Finite Group Databasebeta

← #11887171

Subgroups — #11887171

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595371C211yesmaximal, characteristic, complemented
2#10594621C211yesmaximal, characteristic
3#10592506C211yesmaximal, characteristic, complemented
4C3×#4807C211yesmaximal, characteristic, complemented
5C3×#4788C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591651C211yesmaximal, characteristic, complemented
8#10591617C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10D3×#821C211yesmaximal, characteristic, complemented
11#10590878C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590558C211yesmaximal, characteristic, complemented
14#10590445C211yesmaximal, characteristic, complemented
15#10590441C211yesmaximal, characteristic, complemented
16#80680—31nomaximal
17#79676—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21#64155C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24#64104C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#893C2211yescharacteristic
32#63923—21no—
33#63922—21no—
34#63918C2211yescharacteristic, complemented
35#63911C2211yescharacteristic
36#63906—21no—
37C4×#626C2211yescharacteristic
38#63900C2211yescharacteristic, complemented
39#63899—21no—
40#63895—21no—
41D3×C4⋊Dic3C2211yescharacteristic, complemented
42#63880—21no—
43#63867—21no—
44C32×#103C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×C8×Dic3C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5635—31no—
62#5609—31no—
63#5579—31no—
64D4×D12—31no—
65C3×#465—31no—
66C3×C4×SD16—31no—
67#5169—31no—
68#5169—31no—
69#5169—31no—
70#5163—31no—
71C2×#821—31no—
72C8×#67—31no—
73#5046—31no—
74#5034—31no—
75#5027—31no—
76#5008—31no—
77#4870—31no—
78#4863—31no—
79#4863—31no—
80#4863—31no—
81#4807—31no—
82#4807—31no—
83#4807—61no—
84#4807D311yescharacteristic, complemented
85#4788D311yescharacteristic, complemented
86D3×#102—31no—
87D3×#102—31no—
88D3×#102—31no—
89#4760—31no—
90#4694—31no—
91C8×D12—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×#625—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3802—22no—
112#3802—41no—
113D3×D12—22no—
114D3×D12—41no—
115D3×D12—44no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3755—41no—
119#3752—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C8×C3⋊D3—41no—
125C3×#215—22no—
126C3×#215—41no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D3×C8—41no—
139#3724—21no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3D411yescharacteristic
143#3722D411yescharacteristic
144(C2×D3)⋊Dic3D411yescharacteristic
145#3295—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159#946—31no—
160#946—31no—
161#946—61no—
162#946C2×D311yescharacteristic, complemented
163Q8×Dic3C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167C2×#215C2×D311yescharacteristic
168C2×#215C2×D311yescharacteristic, complemented
169#940—31no—
170#937—61no—
171#930—61no—
172C4×#67—31no—
173C2×C4⋊Dic3—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—61no—
177C2×D3×C8C2×D311yescharacteristic, complemented
178#897—61no—
179#896—61no—
180#896—61no—
181#895—31no—
182#895—31no—
183#895—61no—
184#895C2×D311yescharacteristic
185#893C2×D311yescharacteristic
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189#889—61no—
190#888—31no—
191#884—61no—
192#882—61no—
193#882—61no—
194#882—61no—
195#67⋊C4—61no—
196#878—61no—
197#874—31no—
198C4×D12—31no—
199C4×D12—61no—
200#870—61no—
201#869—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×#103—21no—
205C3×#103C2×D311yescharacteristic, complemented
206C3×#103C2×D311yescharacteristic, complemented
207C3×#102—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222#821C2×D311yescharacteristic
223#821C2×D311yescharacteristic, complemented
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227Dic3⋊C8—31no—
228C8×Dic3C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#808—31no—
234#808—31no—
235#808—61no—
236#808C2×D311yescharacteristic, complemented
237#808C2×D311yescharacteristic, complemented
238C4⋊(C3⋊C8)—31no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C32×Q8—21no—
251C32×Q8—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—42no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
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—42no—
275#627—81no—
276#626—42no—
277#626—42no—
278#626—81no—
279#626SD1614yescomplemented
280#625—42no—
