Finite Group Databasebeta

← #11675223

Subgroups — #11675223

Order 768.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3503C211yesmaximal, characteristic, complemented
2#86262C211yesmaximal, characteristic, complemented
3#83707C212yesmaximal, complemented
4#83704C212yesmaximal, complemented
5#83698C212yesmaximal, complemented
6#83689C212yesmaximal, complemented
7#83644C212yesmaximal, complemented
8#83637C212yesmaximal, complemented
9#83568C212yesmaximal, complemented
10#83563C212yesmaximal, complemented
11#83480C212yesmaximal, complemented
12#83471C212yesmaximal, complemented
13#83328C211yesmaximal, characteristic, complemented
14#83212C211yesmaximal, characteristic, complemented
15C2×#5093C211yesmaximal, characteristic, complemented
16#82572C212yesmaximal
17#82571C212yesmaximal, complemented
18#82533C211yesmaximal, characteristic, complemented
19C4×#950C211yesmaximal, characteristic
20#61330—31nomaximal, Sylow
21C3×Q82C2212yes—
22C3×#557C2212yes—
23C3×#554—22no—
24C3×#554C2212yes—
25C3×D4×Q8—22no—
26C3×D4×Q8C2212yes—
27C3×#544—22no—
28C3×#544C2212yes—
29C3×#533—21no—
30C3×#533C2211yescharacteristic
31C2×C3×C4⋊Q8—21no—
32C2×C3×C4⋊Q8C2211yescharacteristic
33C3×#520C2212yes—
34C3×C4×#41C2211yescharacteristic
35C2×#951C2212yes—
36C2×#950C2211yescharacteristic
37#5728—21no—
38#5728—21no—
39#5698—22no—
40#5642—22no—
41#5642—22no—
42#5584C2212yes—
43#5584C2212yes—
44#5570C2212yes—
45#5570C2212yes—
46#5526C2212yes—
47#5516C2212yes—
48C4×#235C2211yescharacteristic
49C2×#869C2211yescharacteristic
50#5233C2211yescharacteristic
51#5094C2212yes—
52#5094C2214yes—
53#5093C2214yes—
54#5093C2212yes—
55#5093C2212yes—
56#5093C2212yes—
57#5093C2212yes—
58#5091C2212yes—
59#5091C2214yes—
60#5089C2214yes—
61#5087C2212yes—
62#5084C2212yes—
63#5069C2214yes—
64#5068C2214yes—
65#5063C2214yes—
66#5063C2214yes—
67#5031C2212yes—
68#5031C2212yes—
69#5031C2214yes—
70#5030C2214yes—
71C4×#216C2211yescharacteristic
72C4×#216C2211yescharacteristic
73C4×#216C2214yes—
74#5028C2214yes—
75C4×#215C2211yescharacteristic
76C4×#215C2211yescharacteristic
77#5024C2212yes—
78#5024C2212yes—
79Q8×C3⋊C8C2212yes—
80Q8×C3⋊C8C2212yes—
81#5019C2212yes—
82#5019C2212yes—
83#5019C2214yes—
84#5018C2214yes—
85C4×#214C2211yescharacteristic
86C4×#214C2211yescharacteristic
87C4×#214C2214yes—
88#5016C2214yes—
89C4×#213C2211yescharacteristic
90C4×#213C2211yescharacteristic
91#5004C2212yes—
92#5002C2211yescharacteristic
93#4999C2212yes—
94#4998C2211yescharacteristic
95#4997C2212yes—
96C2×#810C2212yes—
97C2×#810C2212yes—
98#4966C2212yes—
99#4964C2212yes—
100#4924C2211yescharacteristic
101C2×C4×C3⋊C8C2211yescharacteristic
102#3509—31no—
103#3503D311yescharacteristic, complemented
104#3374—32no—
105#3372—32no—
106#3369—32no—
107#3367—32no—
108#3364—32no—
109#3363—32no—
110#3360—32no—
111#3359—32no—
112#3137—32no—
113C2×#487—31no—
114#3082—32no—
