Finite Group Databasebeta

← #10972990

Subgroups — #10972990

Order 768.

2534 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5522C211yesmaximal, characteristic, complemented
2C2×#5510C211yesmaximal, characteristic
3C3×#2317C211yesmaximal, characteristic, complemented
4#82270C211yesmaximal, characteristic, complemented
5#82270C211yesmaximal, characteristic, complemented
6#82228C211yesmaximal, characteristic, complemented
7C2×#4972C211yesmaximal, characteristic, complemented
8#76287C212yesmaximal, complemented
9#76286C212yesmaximal, complemented
10#76249C212yesmaximal, complemented
11#76102C212yesmaximal, complemented
12#74419C214yesmaximal, complemented
13#74418C214yesmaximal, complemented
14#74363C212yesmaximal, complemented
15#74362C212yesmaximal, complemented
16#74232C212yesmaximal, complemented
17#74231C212yesmaximal, complemented
18#35255—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C2×C3×#117C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C2×#930C2214yes—
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28#5522—28no—
29#5510—28no—
30C2×#897C2212yes—
31C2×#897C2212yes—
32C2×#895C2212yes—
33C2×#895C2212yes—
34C2×#894C2214yes—
35C2×#893C2211yescharacteristic
36C2×#893C2211yescharacteristic
37C2×#887C2211yescharacteristic
38C2×#887C2211yescharacteristic
39C2×#67⋊C4C2212yes—
40C2×#67⋊C4C2212yes—
41C2×#872C2212yes—
42C2×C42×D3C2212yes—
43C3×#389C2212yes—
44C3×#389C2212yes—
45C3×#385C2214yes—
46C3×#384C2212yes—
47C3×#382C2212yes—
48C2×C3⋊#95C2212yes—
49#4993C2214yes—
50#4992C2214yes—
51#4991C2214yes—
52#4990C2214yes—
53#4989C2214yes—
54#4988C2211yescharacteristic
55#4988C2211yescharacteristic
56#4987C2212yes—
57#4987C2212yes—
58#4987C2212yes—
59#4987C2212yes—
60#4982C2214yes—
61#4980C2214yes—
62#4973C2211yescharacteristic
63#4973C2211yescharacteristic
64#4972C2212yes—
65#4972C2212yes—
66#4972C2212yes—
67#4972C2212yes—
68#4958C2212yes—
69#4958C2212yes—
70#4958C2214yes—
71#4958C2214yes—
72#4939C2212yes—
73#4939C2212yes—
74C4×(C2×D3)⋊C4C2212yes—
75C4×(C2×D3)⋊C4C2212yes—
76#4929C2212yes—
77#4929C2212yes—
78#4675C2214yes—
79#4675C2214yes—
80#4672C2214yes—
81#4669C2214yes—
82#4665C2214yes—
83#4664C2214yes—
84#4660C2214yes—
85#4655C2214yes—
86C2×#537—31no—
87C2×C4×#41—31no—
88#2855—32no—
89#2854—32no—
90#2625—32no—
91#2624—32no—
92#2444—34no—
93#2443—34no—
94#2423—32no—
95#2422—32no—
96#2421—32no—
97#2420—32no—
98#2317D311yescharacteristic, complemented
99#2311—31no—
100#2311—31no—
101#2297—31no—
102C2×#389—31no—
103C23×C3×C4C2312yes—
104C23×C3×C4C2311yescharacteristic
105C22×#67C2312yes—
106C22×#67C2312yes—
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2312yes—
110C2×#235—24no—
111C2×#235—24no—
112C2×#235—24no—
113C2×#235—24no—
114C2×#235—24no—
115C2×#235D418yes—
116C22×D12C2311yescharacteristic
117C22×D12C2311yescharacteristic
118C22×D12C2314yes—
119C22×C4×D3C2312yes—
120C22×C4×D3C2312yes—
121C22×C4×D3C2312yes—
122C22×C4×D3C2312yes—
123C22×Dic6C2311yescharacteristic
124C22×Dic6C2311yescharacteristic
125C3×#117—24no—
126C3×#117—24no—
127C2×C3×C4⋊C4—24no—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C42C2312yes—
139C2×C3×C42C2312yes—
140#930—216no—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×C4⋊Dic3—24no—
154C2×C4⋊Dic3C2314yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×Dic3⋊C4—44no—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2314yes—
162C2×C4×Dic3—24no—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2311yescharacteristic
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2311yescharacteristic
169#897—28no—
170#897—28no—
171#895—28no—
172#895—28no—
173#894—48no—
174#893—24no—
175#893—24no—
176#887—24no—
177#887—24no—
178#67⋊C4—28no—