281#624—81no—
282D3×Dic3—81no—
283C32×C8—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—91no—
289#486—91no—
290#481—91no—
291#481—91no—
292#476—91no—
293#465—31no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—31no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—21no—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C2×#67—31no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C22×Dic3—61no—
321D3×D4—62no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—121no—
325D3×D4—124no—
326D3×D4—121no—
327D3×D4—121no—
328C2×D12—21no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—61no—
333C2×D12—62no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—121no—
340C2×D12—121no—
341C2×D12—124no—
342C2×D12C22×D311yescharacteristic
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—21no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—61no—
353C2×Dic6—61no—
354C3×SD16—62no—
355C3×SD16—121no—
356C2×C3×C8—21no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—121no—
360C2×C3×C8C22×D311yescharacteristic
361C2×C3×C8C22×D311yescharacteristic
362C3×C4⋊C4—21no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—31no—
373C3×C42—61no—
374#217—31no—
375#215—22no—
376#215—41no—
377#215—121no—
378#215—121no—
379#215—122no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—121no—
391(C2×D3)⋊C4—121no—
392C4⋊Dic3—21no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4—21no—
402Dic3⋊C4—31no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—121no—
410C4×Dic3—21no—
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417D3×C8—41no—
418D3×C8—121no—
419D3×C8—121no—
420D3×C8—122no—
421C22×C32C22×D411yescharacteristic
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3C2×SD1612yes—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3C2×SD1612yes—
437D32—84no—
438D32—84no—
439C32×C4—41no—
440C32×C4—41no—
441C32×C4C2×#4111yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3⋊Dic3—21no—
444C3⋊Dic3—41no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3C2×SD1612yes—
450C22×D4—91no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—31no—
454C2×SD16—31no—
455C2×SD16—91no—
456C22×C8—31no—
457C22×C8—91no—
458C4⋊Q8—91no—
459#127—91no—
460#125—181no—
461C22⋊Q8—31no—
462C22⋊Q8—91no—
463C22⋊Q8—181no—
464C22⋊Q8—181no—
465#121—31no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—31no—
471C4×D4—31no—
472C4×D4—91no—
473C4×D4—181no—
474C2×C4⋊C4—91no—
475C2×C4⋊C4—91no—
476#106—31no—
477#106—31no—
478#106—91no—
479C4⋊C8—91no—
480#103D3211yescharacteristic, complemented
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—91no—
491C22⋊C8—91no—
492C4×C8—31no—
493C23×C3—31no—
494C23×C3—61no—
495C23×C3—61no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3D3×D411yescharacteristic
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—21no—
520C3×Q8—21no—
521C3×Q8—41no—
522C3×Q8—41no—
523C3×D4—32no—
524C3×D4—61no—
525C3×D4—61no—
526C3×D4—61no—
527C3×D4—122no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—34no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—241no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—121no—
559C2×Dic3—241no—
560C2×Dic3D3×D411yescharacteristic
561C2×Dic3D3×D411yescharacteristic
562C2×Dic3D3×D411yescharacteristic
563D12—21no—
564D12—21no—
565D12—21no—
566D12—34no—
567D12—42no—
568D12—61no—
569D12—61no—
570D12—61no—
571D12—61no—
572D12—121no—
573D12—121no—
574D12—122no—
575D12—122no—
576D12—122no—
577D12—122no—
578D12—242no—
579D12—241no—
580D12#23512yes—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—42no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—61no—
587C4×D3—61no—
588C4×D3—121no—
589C4×D3—121no—
590C4×D3—241no—
591C4×D3—241no—
592C4×D3—241no—
593Dic6—241no—
594Dic6—241no—
595C3×C8—21no—
596C3×C8—21no—
597C3×C8—41no—
598C3×C8—61no—
599C3×C8—61no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C3⋊C8—62no—
603C3⋊C8—61no—
604C3⋊C8—61no—
605C2×C32#54611yescharacteristic
606C2×C32C22×SD1611yescharacteristic
607C2×C32#57611yescharacteristic
608C3⋊D3—22no—
609C3⋊D3—81no—
610C3×D3—22no—
611C3×D3—42no—
612C3×D3—81no—
613C24—181no—
614C24—181no—
615C2×Q8—181no—
616C2×Q8C2×D3211yescharacteristic
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—61no—
620C2×D4—91no—
621C2×D4—91no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—182no—
627C2×D4—181no—
628C2×D4—182no—
629C2×D4—361no—