115#3079—31no—
116#3046—32no—
117#3039—31no—
118#2960—31no—
119#2947—32no—
120C4×#135—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8—22no—
123C22×C3×Q8—21no—
124C2×#235C2311yescharacteristic
125C22×Dic6C2312yes—
126C3×C4⋊Q8—22no—
127C3×C4⋊Q8—22no—
128C3×C4⋊Q8—24no—
129C3×C4⋊Q8—22no—
130C3×C4⋊Q8—21no—
131C3×C4⋊Q8—21no—
132C3×C4⋊Q8D411yescharacteristic
133C3×C4⋊Q8D411yescharacteristic
134C3×C4⋊Q8C2312yes—
135C3×C4⋊Q8C2314yes—
136C3×C4⋊Q8C2312yes—
137C3×#125—22no—
138C3×#125—24no—
139C3×#125D412yes—
140C3×#125C2314yes—
141C3×C22⋊Q8—22no—
142C3×C22⋊Q8—22no—
143C3×C22⋊Q8—24no—
144C3×C22⋊Q8—24no—
145C3×C22⋊Q8—24no—
146C3×C22⋊Q8D412yes—
147C3×C22⋊Q8D412yes—
148C3×C4×Q8—22no—
149C3×C4×Q8—22no—
150C3×C4×Q8C2311yescharacteristic
151C3×C4×Q8C2314yes—
152C3×C4×Q8C2311yescharacteristic
153C3×C4×Q8C2312yes—
154C3×C4×Q8C2312yes—
155C3×C4×D4—21no—
156C3×C4×D4—21no—
157C3×C4×D4—24no—
158C3×C4×D4C2311yescharacteristic
159C3×C4×D4C2311yescharacteristic
160C3×C4×D4C2314yes—
161C3×#117—22no—
162C3×#117—21no—
163C3×#117C2311yescharacteristic
164C3×#117C2312yes—
165C2×C3×C4⋊C4—21no—
166C2×C3×C4⋊C4—22no—
167C2×C3×C4⋊C4—22no—
168C2×C3×C4⋊C4C2312yes—
169C2×C3×C42—21no—
170C2×C3×C42C2311yescharacteristic
171#951—28no—
172#950—24no—
173#946—22no—
174#946—22no—
175Q8×Dic3—22no—
176Q8×Dic3—22no—
177C2×#216C2314yes—
178C2×#216C2311yescharacteristic
179C2×#215C2311yescharacteristic
180C2×#214C2314yes—
181C2×#214C2311yescharacteristic
182C2×#213C2311yescharacteristic
183C4×#67—21no—
184C4×#67—21no—
185#926C2311yescharacteristic
186C2×C4⋊Dic3—21no—
187C2×C4⋊Dic3—21no—
188C2×#208C2312yes—
189C22×C3⋊C8C2311yescharacteristic
190C22×C3⋊C8C2311yescharacteristic
191#898—24no—
192#898—24no—
193#897—22no—
194#897—22no—
195#892—22no—
196#892—22no—
197#890—24no—
198#890—24no—
199#890—22no—
200#890—22no—
201#887—22no—
202#887—22no—
203#886—24no—
204#877—24no—
205#875C2314yes—
206C4×D12C2311yescharacteristic
207C4×D12C2311yescharacteristic
208#872—21no—
209C42×D3—21no—
210#869—21no—
211#869—21no—
212#869C2312yes—
213#869C2312yes—
214#869C2314yes—
215C4×Dic6C2311yescharacteristic
216C4×Dic6C2311yescharacteristic
217C4×Dic6C2314yes—
218C4×Dic6C2314yes—
219#835C2311yescharacteristic
220#835C2311yescharacteristic
221#832C2311yescharacteristic
222#832C2311yescharacteristic
223#810C2314yes—
224#810C2314yes—
225#810C2314yes—
226#810C2314yes—
227#810C2314yes—
228#810C2311yescharacteristic
229#810C2311yescharacteristic
230#810C2314yes—
231#810C2314yes—
232#809C2314yes—
233#809C2311yescharacteristic
234#809C2311yescharacteristic
235#808C2314yes—
236#808C2311yescharacteristic
237#808C2311yescharacteristic
238#807C2314yes—
239#807C2311yescharacteristic
240#807C2311yescharacteristic
241C4⋊(C3⋊C8)C2312yes—
242C4⋊(C3⋊C8)C2312yes—
243C4⋊(C3⋊C8)C2314yes—
244C4⋊(C3⋊C8)C2314yes—
245#803C2314yes—
246C4×C3⋊C8C2311yescharacteristic