179#67⋊C4—28no—
180#872—28no—
181C42×D3—28no—
182C3×#95C2314yes—
183C3×#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C22×#41—31no—
195C22×#41—31no—
196#537—68no—
197C2×#123—34no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×#121—34no—
201C2×#121—32no—
202C2×#121—32no—
203C4×#41—68no—
204C2×C4×Q8—31no—
205C2×C4×Q8—31no—
206C2×C4×D4—31no—
207C2×C4×D4—31no—
208C2×C4×D4—32no—
209C2×C4×D4—32no—
210C2×#117—32no—
211C2×#117C2×D311yescharacteristic
212C2×#117C2×D311yescharacteristic
213C22×C4⋊C4—31no—
214C22×C4⋊C4—32no—
215C22×C4⋊C4C2×D311yescharacteristic
216C22×C42—31no—
217C22×C42—32no—
218#400—34no—
219#399—34no—
220#398—34no—
221#397—34no—
222#397—34no—
223#397—34no—
224#394—34no—
225#394—34no—
226#391—31no—
227#391—31no—
228#391—32no—
229#391—32no—
230#390—31no—
231#390—31no—
232#390—32no—
233#390—32no—
234#389—32no—
235#389—32no—
236#389—32no—
237#389—32no—
238#389C2×D312yes—
239#389C2×D312yes—
240#388—34no—
241#388—34no—
242#387—34no—
243#387—34no—
244#386—34no—
245#386—34no—
246#386—32no—
247#386—32no—
248#386—34no—
249#385—34no—
250#385C2×D314yes—
251#384C2×D312yes—
252#382C2×D312yes—
253#381—34no—
254#380—32no—
255#380—32no—
256#380—32no—
257#380—32no—
258C4×C22⋊C4—32no—
259C4×C22⋊C4—32no—
260C2×#95—32no—
261C24×C3C2411yescharacteristic
262C23×D3C2412yes—
263C23×D3C2412yes—
264C22×C3×C4—24no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4C2×D414yes—
268C22×C3×C4#4114yes—
269C22×C3×C4#4114yes—
270C22×C3×C4C2412yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2414yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—24no—
278C2×#67—24no—
279C2×#67—24no—
280C2×#67—24no—
281C2×#67—24no—
282C2×#67C2×D418yes—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—24no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—42no—
289C22×Dic3—41no—
290C22×Dic3—41no—
291C22×Dic3—42no—
292C22×Dic3C2412yes—
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2414yes—
295C22×Dic3C2411yescharacteristic
296C22×Dic3C2412yes—
297C22×Dic3C2411yescharacteristic
298C22×Dic3C2411yescharacteristic
299#235—232no—
300#235—416no—
301C2×D12—22no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—22no—
305C2×D12—22no—
306C2×D12—28no—
307C2×D12—44no—
308C2×D12—44no—
309C2×D12C2×D414yes—
310C2×C4×D3—24no—
311C2×C4×D3—24no—
312C2×C4×D3—24no—
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—24no—
317C2×C4×D3—24no—
318C2×C4×D3—24no—
319C2×C4×D3—42no—
320C2×C4×D3—42no—
321C2×C4×D3C2×D418yes—
322C2×Dic6—22no—
323C2×Dic6—22no—
324C2×Dic6—22no—
325C2×Dic6—22no—
326C2×Dic6—22no—
327C2×Dic6C2×D414yes—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—24no—
331C3×C4⋊C4—24no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—44no—
335C3×C4⋊C4—44no—
336C3×C22⋊C4—24no—
337C3×C22⋊C4—24no—
338C3×C42—24no—
339C3×C42—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—28no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—44no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—42no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—42no—
352C4⋊Dic3—24no—
353C4⋊Dic3—24no—
354C4⋊Dic3—28no—
355Dic3⋊C4—24no—
356Dic3⋊C4—24no—
357Dic3⋊C4—28no—
358Dic3⋊C4—44no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—22no—
362C4×Dic3—22no—
363C4×Dic3—24no—
364C4×Dic3—24no—
365C2×#41—38no—
366C2×#41—64no—
367C2×#41—64no—
368C2×#41—64no—
369C2×#41—64no—
370C2×#41—64no—
371C22×Q8—31no—
372C22×Q8—31no—
373C22×D4—32no—
374C22×D4—32no—
375C22×D4—31no—
376C22×D4—31no—
377C22×D4—34no—
378C23×C4—32no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—32no—
382C23×C4—32no—
383C23×C4—32no—
384C23×C4—32no—
385C23×C4C22×D312yes—
386C23×C4C22×D311yescharacteristic
387#123—128no—
388C22⋊Q8—68no—
389C22⋊Q8—68no—
390#121—68no—