630C2×D4—364no—
631C2×D4—361no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—91no—
635C22×C4—181no—
636C22×C4—181no—
637SD16—62no—
638SD16—121no—
639SD16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8—121no—
644C2×C8—361no—
645C2×C8C2×D3211yescharacteristic
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4C2×D3211yescharacteristic
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—61no—
666C22×C3—21no—
667C22×C3—32no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—62no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—22no—
681C2×D3—32no—
682C2×D3—32no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—62no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—241no—
702C2×D3—241no—
703C2×D3—241no—
704C2×D3—244no—
705C2×D3—244no—
706C2×D3—244no—
707C2×D3—244no—
708C2×D3D3×SD1612yes—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—32no—
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—61no—
731Dic3—61no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736Dic3D3×SD1612yes—
737C32#329511yescharacteristic, complemented, Sylow
738C23—31no—
739C23—61no—
740C23—61no—
741C23—91no—
742C23—181no—
743C23—362no—
744C23—362no—
745C23—362no—
746C23—362no—
747C23—721no—
748C23—721no—
749Q8—21no—
750Q8—21no—
751Q8—721no—
752D4—32no—
753D4—61no—
754D4—61no—
755D4—61no—
756D4—94no—
757D4—122no—
758D4—181no—
759D4—181no—
760D4—362no—
761D4—362no—
762D4—362no—
763D4—362no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—91no—
775C2×C4—122no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—721no—
780C2×C4—721no—
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—61no—
784C8—61no—
785C8—181no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—62no—
790C2×C3—122no—
791C2×C3—241no—
792C2×C3#555011yescharacteristic
793C2×C3#561011yescharacteristic
794C2×C3C2×D3×SD1611yescharacteristic
795C2×C3C2×D3×SD1611yescharacteristic
796C2×C3#576911yescharacteristic
797C2×C3#576911yescharacteristic
798D3—22no—
799D3—42no—
800D3—62no—
801D3—62no—
802D3—81no—
803D3—122no—
804D3—241no—
805D3—241no—
806D3—481no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—62no—
811C22—92no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—181no—
818C22—181no—
819C22—361no—
820C22—361no—
821C22—361no—
822C22—724no—
823C22—724no—
824C22D32×D411yescharacteristic
825C4—32no—
826C4—41no—
827C4—41no—
828C4—61no—
829C4—61no—
830C4—121no—
831C4—121no—
832C4—181no—
833C4—361no—
834C4D3×#23511yescharacteristic
835C4#6431411yescharacteristic
836C3—21no—
837C3#7967611yescharacteristic, complemented
838C3#8068011yescharacteristic, complemented
839C2—62no—
840C2—122no—
841C2—182no—
842C2—241no—
843C2—721no—
844C2#1059428311yescharacteristic
845C2D32×SD1611yescharacteristic
846C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594621C2
hypercenter#103D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595371C2semidirect
3. #10592506C2semidirect
4. C3×#4807C2semidirect
5. C3×#4788C2semidirect
6. #10591652C2semidirect
7. #10591651C2semidirect
8. #10591617C2semidirect
9. #10590940C2semidirect
10. D3×#821C2semidirect
11. #10590878C2semidirect
12. C8×#626C2semidirect
13. #10590558C2semidirect
14. #10590445C2semidirect
15. #10590441C2semidirect
21. #64155C22semidirect
22. C2×#3755C22semidirect
23. C2×C8×C3⋊D3C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×D3×C8C22semidirect
34. #63918C22semidirect
38. #63900C22semidirect
41. D3×C4⋊Dic3C22semidirect
44. C32×#103C22semidirect
45. #63648C22semidirect
46. #63635C22semidirect
48. C3×#821C22semidirect
49. C3×C8×Dic3C22semidirect
50. C3×#808C22semidirect
51. C3×#808C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4807D3semidirect
85. #4788D3semidirect
162. #946C2×D3semidirect
163. Q8×Dic3C2×D3semidirect
168. C2×#215C2×D3semidirect
177. C2×D3×C8C2×D3semidirect
205. C3×#103C2×D3semidirect
206. C3×#103C2×D3semidirect
223. #821C2×D3semidirect
228. C8×Dic3C2×D3semidirect
236. #808C2×D3semidirect
237. #808C2×D3semidirect
279. #626SD16semidirect
480. #103D32semidirect
737. C32#3295semidirect
837. C3#79676semidirect
838. C3#80680semidirect

Maximal subgroups

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

subgroupindex
#105953712
#105946212
#105925062
C3×#48072
C3×#47882
#105916522
#105916512
#105916172
#105909402
D3×#8212
#105908782
C8×#6262
#105905582
#105904452
#105904412
#806803
#796763