247C4×C3⋊C8C2311yescharacteristic
248C4×C3⋊C8C2311yescharacteristic
249C4×C3⋊C8C2311yescharacteristic
250C4×C3⋊C8C2314yes—
251C2×#137—32no—
252C2×#135—31no—
253Q82C2×D312yes—
254#557—32no—
255#557—32no—
256#557C2×D312yes—
257#556—32no—
258#556—32no—
259#554—22no—
260#554C2×D312yes—
261#552—62no—
262#552—62no—
263D4×Q8—22no—
264D4×Q8C2×D312yes—
265#544—22no—
266#544C2×D312yes—
267#541—62no—
268#536—32no—
269#533—21no—
270#533—61no—
271#533—61no—
272#533C2×D311yescharacteristic
273C2×C4⋊Q8—21no—
274C2×C4⋊Q8—31no—
275C2×C4⋊Q8C2×D311yescharacteristic
276#520C2×D312yes—
277#519—32no—
278C4×#41—31no—
279C4×#41C2×D311yescharacteristic
280#491—34no—
281#489—34no—
282#488—34no—
283#487—34no—
284#487—32no—
285#487—32no—
286#487—32no—
287#487—32no—
288#479—34no—
289#479—34no—
290#477—32no—
291#477—34no—
292#476—32no—
293#475—32no—
294#475—34no—
295#474—32no—
296#464—34no—
297#463—34no—
298#462—32no—
299#462—34no—
300#462—32no—
301#461—32no—
302#461—34no—
303#461—32no—
304#446—32no—
305#446—32no—
306C8×Q8—32no—
307C8×Q8—32no—
308#441—34no—
309#440—34no—
310C4×Q16—31no—
311C4×Q16—34no—
312C4×Q16—31no—
313C4×SD16—31no—
314C4×SD16—31no—
315C4×SD16—31no—
316C4×SD16—34no—
317C4×SD16—31no—
318C4×D8—31no—
319C4×D8—31no—
320#428—32no—
321#427—31no—
322#424—32no—
323#423—31no—
324#419—32no—
325#417—32no—
326#416—31no—
327#416—31no—
328C2×#103—32no—
329C2×#103—32no—
330#405—32no—
331C2×C4×C8—31no—
332C3×#41—22no—
333C3×#41#4114yes—
334C2×C3×Q8—22no—
335C2×C3×Q8—24no—
336C2×C3×Q8—22no—
337C2×C3×Q8—82no—
338C2×C3×Q8—84no—
339C2×C3×Q8C2×D412yes—
340C2×C3×Q8C2×D412yes—
341C2×C3×Q8C2411yescharacteristic
342C2×C3×D4—21no—
343C2×C3×D4C2411yescharacteristic
344C22×C3×C4—21no—
345C22×C3×C4—22no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—24no—
349C22×C3×C4C2×D411yescharacteristic
350C22×C3×C4C2×D411yescharacteristic
351C22×C3×C4C2411yescharacteristic
352C2×#67—21no—
353C22×Dic3—22no—
354#235—22no—
355#235—22no—
356C2×D12C2411yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×Dic6—24no—
361C2×Dic6—24no—
362C2×Dic6—22no—
363C2×Dic6C2411yescharacteristic
364C2×Dic6C2414yes—
365C3×C4⋊C4—22no—
366C3×C4⋊C4—22no—
367C3×C4⋊C4—24no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—24no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—24no—
373C3×C4⋊C4—24no—
374C3×C4⋊C4C2×D412yes—
375C3×C4⋊C4C2×D412yes—
376C3×C4⋊C4C2×D412yes—
377C3×C4⋊C4C2×D412yes—
378C3×C4⋊C4C2×D414yes—
379C3×C4⋊C4C2×D414yes—
380C3×C4⋊C4C2414yes—
381C3×C4⋊C4C2411yescharacteristic
382C3×C4⋊C4C2411yescharacteristic
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—24no—
387C3×C22⋊C4C2×D414yes—
388C3×C42—21no—
389C3×C42—21no—
390C3×C42—21no—
391C3×C42—24no—
392C3×C42C2×D411yescharacteristic
393C3×C42C2×D411yescharacteristic
394C3×C42C2411yescharacteristic
395C3×C42C2411yescharacteristic
396C3×C42C2414yes—
397#217—21no—
398#216—22no—
399#216—28no—
