Finite Group Databasebeta

← #11889745

Subgroups — #11889745

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic, complemented
2#10594007C211yesmaximal, characteristic
3#10592725C211yesmaximal, characteristic, complemented
4C3×#5028C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591587C211yesmaximal, characteristic, complemented
9#10590609C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic, complemented
11#10590517C211yesmaximal, characteristic, complemented
12#10590498C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic, complemented
14#10590313C211yesmaximal, characteristic, complemented
15#10590280C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#80619—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×#896—21no—
28C3×#896—21no—
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×D3×C4⋊C4C2211yescharacteristic, complemented
31C3×#875C2211yescharacteristic
32C3×C4×D12—21no—
33C3×C4×D12C2211yescharacteristic
34C3×#870—21no—
35C3×#869C2211yescharacteristic, complemented
36#63922—21no—
37#63921—21no—
38#63912—21no—
39#63908C2211yescharacteristic
40#63856C2211yescharacteristic
41#63854—21no—
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63634C2211yescharacteristic, complemented
47#63630C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#554—31no—
62#5676—31no—
63#5579D311yescharacteristic, complemented
64#5550—31no—
65C3×#464—31no—
66#5188—31no—
67#5187—31no—
68#5174—31no—
69#5169—31no—
70#5089—31no—
71#5087—31no—
72#5055—31no—
73#5051—31no—
74#5049—31no—
75#5047—31no—
76#5046—31no—
77#5028D311yescharacteristic, complemented
78#5026—31no—
79#5026—31no—
80#5026—61no—
81#5011—31no—
82#4970—31no—
83#4967—31no—
84#4966—31no—
85C2×#809—31no—
86#4846—31no—
87#4836—31no—
88#4811—31no—
89#4803—31no—
90#4774—31no—
91D3×#102—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3799—22no—
111#3799—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3755—22no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#216—41no—
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3724—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C3×C4⋊Q8—31no—
152C3×#125—61no—
153C3×#124—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×C4×Q8—21no—
159C3×C4×Q8C2×D311yescharacteristic, complemented
160C3×C4×Q8C2×D311yescharacteristic, complemented
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165#946—31no—
166#946C2×D311yescharacteristic
167#946C2×D311yescharacteristic, complemented
168C2×#216C2×D311yescharacteristic, complemented
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—61no—
172C2×#215C2×D311yescharacteristic
173#938—31no—
174#937—61no—
175#930—31no—
176#924—31no—
177C2×#208—31no—
178C22×C3⋊C8—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×D3×C8—31no—
181#896—21no—
182#896—21no—
183#894—61no—
184D3×C4⋊C4C2×D311yescharacteristic
185D3×C4⋊C4C2×D311yescharacteristic, complemented
186#884—61no—
187#884—61no—
188#883—61no—
189#882—61no—
190D3×C22⋊C4—61no—
191D3×C22⋊C4—61no—
192#875C2×D311yescharacteristic
193C4×D12—21no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198#870—21no—
199#869C2×D311yescharacteristic, complemented
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#102—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#832—31no—
209#832—31no—
210#830—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216#818—31no—
217#818—31no—
218#810—31no—
219#810—31no—
220#810C2×D311yescharacteristic, complemented
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235#803—31no—
236#803—31no—
237#803—61no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
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—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—22no—
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—81no—
273#626—42no—
274#626—42no—
275#625—81no—
276#624—42no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—31no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—31no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313#239—62no—
314#239—121no—
315D3×D4—62no—
316D3×D4—121no—
317#235—62no—
318#235—121no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—121no—
326C2×D12#6711yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—21no—
338C2×Dic6C22×D311yescharacteristic
339C3×Q16—121no—
340C3×SD16—121no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—21no—
366C3×C42—41no—
367C3×C42C22×D311yescharacteristic
368C3×C42C22×D311yescharacteristic
369#217—61no—
370#217—61no—
371#216—41no—
372#215—41no—
373#215—62no—
374#215—62no—
375#215—64no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4#6711yescharacteristic
386(C2×D3)⋊C4#6711yescharacteristic
387C4⋊Dic3—21no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3#6711yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410ΓL(1,𝔽25)—121no—
411D3×C8—121no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—22no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3#13712yes—
425D32—84no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—31no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—91no—
444C22×C8—91no—
445C4⋊Q8—31no—
446#125—61no—
447#124—31no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451C22⋊Q8—61no—
