Finite Group Databasebeta

← #11887023

Subgroups — #11887023

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic, complemented
2#10594907C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic, complemented
5#10591498C211yesmaximal, characteristic, complemented
6#10591487C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic, complemented
8#10591428C211yesmaximal, characteristic, complemented
9Dic3×#213C211yesmaximal, characteristic, complemented
10#10591413C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10591410C211yesmaximal, characteristic, complemented
13#10591166C211yesmaximal, characteristic, complemented
14#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591094C211yesmaximal, characteristic, complemented
16#83482—31nomaximal
17#80014—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3805—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×#953—21no—
25C3×#940C2211yescharacteristic
26C3×#939—21no—
27C3×#938C2211yescharacteristic
28C3×#937—21no—
29C3×D4×Dic3C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic, complemented
32C3×#930C2211yescharacteristic
33C3×#930C2211yescharacteristic, complemented
34C3×C4×#67C2211yescharacteristic
35#63962—21no—
36#63918C2211yescharacteristic, complemented
37#63908C2211yescharacteristic, complemented
38#63893—21no—
39Dic3×D12C2211yescharacteristic, complemented
40#63891—21no—
41D3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×#3713C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic, complemented
47#63659C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic, complemented
50C3×#830C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×D42—31no—
62D4×#67D311yescharacteristic, complemented
63#5611—31no—
64#5555—31no—
65C3×#447—31no—
66#5217—31no—
67#5217D311yescharacteristic, complemented
68C2×#832—31no—
69C2×#832—31no—
70C2×#832—31no—
71C2×#832—61no—
72#5157—31no—
73#5156—31no—
74#5150—31no—
75Dic3×D8—31no—
76#5072—31no—
77#5070—31no—
78#5038—31no—
79#5038—31no—
80#5038—31no—
81#5033—31no—
82#5033—31no—
83C4×#213—31no—
84D4×C3⋊C8—31no—
85#5007—31no—
86#4774—31no—
87D3×#102—31no—
88#4760—31no—
89#4759—31no—
90#4736—31no—
91#67⋊C8—31no—
92C24×C32—21no—
93C23×C3×D3—21no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4—41no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—44no—
108C2×C3×#67D411yescharacteristic
109C22×C3×Dic3—21no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×#627—21no—
116C2×#625—21no—
117#3805—44no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120C4⋊(C3⋊Dic3)—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#217D411yescharacteristic
129C3×#213—22no—
130C3×#213—41no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144#3713—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—21no—
148C22×C3×D4—31no—
149C22×C3×D4—61no—
150C22×C3×D4C2×D311yescharacteristic
151C22×C3×D4C2×D311yescharacteristic
152C22×#67—21no—
153C2×#237—61no—
154C2×#237—61no—
155C2×D3×D4C2×D311yescharacteristic
156C2×C3×D8—31no—
157C2×C3×D8—31no—
158C3×#127—31no—
159C3×#121—31no—
160C3×#121—31no—
161C3×#121—31no—
162C3×#121—61no—
163C3×#120—61no—
164C3×#120—61no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167#953—21no—
168#940C2×D311yescharacteristic
169#939—21no—
170#938—31no—
171#938C2×D311yescharacteristic
172#937—21no—
173#935—61no—
174D4×Dic3—31no—
175D4×Dic3C2×D311yescharacteristic
176C2×#213—31no—
177C2×#213—31no—
178C2×#213C2×D311yescharacteristic
179C2×#213C2×D311yescharacteristic, complemented
180#930—31no—
181#930C2×D311yescharacteristic
182#930C2×D311yescharacteristic, complemented
183C4×#67C2×D311yescharacteristic
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—61no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—31no—
190C22×C3⋊C8—31no—