400#215—22no—
401#214—22no—
402#214—28no—
403#213—22no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—24no—
407(C2×D3)⋊C4—24no—
408C4⋊Dic3—22no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3—22no—
412C4⋊Dic3—24no—
413C4⋊Dic3—24no—
414C4⋊Dic3C2411yescharacteristic
415C4⋊Dic3C2411yescharacteristic
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—24no—
419Dic3⋊C4—24no—
420C4×Dic3—21no—
421C4×Dic3—21no—
422C4×Dic3—24no—
423C4×Dic3—24no—
424C4×Dic3—21no—
425#208—24no—
426C2×C3⋊C8—22no—
427C2×C3⋊C8—22no—
428C2×C3⋊C8C2411yescharacteristic
429C2×C3⋊C8C2411yescharacteristic
430C2×C3⋊C8C2411yescharacteristic
431C2×C3⋊C8C2411yescharacteristic
432C2×C3⋊C8C2414yes—
433C2×#41—31no—
434C2×#41C22×D311yescharacteristic
435C22×Q8—22no—
436C22×Q8—21no—
437C22×Q8—32no—
438#137—68no—
439#135—64no—
440C2×Q16—31no—
441C2×Q16—34no—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×SD16—34no—
445C2×D8—31no—
446C2×M16—32no—
447C22×C8—31no—
448C22×C8—31no—
449C4⋊Q8—22no—
450C4⋊Q8—22no—
451C4⋊Q8—22no—
452C4⋊Q8—24no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—32no—
456C4⋊Q8—32no—
457C4⋊Q8—34no—
458C4⋊Q8—61no—
459C4⋊Q8—61no—
460C4⋊Q8#6711yescharacteristic
461C4⋊Q8#6711yescharacteristic
462C4⋊Q8C22×D312yes—
463C4⋊Q8C22×D312yes—
464C4⋊Q8C22×D314yes—
465#126—64no—
466#126—64no—
467#125—22no—
468#125—24no—
469#125—62no—
470#125—62no—
471#125—64no—
472#125—64no—
473#125#6712yes—
474#125C22×D314yes—
475#124—34no—
476#123—64no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—24no—
480C22⋊Q8—24no—
481C22⋊Q8—24no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C22⋊Q8#6712yes—
487C22⋊Q8#6712yes—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—31no—
491C4×Q8—31no—
492C4×Q8—34no—
493C4×Q8—34no—
494C4×Q8—62no—
495C4×Q8—62no—
496C4×Q8—62no—
497C4×Q8—62no—
498C4×Q8C22×D311yescharacteristic
499C4×Q8C22×D311yescharacteristic
500C4×Q8C22×D314yes—
501C4×Q8C22×D312yes—
502C4×Q8C22×D312yes—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—24no—
506C4×D4—31no—
507C4×D4—31no—
508C4×D4—61no—
509C4×D4—61no—
510C4×D4C22×D311yescharacteristic
511C4×D4C22×D311yescharacteristic
512C4×D4C22×D314yes—
513#117—22no—
514#117—21no—
515#117—31no—
516#117—62no—
517#117—62no—
518#117—64no—
519#117—61no—
520#117C22×D311yescharacteristic
521#117C22×D312yes—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—61no—
526C2×C4⋊C4—61no—
527C2×C4⋊C4C22×D312yes—
528C2×C42—21no—
529C2×C42—61no—
530C2×C42C22×D311yescharacteristic
531#107—31no—
532#107—31no—
533#107—34no—
534#106—31no—
535#106—31no—
536#106—34no—
537C4⋊C8—32no—
538C4⋊C8—32no—
539C4⋊C8—34no—
540C4⋊C8—34no—
541#103—31no—
542#103—31no—
543#103—34no—
544#103—34no—
545#103—34no—
546#103—34no—
547#103—31no—
548#103—31no—
549#103—34no—
550#103—34no—
551#103—34no—
552#102—31no—
553#102—31no—
554#102—31no—
555#102—31no—
556#102—34no—
557#97—34no—
558C4×C8—31no—
