Finite Group Databasebeta

← #11865789

Subgroups — #11865789

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic, complemented
2#10595032C211yesmaximal, characteristic, complemented
3#10594958C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5C2×#63641C211yesmaximal, characteristic, complemented
6C3×#5113C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590876C211yesmaximal, characteristic, complemented
9#10590798C211yesmaximal, characteristic, complemented
10#10590797C211yesmaximal, characteristic, complemented
11#10590796C211yesmaximal, characteristic, complemented
12#10590751C211yesmaximal, characteristic, complemented
13#10590750C211yesmaximal, characteristic, complemented
14#10590749C211yesmaximal, characteristic, complemented
15#10590748C211yesmaximal, characteristic, complemented
16#83900—31nomaximal
17#78861—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C3×#904—24no—
27C2×C3×D24C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30#63980—21no—
31#63980—21no—
32#67⋊Dic3—21no—
33#67⋊Dic3—21no—
34#63914C2211yescharacteristic
35C4×#625—21no—
36C4×#625—21no—
37#63898C2211yescharacteristic
38#63898C2211yescharacteristic
39C4×D3×Dic3—21no—
40#63873C2211yescharacteristic
41#63863C2211yescharacteristic
42#63863C2211yescharacteristic
43#63855—21no—
44#63843C2211yescharacteristic
45#63843C2211yescharacteristic
46C2×#3718C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49#63822—24no—
50C2×#3713C2211yescharacteristic
51#63641C2211yescharacteristic
52#63641C2211yescharacteristic
53#63641C2211yescharacteristic
54#63641C2211yescharacteristic
55C3×#821C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#816C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic
63C2×C3×#135—31no—
64#5832—31no—
65#5832—31no—
66Dic3×#41—31no—
67C2×#950—31no—
68C2×#950—31no—
69C2×#904D311yescharacteristic, complemented
70#5522—31no—
71C3×#416—31no—
72#5233—31no—
73#5185—31no—
74#5182—31no—
75#5166—31no—
76#5165—31no—
77#5163—31no—
78#5162—31no—
79#5153—31no—
80#5150—31no—
81#5113D311yescharacteristic, complemented
82C2×Dic3⋊C8—31no—
83C2×Dic3⋊C8—31no—
84C2×Dic3⋊C8—61no—
85#5002—31no—
86#4819—31no—
87#4818—31no—
88#4798—31no—
89#4795—31no—
90#4787—31no—
91#4786—31no—
92#4767—31no—
93#4762—31no—
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3D411yescharacteristic
96C22×C3⋊Dic3D411yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×#235—22no—
101C3×#235—22no—
102C3×#235—22no—
103C3×#235—22no—
104C3×#235—22no—
105C3×#235D414yescomplemented
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#625—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119C2×C32×C8—22no—
120C2×C32×C8C2311yescharacteristic
121C2×C32×C8C2311yescharacteristic
122C4×C3⋊Dic3D411yescharacteristic
123C4×C3⋊Dic3D411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C4×C3⋊Dic3C2311yescharacteristic
126C2×C3⋊(C3⋊C8)—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4×Dic3—21no—
133C3×Dic12—22no—
134C3×D24—22no—
135C3×#204—22no—
136C3×#204—22no—
137#3724—21no—
138#3724—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32—21no—
148Dic32—21no—
149#3718—22no—
150#3715—22no—
151#3715—22no—
152#3713—22no—
153#3035—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×C3×#41—31no—
157C2×#235C2×D311yescharacteristic
158C2×#235C2×D311yescharacteristic
159C2×#235C2×D311yescharacteristic
160C3×#135—64no—
161C2×C3×Q16—31no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C22×C3×C8—21no—
166C22×C3×C8C2×D311yescharacteristic
167C22×C3×C8C2×D311yescharacteristic
168C3×#117—31no—
169#950—64no—
170#950—64no—
171#947—31no—
172#947—31no—
173Q8×Dic3—31no—
174Q8×Dic3—31no—
175#944—31no—
176#944—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#215—31no—
180C2×#215—31no—
181#940—31no—
182#940—31no—
183#939—61no—
184#939—61no—
185#939—61no—
186#939—61no—
187#936—31no—
188#936—31no—
189D4×Dic3—31no—
190D4×Dic3—31no—
191D4×Dic3—61no—
192D4×Dic3—61no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#213—31no—
196C2×#213—31no—
197C4×#67—61no—
198C4×#67—61no—
199C4×#67—61no—
200C4×#67—61no—
201#926—61no—
202#926C2×D311yescharacteristic
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—61no—
206C2×C4×Dic3—61no—
207C22×C3⋊C8—31no—
208C22×C3⋊C8—31no—
209C22×C3⋊C8—61no—
210C2×Dic12C2×D311yescharacteristic
211#904—24no—
212C2×D24C2×D311yescharacteristic
213C2×#204C2×D311yescharacteristic
214C2×#204C2×D311yescharacteristic
215#893—31no—
216#893—31no—
217#887—31no—
218#887—31no—
219#67⋊C4—61no—
220#67⋊C4—61no—
221#872—61no—
222C42×D3—61no—
223C3×#103—31no—
224C3×#103—31no—
225C3×#102—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#832—31no—