191C22×C3⋊C8—61no—
192C2×D3×C8—31no—
193#897—61no—
194D3×C4⋊C4—31no—
195#888—31no—
196#886—61no—
197#886—61no—
198#883—61no—
199#878—61no—
200C4×D12—31no—
201#869—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—61no—
218#832—61no—
219#832—61no—
220#832—61no—
221#832C2×D311yescharacteristic
222#832C2×D311yescharacteristic, complemented
223#830—31no—
224#830C2×D311yescharacteristic, complemented
225#821—31no—
226#821—31no—
227(C2×D3)⋊C8—31no—
228#818—31no—
229#818—31no—
230Dic3⋊C8—31no—
231C8×Dic3—31no—
232#809—31no—
233#809—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238C4⋊(C3⋊C8)—31no—
239C4×C3⋊C8—31no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—42no—
243C23×C32—42no—
244C23×C32—81no—
245C23×C32C2×D411yescharacteristic
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3—81no—
251C22×C3×D3C2×D411yescharacteristic
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—21no—
255C32×D4—42no—
256C32×D4#4112yescomplemented
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—42no—
268C3×#67—42no—
269C3×#67—81no—
270C3×#67D814yescomplemented
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—42no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283#627—42no—
284#625—42no—
285D3×Dic3—42no—
286D3×Dic3—42no—
287C3⋊(C3⋊C8)—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—31no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—31no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C24×C3—21no—
307C24×C3—21no—
308C24×C3—41no—
309C24×C3—61no—
310C23×D3—21no—
311C2×C3×D4—24no—
312C2×C3×D4—22no—
313C2×C3×D4—22no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—41no—
322C2×C3×D4—41no—
323C2×C3×D4—41no—
324C2×C3×D4—42no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4—62no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—121no—
333C2×C3×D4—124no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—21no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—44no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67#6711yescharacteristic
353C22×Dic3—21no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—121no—
359#237—124no—
360#237—124no—
361D3×D4—22no—
362D3×D4—41no—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—61no—
369C2×Dic6—61no—
370C3×D8—62no—
371C3×D8—121no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C42—31no—
384#217—21no—
385#217—21no—
386#217—61no—
387#217—61no—
388#217#6711yescharacteristic
389#213—22no—
390#213—41no—
391#213—121no—
392#213—121no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4#6711yescharacteristic
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—121no—
409C4⋊Dic3C22×D311yescharacteristic
410C4⋊Dic3C22×D311yescharacteristic
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4#6711yescharacteristic
414C4×Dic3C22×D311yescharacteristic
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8—121no—
422C2×C3⋊C8—121no—
423C2×C3⋊C8—121no—
424C2×C3⋊C8—122no—
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427D3×C8—121no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—22no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—84no—
437C22×C32C2×D812yes—
438C22×C32C22×D411yescharacteristic
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—84no—
448C2×C3×D3C2×D812yes—
449C32×C4—21no—
450C32×C4C2×#4111yescharacteristic
451C32×C4H(5,𝔽2)11yescharacteristic
452C3⋊Dic3—41no—
453C3⋊Dic3—41no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3C2×D812yes—
459C2×#41—181no—
460C22×D4—31no—
461C22×D4—61no—
462C22×D4D3211yescharacteristic
463C2×D8—31no—
464C2×D8—31no—
465C2×D8—91no—
466C22×C8—91no—
467C22×C8—91no—
468C4⋊Q8—91no—
469#127—31no—
470#123—181no—
471#123—181no—
472C22⋊Q8—181no—
473#121—31no—
474#121—31no—
475#121—31no—
476#121—61no—
477#121—91no—
478#120—61no—