559C4×C8—31no—
560C4×C8—31no—
561C4×C8—31no—
562C4×C8—34no—
563C23×C3—21no—
564C23×C3C22×D411yescharacteristic
565C22×D3—21no—
566C3×Q8—24no—
567C3×Q8—24no—
568C3×Q8—21no—
569C3×Q8—44no—
570C3×Q8—82no—
571C3×Q8—84no—
572C3×Q8C2×#4112yes—
573C3×D4—24no—
574C3×D4—21no—
575C3×D4C2×#4112yes—
576C2×C3×C4—21no—
577C2×C3×C4—24no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—24no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—84no—
586C2×C3×C4—82no—
587C2×C3×C4C22×D414yes—
588C2×C3×C4C22×D414yes—
589C2×C3×C4C22×D411yescharacteristic
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D411yescharacteristic
593C2×C3×C4C22×D411yescharacteristic
594C2×C3×C4C2×#4112yes—
595C2×C3×C42−1+412yes—
596C2×C3×C4C2511yescharacteristic
597#67—42no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—24no—
602C2×Dic3—44no—
603D12—21no—
604D12—21no—
605C4×D3—42no—
606C4×D3—42no—
607C4×D3—42no—
608Dic6—24no—
609Dic6—21no—
610Dic6—24no—
611Dic6—21no—
612Dic6—44no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—24no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618#41—22no—
619#41—62no—
620#41—62no—
621#41#23914yes—
622C2×Q8—22no—
623C2×Q8—24no—
624C2×Q8—22no—
625C2×Q8—34no—
626C2×Q8—31no—
627C2×Q8—62no—
628C2×Q8—64no—
629C2×Q8—64no—
630C2×Q8—82no—
631C2×Q8—84no—
632C2×Q8C2×#6712yes—
633C2×Q8C2×#6712yes—
634C2×Q8C23×D311yescharacteristic
635C2×D4—21no—
636C2×D4—31no—
637C2×D4—61no—
638C2×D4C23×D311yescharacteristic
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4C2×#6711yescharacteristic
649C22×C4C2×#6711yescharacteristic
650C22×C4C23×D311yescharacteristic
651Q16—62no—
652Q16—68no—
653SD16—62no—
654SD16—62no—
655SD16—68no—
656D8—62no—
657M16—64no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—34no—
663C2×C8—62no—
664C2×C8—62no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—22no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—31no—
675C4⋊C4—31no—
676C4⋊C4—62no—
677C4⋊C4—62no—
678C4⋊C4—62no—
679C4⋊C4—62no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—64no—
683C4⋊C4—64no—
684C4⋊C4—64no—
685C4⋊C4—64no—
686C4⋊C4C2×#6712yes—
687C4⋊C4C2×#6712yes—
688C4⋊C4C2×#6712yes—
689C4⋊C4C2×#6712yes—
690C4⋊C4C2×#6714yes—
691C4⋊C4C2×#6714yes—
692C4⋊C4C23×D314yes—
693C4⋊C4C23×D311yescharacteristic
694C4⋊C4C23×D311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—24no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—64no—
703C22⋊C4—64no—
704C22⋊C4C2×#6714yes—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—24no—
709C42—61no—
710C42—61no—
711C42—61no—
712C42—64no—
713C42—64no—
714C42C2×#6711yescharacteristic
715C42C2×#6711yescharacteristic
716C42C23×D311yescharacteristic
717C42C23×D311yescharacteristic
718C42C23×D314yes—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—22no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3#54812yes—
725C22×C3C23×D411yescharacteristic