391#121—68no—
392#121—616no—
393C4×Q8—64no—
394C4×Q8—64no—
395C4×D4—68no—
396C4×D4—68no—
397C4×D4—64no—
398C4×D4—64no—
399#117—24no—
400#117—24no—
401#117—68no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—64no—
411C2×C4⋊C4—124no—
412C2×C4⋊C4C22×D312yes—
413C2×C4⋊C4C22×D312yes—
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C4⋊C4C22×D314yes—
419C2×C4⋊C4C22×D314yes—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4C22×D312yes—
433C2×C22⋊C4C22×D312yes—
434C2×C42—31no—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42—32no—
438C2×C42—32no—
439C2×C42—31no—
440C2×C42—68no—
441C2×C42—64no—
442C2×C42C22×D312yes—
443C2×C42C22×D312yes—
444#95—34no—
445#95—34no—
446#95—32no—
447#95—32no—
448#95—32no—
449#95—32no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95C22×D314yes—
455#95C22×D314yes—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3C22×D412yes—
461C23×C3C2×#4112yes—
462C23×C3C2×#4112yes—
463C23×C3C2511yescharacteristic
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3C22×D414yes—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—24no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—24no—
493C2×C3×C4—84no—
494C2×C3×C4#123116yescomplemented
495C2×C3×C4C22×D412yes—
496C2×C3×C4C22×D412yes—
497C2×C3×C4C2×#4112yes—
498C2×C3×C4C2×#4112yes—
499C2×C3×C4C2×#4112yes—
500C2×C3×C4C2×#4112yes—
501#67—216no—
502#67—48no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—22no—
512C2×Dic3—24no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—24no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—24no—
520C2×Dic3—21no—
521C2×Dic3—44no—
522C2×Dic3—44no—
523C2×Dic3—48no—
524C2×Dic3C22×D414yes—
525C2×Dic3H(5,𝔽2)12yes—
526C2×Dic32−1+412yes—
527D12—28no—
528D12—44no—
529D12—88no—
530C4×D3—216no—
531C4×D3—48no—
532C4×D3—48no—
533C4×D3—48no—
534Dic6—28no—
535Dic6—44no—
536C24—32no—
537C24—32no—
538C24C23×D311yescharacteristic
539#41—632no—
540#41—1216no—
541C2×Q8—34no—
542C2×Q8—62no—
543C2×Q8—62no—
544C2×Q8—62no—
545C2×Q8—62no—
546C2×Q8—62no—
547C2×D4—38no—
548C2×D4—34no—
549C2×D4—68no—
550C2×D4—64no—
551C2×D4—64no—
552C2×D4—64no—
553C2×D4—64no—
554C2×D4—64no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—62no—
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—124no—
561C2×D4—124no—
562C22×C4—24no—
563C22×C4—31no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—38no—
567C22×C4—32no—
568C22×C4—31no—
569C22×C4—34no—
570C22×C4—31no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—64no—
574C22×C4—64no—
575C22×C4—64no—
576C22×C4—64no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—64no—
580C22×C4—64no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—64no—
584C22×C4—64no—
585C22×C4—64no—
586C22×C4—64no—
587C22×C4—122no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4—121no—
591C22×C4—121no—
592C22×C4—122no—
593C22×C4#23514yes—
594C22×C4D3×D414yes—
595C22×C4#23914yes—
596C22×C4C23×D312yes—
597C22×C4C23×D312yes—
598C22×C4C23×D312yes—
599C22×C4C23×D314yes—
600C22×C4C23×D312yes—
601C22×C4C23×D311yescharacteristic
602C22×C4C23×D311yescharacteristic
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—68no—
612C4⋊C4—64no—
613C4⋊C4—64no—
614C4⋊C4—68no—
615C4⋊C4—64no—
616C4⋊C4—64no—
617C4⋊C4—124no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—68no—
621C22⋊C4—64no—
622C22⋊C4—64no—
623C22⋊C4—64no—
624C22⋊C4—64no—
625C22⋊C4—68no—
626C22⋊C4—124no—
627C22⋊C4—124no—
628C22⋊C4—122no—
629C22⋊C4—124no—
630C22⋊C4—122no—
631C22⋊C4—124no—
632C42—24no—
633C42—24no—
634C42—64no—
635C42—64no—
636C42—62no—
637C42—62no—
638C42—62no—
639C42—62no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3C2×#12314yes—
647C22×C3C23×D411yescharacteristic