479#120—61no—
480C4×D4—31no—
481C4×D4—31no—
482C4×D4—91no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485#107—91no—
486#107—91no—
487#107—91no—
488C4⋊C8—91no—
489#102—31no—
490#102—31no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102—91no—
499C22⋊C8—31no—
500C22⋊C8—91no—
501C4×C8—91no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—31no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—42no—
511C23×C3—42no—
512C23×C3—44no—
513C23×C3—42no—
514C23×C3—42no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—82no—
518C23×C3—81no—
519C23×C3—81no—
520C23×C3—82no—
521C23×C3—122no—
522C23×C3—122no—
523C23×C3—241no—
524C23×C3D3×D411yescharacteristic
525C23×C3C2×#6711yescharacteristic
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—42no—
529C22×D3—42no—
530C22×D3—81no—
531C22×D3C2×#6711yescharacteristic
532C3×D4—22no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—22no—
540C3×D4—34no—
541C3×D4—41no—
542C3×D4—41no—
543C3×D4—42no—
544C3×D4—42no—
545C3×D4—44no—
546C3×D4—61no—
547C3×D4—61no—
548C3×D4—61no—
549C3×D4—61no—
550C3×D4—122no—
551C3×D4—122no—
552C3×D4—122no—
553C3×D4—122no—
554C3×D4—122no—
555C3×D4—241no—
556C3×D4#23712yescomplemented
557C3×D4#23712yescomplemented
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—122no—
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4C2×#6711yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—42no—
579#67—42no—
580#67—42no—
581#67—42no—
582#67—42no—
583#67—81no—
584#67—122no—
585#67—122no—
586#67#21314yescomplemented
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—42no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—122no—
597C2×Dic3—122no—
598C2×Dic3—122no—
599C2×Dic3—122no—
600C2×Dic3—242no—
601C2×Dic3C2×#6711yescharacteristic
602C2×Dic3C2×#6711yescharacteristic
603C2×Dic3C2×#6711yescharacteristic
604D12—21no—
605D12—21no—
606D12—21no—
607D12—21no—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—122no—
611C4×D3—122no—
612Dic6—122no—
613Dic6—122no—
614C3×C8—61no—
615C3×C8—61no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C3⋊C8—61no—
619C3⋊C8—61no—
620C3⋊C8—61no—
621C3⋊C8—61no—
622C3⋊C8—121no—
623C3⋊C8—121no—
624C2×C32—22no—
625C2×C32—42no—
626C2×C32—81no—
627C2×C32#54611yescharacteristic
628C2×C32C22×D811yescharacteristic
629C2×C32#57711yescharacteristic
630C3×D3—22no—
631C3×D3—81no—
632C3×D3—81no—
633C24—21no—
634C24—61no—
635#41—364no—
636C2×Q8—181no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—31no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—41no—
643C2×D4—61no—
644C2×D4—61no—
645C2×D4—61no—
646C2×D4—62no—
647C2×D4—61no—
648C2×D4—61no—
649C2×D4—61no—
650C2×D4—121no—
651C2×D4—124no—
652C2×D4—181no—
653C2×D4C2×D3211yescharacteristic
654C2×D4C2×D3211yescharacteristic
655C22×C4—31no—
656C22×C4—61no—
657C22×C4—181no—
658C22×C4—181no—
659C22×C4—181no—
660C22×C4C2×D3211yescharacteristic
661D8—62no—
662D8—121no—
663D8—361no—
664C2×C8—31no—
665C2×C8—31no—
666C2×C8—91no—
667C2×C8—91no—
668C2×C8—361no—
669C2×C8—361no—
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—31no—
673C4⋊C4—91no—
674C4⋊C4—91no—
675C4⋊C4—181no—
676C4⋊C4—181no—
677C4⋊C4—181no—
678C22⋊C4—31no—
679C22⋊C4—31no—
680C22⋊C4—61no—
681C22⋊C4—61no—
682C22⋊C4—61no—
683C22⋊C4—61no—
684C22⋊C4—181no—
685C22⋊C4—181no—
686C42—31no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—21no—
696C22×C3—22no—
697C22×C3—32no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—84no—
717C22×C3—84no—
718C22×C3—88no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—244no—
726C22×C3D3×D812yes—
727C22×C3C2×#21312yes—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C22×#6711yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—84no—