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
729C3×C4—22no—
730C3×C4—21no—
731C3×C4—24no—
732C3×C4—21no—
733C3×C4—24no—
734C3×C4—41no—
735C3×C4—44no—
736C3×C4—41no—
737C3×C4#54812yes—
738C3×C4#57712yes—
739C3×C4#57812yes—
740C3×C4C22×#4111yescharacteristic
741C3×C4C2×2−1+411yescharacteristic
742Dic3—44no—
743Dic3—41no—
744Dic3—41no—
745Dic3—41no—
746C23—21no—
747C23—61no—
748C23C22×#6711yescharacteristic
749Q8—21no—
750Q8—24no—
751Q8—24no—
752Q8—44no—
753Q8—64no—
754Q8—61no—
755Q8—64no—
756Q8—61no—
757Q8—82no—
758Q8—84no—
759Q8—124no—
760Q8C2×#23912yes—
761D4—24no—
762D4—21no—
763D4—61no—
764D4—61no—
765D4—122no—
766D4C2×#23912yes—
767C2×C4—21no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—24no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—64no—
779C2×C4—61no—
780C2×C4—84no—
781C2×C4—82no—
782C2×C4—124no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4—122no—
786C2×C4C2×#23912yes—
787C2×C4#100712yes—
788C2×C4C22×#6714yes—
789C2×C4C22×#6714yes—
790C2×C4C22×#6711yescharacteristic
791C2×C4C22×#6711yescharacteristic
792C2×C4C22×#6711yescharacteristic
793C2×C4C22×#6711yescharacteristic
794C2×C4C22×#6711yescharacteristic
795C2×C4C24×D311yescharacteristic
796C8—61no—
797C8—61no—
798C8—64no—
799C8—61no—
800C8—61no—
801C2×C3—22no—
802C2×C3—42no—
803C2×C3C2×#54811yescharacteristic
804C2×C3C2×#57711yescharacteristic
805C2×C3C2×#57811yescharacteristic
806D3—81no—
807C22—21no—
808C22—21no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22#581712yes—
816C22C23×#6711yescharacteristic
817C4—22no—
818C4—21no—
819C4—24no—
820C4—21no—
821C4—24no—
822C4—41no—
823C4—44no—
824C4—41no—
825C4—121no—
826C4—124no—
827C4—121no—
828C4—121no—
829C4#581712yes—
830C4#583612yes—
831C4#583812yes—
832C4C22×#23911yescharacteristic
833C4C2×#100711yescharacteristic
834C3#6133011yescharacteristic, complemented, Sylow
835C2—22no—
836C2—42no—
837C2—241no—
838C2C2×#581711yescharacteristic
839C2C2×#583611yescharacteristic
840C2C2×#583811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3503C2
socleC22×C3C23×D4
prime radicalC2×#950C22
hypercenter#3503D3
hypocenterC3#61330
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. C3×#3503C2semidirect
2. #86262C2semidirect
3. #83707C2semidirect
4. #83704C2semidirect
5. #83698C2semidirect
6. #83689C2semidirect
7. #83644C2semidirect
8. #83637C2semidirect
9. #83568C2semidirect
10. #83563C2semidirect
11. #83480C2semidirect
12. #83471C2semidirect
13. #83328C2semidirect
14. #83212C2semidirect
15. C2×#5093C2semidirect
17. #82571C2semidirect
18. #82533C2semidirect
103. #3503D3semidirect
834. C3#61330semidirect

Maximal subgroups

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

subgroupindex
C3×#35032
#862622
#837072
#837042
#836982
#836892
#836442
#836372
#835682
#835632
#834802
#834712
#833282
#832122
C2×#50932
#825722
#825712
#825332
C4×#9502
#613303