648C22×C3C22×#4111yescharacteristic
649C22×C3C22×#4111yescharacteristic
650C22×C3C2×H(5,𝔽2)11yescharacteristic
651C22×C3C2×2−1+411yescharacteristic
652C22×C3#58511yescharacteristic
653C22×C3#58511yescharacteristic
654C2×D3—24no—
655C2×D3—24no—
656C2×D3—24no—
657C2×D3—42no—
658C2×D3—42no—
659C2×D3—42no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C3×C4—42no—
669C3×C4—44no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4—42no—
673C3×C4C2×#12314yes—
674C3×C4C2×#12314yes—
675Dic3—24no—
676Dic3—22no—
677Dic3—22no—
678Dic3—42no—
679Dic3—44no—
680Dic3—41no—
681Dic3—41no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—34no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23—62no—
692C23—62no—
693C23—62no—
694C23—62no—
695C23—62no—
696C23—62no—
697C23—62no—
698C23—62no—
699C23—62no—
700C23C2×#23512yes—
701C23C2×D3×D412yes—
702C23C2×#23912yes—
703C23C24×D311yescharacteristic
704Q8—68no—
705Q8—124no—
706D4—616no—
707D4—68no—
708D4—128no—
709D4—124no—
710D4—248no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—34no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—62no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—616no—
736C2×C4—62no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—62no—
740C2×C4—64no—
741C2×C4—62no—
742C2×C4—64no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—64no—
747C2×C4—61no—
748C2×C4—84no—
749C2×C4—128no—
750C2×C4—128no—
751C2×C4—124no—
752C2×C4—124no—
753C2×C4—128no—
754C2×C4—128no—
755C2×C4#894116yescomplemented
756C2×C4C2×#23512yes—
757C2×C4C2×#23512yes—
758C2×C4C2×D3×D412yes—
759C2×C4C2×D3×D412yes—
760C2×C4C2×#23912yes—
761C2×C4C2×#23912yes—
762C2×C3—24no—
763C2×C3C22×#12311yescharacteristic
764C2×C3#346011yescharacteristic
765C2×C3#346111yescharacteristic
766C2×C3#348811yescharacteristic
767C2×C3#348911yescharacteristic
768C2×C3#351111yescharacteristic
769C2×C3#351211yescharacteristic
770D3—44no—
771D3—82no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—64no—
779C22—64no—
780C22—64no—
781C22—122no—
782C22—122no—
783C22—122no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22C2×#89414yes—
793C22C22×#23511yescharacteristic
794C22C22×D3×D411yescharacteristic
795C22C22×#23911yescharacteristic
796C22D3×H(5,𝔽2)11yescharacteristic
797C22#596611yescharacteristic
798C22D3×2−1+411yescharacteristic
799C22#596811yescharacteristic
800C4—44no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—62no—
806C4—62no—
807C4—64no—
808C4—124no—
809C4—121no—
810C4—121no—
811C4—122no—
812C4C2×#89414yes—
813C4C2×#89414yes—
814C3#3525511yescharacteristic, complemented, Sylow
815C2—24no—
816C2—124no—
817C2—242no—
818C2C22×#89411yescharacteristic
819C2#8589311yescharacteristic
820C2#8589411yescharacteristic
821C2#8633111yescharacteristic
822C2#8635611yescharacteristic
823C2#8658211yescharacteristic
824C2#8658311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2317C2
prime radicalC2×#5510C2
hypercenter#2317D3
hypocenterC3#35255
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
1. C2×#5522C2semidirect
3. C3×#2317C2semidirect
4. #82270C2semidirect
5. #82270C2semidirect
6. #82228C2semidirect
7. C2×#4972C2semidirect
8. #76287C2semidirect
9. #76286C2semidirect
10. #76249C2semidirect
11. #76102C2semidirect
12. #74419C2semidirect
13. #74418C2semidirect
14. #74363C2semidirect
15. #74362C2semidirect
16. #74232C2semidirect
17. #74231C2semidirect
98. #2317D3semidirect
494. C2×C3×C4#123semidirect
755. C2×C4#894semidirect
814. C3#35255semidirect

Maximal subgroups

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

subgroupindex
C2×#55222
C2×#55102
C3×#23172
#822702
#822282
C2×#49722
#762872
#762862
#762492
#761022
#744192
#744182
#743632
#743622
#742322
#742312
#352553