Finite Group Databasebeta

← #11887115

Subgroups — #11887115

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5511C211yesmaximal, characteristic, complemented
2D12×#67C211yesmaximal, characteristic
3#10592667C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591177C211yesmaximal, characteristic, complemented
6#10591169C211yesmaximal, characteristic, complemented
7C3⋊C8×#67C211yesmaximal, characteristic, complemented
8#10590596C211yesmaximal, characteristic, complemented
9D3×#809C211yesmaximal, characteristic, complemented
10#10590549C211yesmaximal, characteristic, complemented
11#10590548C211yesmaximal, characteristic, complemented
12#10590501C211yesmaximal, characteristic, complemented
13#10590500C211yesmaximal, characteristic, complemented
14#10590465C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#83634—31nomaximal
17#78758—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22#64139C2211yescharacteristic
23C3×C4×#67—21no—
24C3×C4×#67C2211yescharacteristic
25C3×#924—21no—
26C3×#924C2211yescharacteristic, complemented
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C3×#897C2211yescharacteristic, complemented
29C3×#896—21no—
30C3×D3×C4⋊C4C2211yescharacteristic, complemented
31C3×#889—21no—
32C3×#888C2211yescharacteristic, complemented
33C3×#887C2211yescharacteristic, complemented
34#63977—21no—
35#63922—21no—
36#63911C2211yescharacteristic
37#63908C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63886—21no—
40C2×#3717C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63657C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#554—31no—
62D4×#67—31no—
63D4×D12—31no—
64#5511D311yescharacteristic, complemented
65C2×C3×#102—31no—
66#5218—31no—
67#5114—31no—
68C8×#67—31no—
69#5088—31no—
70#5084—31no—
71#5048—31no—
72#5048—31no—
73#5046—31no—
74#5046—31no—
75#5027—31no—
76C4×#215—31no—
77D4×C3⋊C8—31no—
78#4968—31no—
79#4968—31no—
80#4968—31no—
81#4968—61no—
82C2×#809—31no—
83C2×#809D311yescharacteristic, complemented
84#4778—31no—
85#4777—31no—
86#4776—31no—
87D3×#102—31no—
88#4762—31no—
89#4761—31no—
90#4760—31no—
91#4758—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108D3×#67—44no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#217D411yescharacteristic
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3717—41no—
142#3715—22no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12C2×D311yescharacteristic
152C22×C3×C8—31no—
153C3×C4⋊Q8—31no—
154C3×#125—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
165C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
166#953—61no—
167C2×#215—31no—
168C2×#215—31no—
169C2×#215—31no—
170#940—31no—
171#939—61no—
172#938—31no—
173#937—61no—
174D4×Dic3—31no—
175C2×#214—31no—
176C2×#214—31no—
177#930—31no—
178#930—31no—
179#930—31no—
180#930—61no—
181C4×#67—21no—
182C4×#67C2×D311yescharacteristic
183#924—21no—
184#924C2×D311yescharacteristic, complemented
185C22×C3⋊C8—31no—
186C22×C3⋊C8C2×D311yescharacteristic, complemented
187C2×#204—31no—
188C2×D3×C8—31no—
189#897C2×D311yescharacteristic, complemented
190#896—21no—
191#895—61no—
192D3×C4⋊C4C2×D311yescharacteristic, complemented
193#889—21no—
194#888C2×D311yescharacteristic, complemented
195#887C2×D311yescharacteristic, complemented
196#882—61no—
197#882—61no—
198#874—31no—
199C4×D12—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211#821—31no—
212(C2×D3)⋊C8—31no—
213#817—31no—
214#816—31no—
215Dic3⋊C8—31no—
216C8×Dic3—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—61no—
225#809—61no—
226#809C2×D311yescharacteristic
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic, complemented
229#809C2×D311yescharacteristic, complemented
230#808—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#808—61no—
236#808—61no—
237C4⋊(C3⋊C8)—31no—
238C4×C3⋊C8—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—81no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—42no—
258C2×C3⋊Dic3—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C3×#67SD1614yescomplemented
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—81no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—81no—
278#626—42no—
279#626—42no—
280#626—81no—
281#625—42no—
282D3×Dic3—42no—
283C3⋊(C3⋊C8)—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—31no—
288D42—91no—
289#486—91no—
290#481—91no—
291#481—91no—
292#476—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—31no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—31no—
307C2×C3×Q8—61no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—62no—
312C2×C3×D4—61no—