230#832—31no—
231#821C2×D311yescharacteristic
232#821C2×D311yescharacteristic
233#816C2×D311yescharacteristic
234#816C2×D311yescharacteristic
235Dic3⋊C8—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—61no—
244Dic3⋊C8—61no—
245Dic3⋊C8—61no—
246Dic3⋊C8—61no—
247#810—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251C23×C32C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D412yes—
257C2×C32×C4#4112yes—
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—22no—
260C2×C3⋊Dic3—41no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C3×#67—24no—
266C3×#67—42no—
267C3×#67—42no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12C2×D412yes—
279C3×C4×D3—24no—
280C3×C4×D3—42no—
281C3×C4×D3—42no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6C2×D412yes—
288#625—42no—
289#625—42no—
290D3×Dic3—42no—
291D3×Dic3—42no—
292C32×C8—21no—
293C32×C8—21no—
294C3⋊(C3⋊C8)—21no—
295C3⋊(C3⋊C8)—21no—
296C2×#135—31no—
297C2×#135—91no—
298#532—91no—
299C4×#41—91no—
300#464—91no—
301#464—91no—
302#463—91no—
303#463—91no—
304#462—91no—
305#461—91no—
306#460—91no—
307#459—91no—
308C2×C4⋊C8—91no—
309#416—31no—
310#416—91no—
311C3×#41—34no—
312C3×#41—62no—
313C3×#41—62no—
314C3×#41—62no—
315C3×#41—62no—
316C3×#41—62no—
317C2×C3×Q8—31no—
318C2×C3×Q8—31no—
319C2×C3×Q8—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C22×C3×C4—21no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—21no—
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347#235—22no—
348#235—22no—
349#235—22no—
350#235—22no—
351#235—22no—
352#235#6714yescomplemented
353C2×D12C22×D311yescharacteristic
354C2×D12C22×D311yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×C4×D3—21no—
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×Dic6C22×D311yescharacteristic
362C2×Dic6C22×D311yescharacteristic
363C2×Dic6C22×D311yescharacteristic
364C3×Q16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×D8—62no—
368C2×C3×C8—22no—
369C2×C3×C8—22no—
370C2×C3×C8—21no—
371C2×C3×C8—21no—
372C2×C3×C8—42no—
373C2×C3×C8C22×D311yescharacteristic
374C2×C3×C8C22×D311yescharacteristic
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C3×C4⋊C4—31no—
378C3×C4⋊C4—31no—
379C3×C22⋊C4—61no—
380C3×C42—61no—
381#217—21no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#216—62no—
389#216—62no—
390#215—62no—
391#215—62no—
392#214—62no—
393#214—62no—
394#213—62no—
395#213—62no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412C4×Dic3—21no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8—62no—
437C2×C3⋊C8—122no—
438Dic12—22no—
439D24—22no—
440#204—22no—
441#204—22no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32#12112yes—
445C22×C32C22×D411yescharacteristic
446C2×C3×D3—22no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C32×C4#12112yes—
456C32×C4C22×D411yescharacteristic
457C32×C4C2×#4111yescharacteristic
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3#13512yescomplemented
462C3×Dic3—22no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C2×#41—31no—
468C2×#41—31no—
469C2×#41—31no—
470#135—64no—
471#135—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×D8—31no—
479C2×D8—91no—
480C22×C8—91no—
481C22×C8D3211yescharacteristic
482C4⋊Q8—91no—
483#127—91no—
484#124—91no—
485#124—91no—
486#121—181no—
487#121—181no—
488C4×Q8—91no—
489C4×Q8—91no—
490C4×D4—91no—
491C4×D4—91no—
492C4×D4—181no—
493C4×D4—181no—
494C4×D4—181no—
495C4×D4—181no—
496#117—31no—
497#117—181no—
498C2×C42—91no—
499C2×C42—181no—
500C4⋊C8—91no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504#103—31no—
505#103—31no—
506#103—91no—
507#103—91no—
508#102—31no—
509#102—31no—
510#102—91no—
511#102—91no—
512C23×C3—21no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3D3×D411yescharacteristic
517C23×C3D3×D411yescharacteristic
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C3×Q8—32no—
522C3×Q8—61no—
523C3×Q8—61no—
524C3×Q8—61no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×D4—32no—
528C3×D4—64no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—122no—
535C3×D4—122no—
536C2×C3×C4—21no—
537C2×C3×C4—22no—
538C2×C3×C4—21no—
539C2×C3×C4—22no—
540C2×C3×C4—61no—
541C2×C3×C4—64no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—122no—
547C2×C3×C4—122no—
548C2×C3×C4#23512yes—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D412yes—
552C2×C3×C4#23712yes—
553C2×C3×C4C2×#6712yes—
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—24no—
557#67—42no—
558#67—42no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—62no—
581C2×Dic3—62no—
582C2×Dic3—64no—
583C2×Dic3—122no—