452C22⋊Q8—61no—
453C22⋊Q8—91no—
454#121—91no—
455#121—181no—
456#120—181no—
457C4×Q8D3211yescharacteristic, complemented
458C4×D4—31no—
459C4×D4—61no—
460C4×D4—91no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—31no—
463C2×C22⋊C4—181no—
464#107—91no—
465#107—91no—
466#107—91no—
467C4⋊C8—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—91no—
479C22⋊C8—91no—
480#97—91no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3C2×#6711yescharacteristic
495C22×D3C2×#6711yescharacteristic
496C3×Q8—22no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—41no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—241no—
505C3×D4—62no—
506C3×D4—61no—
507C3×D4—61no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—241no—
527C2×C3×C4—241no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—122no—
535#67—122no—
536#67—241no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546D12—22no—
547D12—21no—
548D12—21no—
549D12—32no—
550D12—32no—
551D12—62no—
552D12—61no—
553D12—61no—
554D12—121no—
555D12—122no—
556D12—122no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—81no—
562C4×D3—81no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—242no—
568Dic6—21no—
569Dic6—21no—
570Dic6—81no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—62no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3⋊D3—42no—
585C3×D3—22no—
586C3×D3—41no—
587C3×D3—81no—
588C24—181no—
589#41—182no—
590#41—361no—
591C2×Q8—31no—
592C2×Q8—61no—
593C2×Q8C2×D3211yescharacteristic
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—91no—
597C2×D4—181no—
598C2×D4—182no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—361no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—121no—
609SD16—121no—
610SD16—182no—
611M16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—91no—
616C2×C8—361no—
617C4⋊C4—21no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—21no—
639C42C2×D3211yescharacteristic
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×#6711yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3#94212yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4#100411yescharacteristic
692C3×C4D3×#4111yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4#100911yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—121no—
701Dic3—121no—
702Dic3—241no—
703C32#331411yescharacteristic, complemented, Sylow
704C23—31no—
705C23—31no—
706C23—61no—
707C23—181no—
708C23—362no—
709C23—362no—
710C23—721no—
711Q8—21no—
712Q8—21no—
713Q8—61no—
714Q8—61no—
715Q8—241no—
716D4—62no—
717D4—61no—
718D4—61no—
719D4—92no—
720D4—181no—
721D4—362no—
722D4—362no—
723D4—721no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—181no—
736C2×C4—241no—
737C2×C4—241no—
738C2×C4—362no—
739C2×C4—721no—
740C2×C4D3×#6711yescharacteristic
741C2×C4D3×#6711yescharacteristic
742C2×C4C22×D3211yescharacteristic
743C8—61no—
744C8—61no—
745C8—181no—
746C8—181no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—62no—
751C2×C3—121no—
752C2×C3—241no—
753C2×C3#561211yescharacteristic
754C2×C3#576911yescharacteristic
755C2×C3D3×#13711yescharacteristic
756C2×C3C2×#94211yescharacteristic
757C2×C3#582911yescharacteristic
758C2×C3#583511yescharacteristic
759D3—22no—
760D3—41no—
761D3—81no—
762D3—122no—
763D3—122no—
764D3—242no—
765C22—32no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—361no—
776C22—361no—
777C22—724no—
778C22C2×D3×#6711yescharacteristic
779C4—21no—
780C4—21no—
781C4—41no—
782C4—41no—
783C4—61no—
784C4—61no—
785C4—121no—
786C4—121no—
787C4—121no—
788C4—361no—
789C4#6430611yescharacteristic
790C4#6430711yescharacteristic
791C3—21no—
792C3#8061911yescharacteristic, complemented
793C3#8363511yescharacteristic, complemented
794C2—62no—
795C2—121no—
796C2—241no—
797C2—362no—
798C2#1059507011yescharacteristic
799C2D3×#94211yescharacteristic
800C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594007C2
hypercenterC4×Q8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5579C2semidirect
3. #10592725C2semidirect
4. C3×#5028C2semidirect
5. #10591657C2semidirect
6. #10591651C2semidirect
7. #10591635C2semidirect
8. #10591587C2semidirect
9. #10590609C2semidirect
10. D3×#809C2semidirect
11. #10590517C2semidirect
12. #10590498C2semidirect
13. #10590330C2semidirect
14. #10590313C2semidirect
15. #10590280C2semidirect
20. C32×C4×Q8C22semidirect
24. C3×#946C22semidirect
25. C2×C3×#216C22semidirect
30. C3×D3×C4⋊C4C22semidirect
35. C3×#869C22semidirect
42. C2×#3711C22semidirect
44. #63662C22semidirect
46. #63634C22semidirect
47. #63630C22semidirect
48. C3×#810C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
63. #5579D3semidirect
77. #5028D3semidirect
159. C3×C4×Q8C2×D3semidirect
160. C3×C4×Q8C2×D3semidirect
167. #946C2×D3semidirect
168. C2×#216C2×D3semidirect
185. D3×C4⋊C4C2×D3semidirect
199. #869C2×D3semidirect
220. #810C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
457. C4×Q8D32semidirect
703. C32#3314semidirect
792. C3#80619semidirect
793. C3#83635semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
#105940072
#105927252
C3×#50282
#105916572
#105916512
#105916352
#105915872
#105906092
D3×#8092
#105905172
#105904982
#105903302
#105903132
#105902802
#836353
#806193