313C2×C3×D4—121no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—41no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—121no—
330C2×#67—124no—
331C2×#67#6711yescharacteristic
332C22×Dic3—61no—
333D3×D4—62no—
334D3×D4—121no—
335D3×D4—124no—
336C2×D12—22no—
337C2×D12—21no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—41no—
341C2×D12—61no—
342C2×D12—62no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—121no—
347C2×D12C22×D311yescharacteristic
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—21no—
350C2×C4×D3—61no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—21no—
353C2×Dic6C22×D311yescharacteristic
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8—121no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—41no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C42—31no—
378C3×C42—61no—
379#217—21no—
380#217—61no—
381#217—61no—
382#217#6711yescharacteristic
383#215—62no—
384#215—121no—
385#215—121no—
386#214—62no—
387#214—121no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—121no—
394(C2×D3)⋊C4#6711yescharacteristic
395C4⋊Dic3—21no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—61no—
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4#6711yescharacteristic
405C4×Dic3—21no—
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—41no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—121no—
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417#204—121no—
418D3×C8—121no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32C2×SD1612yes—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—84no—
435C2×C3×D3C2×SD1612yes—
436D32—84no—
437C32×C4—21no—
438C32×C4—41no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3C2×SD1612yes—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×SD16—91no—
454C22×C8—31no—
455C22×C8—91no—
456C4⋊Q8—31no—
457#127—91no—
458#125—61no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461C22⋊Q8—61no—
462C22⋊Q8—61no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—31no—
469C4×D4—31no—
470C4×D4—61no—
471C4×D4—91no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4D3211yescharacteristic, complemented
474#106—91no—
475#106—91no—
476#106—91no—
477C4⋊C8—91no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—91no—
489C22⋊C8—91no—
490C4×C8—91no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3—241no—
498C23×C3D3×D411yescharacteristic
499C23×C3C2×#6711yescharacteristic
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—42no—
503C22×D3—42no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—81no—
507C22×D3—121no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3C2×#6711yescharacteristic
515C3×Q8—61no—
516C3×Q8—61no—
517C3×Q8—241no—
518C3×D4—34no—
519C3×D4—32no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—122no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—81no—
546C2×C3×C4—81no—
547C2×C3×C4—82no—
548C2×C3×C4—241no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—122no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—122no—
559#67—242no—
560#67—241no—
561#67#21514yescomplemented
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—121no—
567C2×Dic3—122no—
568C2×Dic3C2×#6711yescharacteristic
569C2×Dic3C2×#6711yescharacteristic
570C2×Dic3C2×#6711yescharacteristic
571D12—21no—
572D12—21no—
573D12—21no—
574D12—42no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—121no—
580D12—121no—
581D12—122no—
582D12—122no—
583D12—241no—
584D12#23512yes—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—81no—
588C4×D3—122no—
589Dic6—21no—
590Dic6—21no—
591Dic6—81no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C3⋊C8—61no—
600C3⋊C8—121no—
601C3⋊C8—121no—
602C2×C32—22no—
603C2×C32#54611yescharacteristic
604C2×C32C22×SD1611yescharacteristic
605C2×C32#57611yescharacteristic
606C3⋊D3—81no—
607C3×D3—22no—
608C3×D3—42no—
609C3×D3—81no—
610C24—61no—
611C24—181no—
612C2×Q8—31no—
613C2×Q8—61no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—31no—
617C2×D4—62no—
618C2×D4—61no—
619C2×D4—91no—
620C2×D4—121no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—182no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—361no—
628C2×D4—364no—
629C22×C4—21no—
630C22×C4—31no—
631C22×C4—61no—
632C22×C4—181no—
633C22×C4C2×D3211yescharacteristic
634SD16—182no—
635SD16—361no—
636SD16—361no—
637C2×C8—31no—
638C2×C8—31no—
639C2×C8—91no—
640C2×C8—91no—
641C2×C8—121no—
642C2×C8—361no—
643C4⋊C4—21no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—91no—
652C4⋊C4C2×D3211yescharacteristic
653C4⋊C4C2×D3211yescharacteristic
654C22⋊C4—31no—
655C22⋊C4—31no—