584C2×Dic3—122no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—21no—
592D12—21no—
593D12C2×#6712yes—
594C4×D3—24no—
595C4×D3—42no—
596C4×D3—42no—
597C4×D3—122no—
598C4×D3—122no—
599Dic6—21no—
600Dic6—21no—
601Dic6—21no—
602Dic6—21no—
603Dic6—21no—
604Dic6C2×#6712yes—
605C3×C8—21no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—41no—
610C3×C8—41no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—121no—
616C3⋊C8—121no—
617C2×C32—22no—
618C2×C32C2×#12111yescharacteristic
619C2×C32C2×#13511yescharacteristic
620C2×C32#57511yescharacteristic
621C3×D3—42no—
622C3×D3—81no—
623C3×D3—81no—
624#41—34no—
625#41—62no—
626#41—62no—
627#41—62no—
628#41—62no—
629#41—62no—
630C2×Q8—31no—
631C2×Q8—31no—
632C2×Q8—31no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—181no—
640C2×D4—181no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—91no—
645C22×C4—91no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4C2×D3211yescharacteristic
649Q16—62no—
650Q16—182no—
651SD16—62no—
652SD16—62no—
653SD16—182no—
654SD16—182no—
655D8—62no—
656D8—182no—
657C2×C8—22no—
658C2×C8—91no—
659C2×C8—91no—
660C2×C8—182no—
661C2×C8C2×D3211yescharacteristic
662C2×C8C2×D3211yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C22⋊C4—61no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C42—61no—
677C42—91no—
678C42—91no—
679C42—91no—
680C42—91no—
681C42—181no—
682C42—181no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—22no—
691C22×C3—62no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3#88412yes—
701C22×C3#93912yes—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—22no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—22no—
716C3×C4—62no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4#88412yes—
722C3×C4#93912yes—
723C3×C4C2×#23511yescharacteristic
724C3×C4C2×D3×D411yescharacteristic
725C3×C4C2×#23711yescharacteristic
726C3×C4C22×#6711yescharacteristic
727Dic3—22no—
728Dic3—32no—
729Dic3—32no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—62no—
735Dic3—62no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—121no—
743Dic3—121no—
744C32#303511yescharacteristic, complemented, Sylow
745C23—61no—
746C23—61no—
747C23—61no—
748C23#380211yescharacteristic
749Q8—32no—
750Q8—61no—
751Q8—61no—
752Q8—61no—
753Q8—61no—
754Q8—61no—
755D4—32no—
756D4—64no—
757D4—61no—
758D4—61no—
759D4—61no—
760D4—61no—
761D4—61no—
762D4—122no—
763D4—122no—
764D4—362no—
765D4—362no—
766C2×C4—61no—
767C2×C4—64no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—122no—
777C2×C4—122no—
778C2×C4—182no—
779C2×C4—362no—
780C2×C4—362no—
781C2×C4—361no—
782C2×C4#379512yes—
783C2×C4#380211yescharacteristic
784C2×C4D3×#6712yes—
785C2×C4C22×D3211yescharacteristic
786C8—21no—
787C8—21no—
788C8—181no—
789C8—181no—
790C2×C3—24no—
791C2×C3—22no—
792C2×C3—22no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—122no—
797C2×C3—241no—
798C2×C3—241no—
799C2×C3C2×#88411yescharacteristic
800C2×C3D3×#13511yescharacteristic
801C2×C3D3×#13511yescharacteristic
802C2×C3#576811yescharacteristic
803C2×C3#576811yescharacteristic
804C2×C3C2×#93911yescharacteristic
805D3—42no—
806D3—81no—
807D3—81no—
808C22—21no—
809C22—21no—
810C22—62no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22#6388512yes—
820C22C2×#380211yescharacteristic
821C4—62no—
822C4—92no—
823C4—121no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4—181no—
828C4—181no—
829C4—181no—
830C4#6388512yes—
831C4C2×#379511yescharacteristic
832C4C2×D3×#6711yescharacteristic
833C3—21no—
834C3#7886111yescharacteristic, complemented
835C3#8390011yescharacteristic, complemented
836C2—22no—
837C2—122no—
838C2—241no—
839C2—241no—
840C2#1059468411yescharacteristic
841C2#1059468511yescharacteristic
842C2C2×#6388511yescharacteristic
subgroupG/H
centerC2×C4#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#904C2semidirect
2. #10595032C2semidirect
3. #10594958C2semidirect
4. C2×#63822C2semidirect
5. C2×#63641C2semidirect
6. C3×#5113C2semidirect
7. #10591083C2semidirect
8. #10590876C2semidirect
9. #10590798C2semidirect
10. #10590797C2semidirect
11. #10590796C2semidirect
12. #10590751C2semidirect
13. #10590750C2semidirect
14. #10590749C2semidirect
15. #10590748C2semidirect
69. C2×#904D3semidirect
81. #5113D3semidirect
105. C3×#235D4semidirect
352. #235#67semidirect
461. C3⋊Dic3#135semidirect
744. C32#3035semidirect
834. C3#78861semidirect
835. C3#83900semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
#105950322
#105949582
C2×#638222
C2×#636412
C3×#51132
#105910832
#105908762
#105907982
#105907972
#105907962
#105907512
#105907502
#105907492
#105907482
#839003
#788613