739C2×D3C2×#21312yes—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—32no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4C2×#23711yescharacteristic
751C3×C4C2×#23711yescharacteristic
752C3×C4#100411yescharacteristic
753C3×C4#100411yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—41no—
757Dic3—41no—
758Dic3—121no—
759Dic3—121no—
760Dic3—121no—
761Dic3—121no—
762Dic3—241no—
763Dic3—241no—
764Dic3C2×#21312yes—
765C32#329411yescharacteristic, complemented, Sylow
766C23—21no—
767C23—21no—
768C23—31no—
769C23—42no—
770C23—42no—
771C23—61no—
772C23—61no—
773C23—81no—
774C23—122no—
775C23—122no—
776C23—241no—
777C23D3×#6711yescharacteristic
778Q8—362no—
779D4—21no—
780D4—21no—
781D4—21no—
782D4—34no—
783D4—42no—
784D4—61no—
785D4—61no—
786D4—61no—
787D4—61no—
788D4—122no—
789D4—122no—
790D4—122no—
791D4—122no—
792D4—122no—
793D4—241no—
794D4—362no—
795D4#380512yescomplemented
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—122no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—362no—
809C2×C4—362no—
810C2×C4—362no—
811C2×C4D3×#6711yescharacteristic
812C2×C4C22×D3211yescharacteristic
813C8—61no—
814C8—61no—
815C8—181no—
816C8—181no—
817C2×C3—24no—
818C2×C3—22no—
819C2×C3—22no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—42no—
824C2×C3—42no—
825C2×C3—62no—
826C2×C3—82no—
827C2×C3—82no—
828C2×C3—81no—
829C2×C3—81no—
830C2×C3—241no—
831C2×C3—241no—
832C2×C3#559111yescharacteristic
833C2×C3C2×D3×D811yescharacteristic
834C2×C3#577511yescharacteristic
835C2×C3C22×#21311yescharacteristic
836C2×C3#580611yescharacteristic
837C2×C3#583611yescharacteristic
838D3—22no—
839D3—81no—
840D3—81no—
841C22—21no—
842C22—21no—
843C22—22no—
844C22—32no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—61no—
851C22—61no—
852C22—84no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—244no—
860C22D3×#21312yes—
861C22C2×D3×#6711yescharacteristic
862C4—21no—
863C4—32no—
864C4—61no—
865C4—61no—
866C4—121no—
867C4—121no—
868C4—361no—
869C4—361no—
870C4C2×#380511yescharacteristic
871C4#6433011yescharacteristic
872C3—21no—
873C3#8001411yescharacteristic, complemented
874C3#8348211yescharacteristic, complemented
875C2—22no—
876C2—42no—
877C2—62no—
878C2—81no—
879C2—241no—
880C2—241no—
881C2C2×D3×#21311yescharacteristic
882C2#1059510611yescharacteristic
883C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3294
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×D4×#67C2semidirect
2. #10594907C2semidirect
3. C2×#63659C2semidirect
4. C3×#5217C2semidirect
5. #10591498C2semidirect
6. #10591487C2semidirect
7. #10591447C2semidirect
8. #10591428C2semidirect
9. Dic3×#213C2semidirect
10. #10591413C2semidirect
11. D3×#832C2semidirect
12. #10591410C2semidirect
13. #10591166C2semidirect
14. #67⋊(C3⋊C8)C2semidirect
15. #10591094C2semidirect
22. C2×C4⋊(C3⋊Dic3)C22semidirect
23. C22×C3⋊(C3⋊C8)C22semidirect
31. C2×C3×#213C22semidirect
33. C3×#930C22semidirect
36. #63918C22semidirect
37. #63908C22semidirect
39. Dic3×D12C22semidirect
41. D3×C4⋊Dic3C22semidirect
42. C2×#3713C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63659C22semidirect
47. #63659C22semidirect
49. C3×#832C22semidirect
50. C3×#830C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. D4×#67D3semidirect
67. #5217D3semidirect
179. C2×#213C2×D3semidirect
182. #930C2×D3semidirect
222. #832C2×D3semidirect
224. #830C2×D3semidirect
256. C32×D4#41semidirect
270. C3×#67D8semidirect
556. C3×D4#237semidirect
557. C3×D4#237semidirect
586. #67#213semidirect
765. C32#3294semidirect
795. D4#3805semidirect
873. C3#80014semidirect
874. C3#83482semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
#105949072
C2×#636592
C3×#52172
#105914982
#105914872
#105914472
#105914282
Dic3×#2132
#105914132
D3×#8322
#105914102
#105911662
#67⋊(C3⋊C8)2
#105910942
#834823
#800143