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C42—31no—
662C42—61no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—22no—
669C22×C3—32no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—62no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—244no—
681C22×C3D3×SD1612yes—
682C22×C3C2×#21512yes—
683C22×C3C2×D3×D411yescharacteristic
684C22×C3C22×#6711yescharacteristic
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—22no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—84no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—241no—
701C2×D3—241no—
702C2×D3—241no—
703C2×D3—244no—
704C2×D3—244no—
705C2×D3C2×#21512yes—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—32no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—81no—
719C3×C4—81no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4C2×#23511yescharacteristic
723C3×C4#100411yescharacteristic
724C3×C4D3×#4111yescharacteristic
725C3×C4#100911yescharacteristic
726Dic3—21no—
727Dic3—21no—
728Dic3—41no—
729Dic3—41no—
730Dic3—121no—
731Dic3—121no—
732Dic3—241no—
733Dic3C2×#21512yes—
734C32#329511yescharacteristic, complemented, Sylow
735C23—31no—
736C23—61no—
737C23—61no—
738C23—122no—
739C23—122no—
740C23—181no—
741C23—241no—
742C23—362no—
743C23—362no—
744C23—721no—
745C23D3×#6711yescharacteristic
746Q8—61no—
747Q8—61no—
748Q8—241no—
749D4—34no—
750D4—32no—
751D4—61no—
752D4—61no—
753D4—61no—
754D4—122no—
755D4—181no—
756D4—181no—
757D4—362no—
758D4—362no—
759D4—362no—
760D4—362no—
761D4—721no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—81no—
774C2×C4—181no—
775C2×C4—241no—
776C2×C4—362no—
777C2×C4D3×#6711yescharacteristic
778C2×C4C22×D3211yescharacteristic
779C8—61no—
780C8—61no—
781C8—181no—
782C8—181no—
783C2×C3—22no—
784C2×C3—22no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—42no—
789C2×C3—62no—
790C2×C3—122no—
791C2×C3—241no—
792C2×C3#549011yescharacteristic
793C2×C3#575711yescharacteristic
794C2×C3C2×D3×SD1611yescharacteristic
795C2×C3C22×#21511yescharacteristic
796C2×C3#582911yescharacteristic
797C2×C3#583511yescharacteristic
798D3—22no—
799D3—42no—
800D3—81no—
801D3—241no—
802D3—241no—
803D3—481no—
804C22—21no—
805C22—21no—
806C22—32no—
807C22—61no—
808C22—61no—
809C22—62no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—244no—
816C22—361no—
817C22—361no—
818C22—361no—
819C22—724no—
820C22D3×#21512yes—
821C22C2×D3×#6711yescharacteristic
822C4—21no—
823C4—32no—
824C4—41no—
825C4—41no—
826C4—61no—
827C4—61no—
828C4—121no—
829C4—121no—
830C4—361no—
831C4D3×#23511yescharacteristic
832C4#6430711yescharacteristic
833C3—21no—
834C3#7875811yescharacteristic, complemented
835C3#8363411yescharacteristic, complemented
836C2—22no—
837C2—62no—
838C2—122no—
839C2—241no—
840C2—721no—
841C2#1059506511yescharacteristic
842C2#1059509611yescharacteristic
843C2C2×D3×#21511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalD12×#67C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5511C2semidirect
3. #10592667C2semidirect
4. C2×C3×#809C2semidirect
5. #10591177C2semidirect
6. #10591169C2semidirect
7. C3⋊C8×#67C2semidirect
8. #10590596C2semidirect
9. D3×#809C2semidirect
10. #10590549C2semidirect
11. #10590548C2semidirect
12. #10590501C2semidirect
13. #10590500C2semidirect
14. #10590465C2semidirect
15. #10590453C2semidirect
21. C2×C32×C4⋊C4C22semidirect
26. C3×#924C22semidirect
27. C22×C3×C3⋊C8C22semidirect
28. C3×#897C22semidirect
30. C3×D3×C4⋊C4C22semidirect
32. C3×#888C22semidirect
33. C3×#887C22semidirect
40. C2×#3717C22semidirect
42. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63657C22semidirect
45. #63636C22semidirect
46. #63636C22semidirect
47. #63635C22semidirect
48. #63635C22semidirect
51. C3×#809C22semidirect
52. C3×#809C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63564C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5511D3semidirect
83. C2×#809D3semidirect
164. C2×C3×C4⋊C4C2×D3semidirect
165. C2×C3×C4⋊C4C2×D3semidirect
184. #924C2×D3semidirect
186. C22×C3⋊C8C2×D3semidirect
189. #897C2×D3semidirect
192. D3×C4⋊C4C2×D3semidirect
194. #888C2×D3semidirect
195. #887C2×D3semidirect
228. #809C2×D3semidirect
229. #809C2×D3semidirect
261. C3×#67SD16semidirect
473. C2×C4⋊C4D32semidirect
561. #67#215semidirect
734. C32#3295semidirect
834. C3#78758semidirect
835. C3#83634semidirect

Maximal subgroups

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

subgroupindex
C3×#55112
D12×#672
#105926672
C2×C3×#8092
#105911772
#105911692
C3⋊C8×#672
#105905962
D3×#8092
#105905492
#105905482
#105905012
#105905002
#105904652
#105904532
#836343
#787583