2×C3×C4—241no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—81no—
542#67—241no—
543#67—241no—
544#67—241no—
545#67—241no—
546#67—242no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—81no—
553C2×Dic3—81no—
554C2×Dic3—81no—
555C2×Dic3—81no—
556C2×Dic3—121no—
557C2×Dic3—241no—
558C2×Dic3C2×#6711yescharacteristic
559C2×Dic3C2×#6711yescharacteristic
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—21no—
563D12—21no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—61no—
568D12—121no—
569D12—121no—
570D12—241no—
571D12—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C3⋊C8—121no—
585C2×C32—41no—
586C2×C32—42no—
587C2×C32—42no—
588C2×C32#52511yescharacteristic
589C2×C32#57611yescharacteristic
590C2×C32#57611yescharacteristic
591C3⋊D3—81no—
592C3×D3—81no—
593C24—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4C2×D3211yescharacteristic
604C2×D4C2×D3211yescharacteristic
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612D8—62no—
613D8—62no—
614D8—182no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—91no—
619C2×C8—91no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—31no—
641C42—61no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—21no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—84no—
671C22×C3—84no—
672C22×C3—88no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C22×#6711yescharacteristic
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—241no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4C2×#23511yescharacteristic
703C3×C4C2×#23511yescharacteristic
704C3×C4C2×#23711yescharacteristic
705C3×C4C2×#23711yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—21no—
709Dic3—21no—
710Dic3—41no—
711Dic3—41no—
712Dic3—41no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716C32#312211yescharacteristic, complemented, Sylow
717C23—24no—
718C23—21no—
719C23—21no—
720C23—61no—
721C23—81no—
722C23—81no—
723C23—181no—
724C23D3×#6711yescharacteristic
725D4—24no—
726D4—21no—
727D4—21no—
728D4—61no—
729D4—61no—
730D4—181no—
731D4—181no—
732D4—241no—
733D4—721no—
734D4—721no—
735D4—721no—
736D4#380412yes—
737D4#380412yes—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—181no—
748C2×C4—241no—
749C2×C4—241no—
750C2×C4—241no—
751C2×C4—241no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4D3×#6711yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—61no—
757C8—61no—
758C8—181no—
759C8—181no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—41no—
765C2×C3—42no—
766C2×C3—42no—
767C2×C3—41no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—82no—
771C2×C3—82no—
772C2×C3—241no—
773C2×C3#558611yescharacteristic
774C2×C3#575711yescharacteristic
775C2×C3#577411yescharacteristic
776C2×C3#579111yescharacteristic
777C2×C3#583511yescharacteristic
778C2×C3#583511yescharacteristic
779D3—81no—
780D3—241no—
781D3—241no—
782D3—481no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—84no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—361no—
797C22—361no—
798C22—361no—
799C22C2×D3×#6711yescharacteristic
800C4—21no—
801C4—61no—
802C4—61no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—361no—
809C4C2×#380411yescharacteristic
810C4C2×#380411yescharacteristic
811C3—21no—
812C3#7999311yescharacteristic, complemented
813C3#8254211yescharacteristic, complemented
814C2—41no—
815C2—42no—
816C2—42no—
817C2—241no—
818C2—721no—
819C2#1059509611yescharacteristic
820C2#1059509711yescharacteristic
821C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5798C2semidirect
2. #10594985C2semidirect
3. #10592916C2semidirect
4. C3×#5217C2semidirect
5. #10591481C2semidirect
6. #10591481C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10591411C2semidirect
10. #10591409C2semidirect
11. #10591404C2semidirect
12. #10591400C2semidirect
13. #10591136C2semidirect
14. #10591090C2semidirect
15. #10591056C2semidirect
37. #63911C22semidirect
38. #63894C22semidirect
39. Dic3×D12C22semidirect
41. #63869C22semidirect
49. #63576C22semidirect
50. #63575C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5798D3semidirect
69. #5217D3semidirect
716. C32#3122semidirect
812. C3#79993semidirect
813. C3#82542semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
#105949852
#105929162
C3×#52172
#105914812
#105914302
Dic3×#2132
#105914112
#105914092
#105914042
#105914002
#105911362
#105910902
#105910562
#825423
#799933