Finite Group Databasebeta

← #13178721

Subgroups — #13178721

Order 1728.

1194 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64156C211yesmaximal, characteristic, complemented
2C3×#64155C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723696C211yesmaximal, characteristic
5#11723691C211yesmaximal, characteristic, complemented
6#11723690C212yesmaximal, complemented
7#11723685C212yesmaximal, complemented
8#11723683C212yesmaximal, complemented
9C4×#6294C211yesmaximal, characteristic, complemented
10#11723680C211yesmaximal, characteristic, complemented
11#11723675C212yesmaximal, complemented
12#10595382—31nomaximal
13#10595377—31nomaximal
14#10595376—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×#6295C2212yes—
19C2×#6294C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×#6294C2212yes—
22C3×#3752C2212yes—
23C3×#3752C2212yes—
24C3×#3752C2212yes—
25C3×C4⋊(C3⋊Dic3)C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2212yes—
29C3×C4×C3⋊Dic3C2211yescharacteristic
30C3×C4×C3⋊Dic3C2212yes—
31C3×C4×C3⋊Dic3C2211yescharacteristic
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88814C2212yes—
36#88813C2211yescharacteristic
37#88813C2211yescharacteristic
38#64156D311yescharacteristic, complemented
39#64155D311yescharacteristic, complemented
40Q8×C3⋊Dic3D311yescharacteristic, complemented
41C3×#947—31no—
42C3×#947—31no—
43C3×#947—61no—
44C3×#946—31no—
45C3×#946—31no—
46C3×#946—61no—
47C3×Q8×Dic3—31no—
48C3×Q8×Dic3—31no—
49C3×Q8×Dic3—61no—
50#63916—31no—
51#63909—31no—
52#63908—31no—
53#63902—32no—
54#63898—31no—
55#63894—31no—
56Dic3×D12—31no—
57#63891—32no—
58#63890—32no—
59C4×#624—31no—
60#63880—32no—
61#63880—32no—
62#63878—32no—
63#63877—32no—
64C4×D3×Dic3—31no—
65C4×D3×Dic3—31no—
66#63872—31no—
67#63869—31no—
68#63869—31no—
69#63861—32no—
70#63858—32no—
71#63854—32no—
72#63848—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C33×Q8—22no—
77C2×C33×C4C2312yes—
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C3×C4⋊(C3⋊D3)—22no—
87C3×C4×C3⋊D3—22no—
88#6295—24no—
89#6294—22no—
90#6294—22no—
91#6294—24no—
92#5680—91no—
93#5624—91no—
94#5580—91no—
95C2×C32×Q8—21no—
96C2×C32×Q8—21no—
97C2×C32×Q8—21no—
98C2×C32×Q8—41no—
99C2×C32×Q8C2×D311yescharacteristic
100C2×C32×Q8C2×D311yescharacteristic
101C2×C32×Q8C2×D311yescharacteristic
102C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C2×C3×D12—31no—
105C2×C3×D12—31no—
106C2×C3×D12—61no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—61no—
110C2×#626—32no—
111C2×#626—32no—
112C2×#625—32no—
113C2×#624—32no—
114C2×#624—31no—
115C2×#624—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—31no—
118C2×D3×Dic3—31no—
119C2×D3×Dic3—31no—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122#3752C2×D312yes—
123#3752C2×D312yes—
124#3752C2×D312yes—
125C4⋊(C3⋊Dic3)C2×D312yes—
126C4⋊(C3⋊Dic3)C2×D311yescharacteristic
127C4⋊(C3⋊Dic3)C2×D311yescharacteristic
128#3750C2×D312yes—
129C4×C3⋊Dic3C2×D311yescharacteristic
130C4×C3⋊Dic3C2×D311yescharacteristic
131C4×C3⋊Dic3C2×D312yes—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—62no—
139C3×(C2×D3)⋊C4—62no—
140C3×(C2×D3)⋊C4—62no—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—32no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3—31no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—61no—
148C3×C4⋊Dic3—62no—
149C3×C4⋊Dic3—61no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—62no—
153C3×C4×Dic3—32no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—32no—
156C3×C4×Dic3—31no—
157C3×C4×Dic3—31no—
158C3×C4×Dic3—31no—
159C3×C4×Dic3—61no—
160C3×C4×Dic3—62no—
161C3×C4×Dic3—61no—
162#3724—32no—
163#3724—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168#3722—32no—
169#3722—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179Dic32—31no—
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3—22no—
185C2×C3×C3⋊D3—22no—
186C2×C3×C3⋊D3#4112yes—
187C33×C4—22no—
188C33×C4#4112yes—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3—22no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3#4112yes—
196C3×#124—91no—
197C3×C22⋊Q8—91no—
198C3×C4×Q8—91no—
199#947—31no—
200#947—31no—
201#947—61no—
202#946—31no—
203#946—31no—
204#946—61no—
205Q8×Dic3—31no—
206Q8×Dic3—31no—
207Q8×Dic3—61no—
208#938—91no—
209D4×Dic3—91no—
210#930—91no—
211C2×C4×Dic3—91no—
212#898—92no—
213#898—92no—
214#895—91no—
215#894—92no—
216#893—91no—
217#892—92no—
218#890—91no—
219#890—91no—
220#886—92no—
221#883—92no—
222#67⋊C4—92no—
223#67⋊C4—92no—
224#879—92no—
225#877—92no—
226C4×D12—91no—
227C4×D12—92no—
228#872—92no—
229C42×D3—91no—
230C42×D3—91no—
231#870—91no—
232C22×C3⋊D3C22×D312yes—
233C22×C3⋊D3C22×D311yescharacteristic
234C22×C3×D3—31no—
235C22×C3×D3—31no—
236C22×C3×D3—32no—
237C22×C3×D3—32no—
238C22×C3×D3—61no—
239C22×C3×D3—62no—
240C32×Q8—22no—
241C32×Q8—24no—
242C32×Q8—22no—
243C32×Q8—22no—
244C32×Q8—42no—
245C32×Q8—42no—
246C32×Q8—44no—
247C2×C32×C4—22no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—22no—
252C2×C32×C4—22no—
253C2×C32×C4—41no—
254C2×C32×C4—42no—
255C2×C32×C4C22×D312yes—
256C2×C32×C4C22×D312yes—
257C2×C32×C4C22×D312yes—
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D312yes—
266C2×C3⋊Dic3C22×D312yes—
267C2×C3⋊Dic3C22×D311yescharacteristic
268C4⋊(C3⋊D3)—22no—
269C4×C3⋊D3—22no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—62no—
291C3×D12—62no—
292C3×D12—62no—
293C3×D12—122no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—122no—
297#626—64no—
298#626—64no—
299#625—64no—
300#624—62no—
301#624—64no—
302#624—62no—
303D3×Dic3—64no—
304D3×Dic3—62no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307D3×Dic3—62no—
308D3×Dic3—64no—
309#529—271noSylow
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C3×C3⋊D3—22no—
314C3×C3⋊D3—42no—
315C2×C3×Q8—21no—
316C2×C3×Q8—21no—
317C2×C3×Q8—21no—
318C2×C3×Q8—41no—
319C2×C3×Q8D3211yescharacteristic
320C2×C3×Q8D3211yescharacteristic
321C2×C3×Q8D3211yescharacteristic
322C2×C3×D4—91no—
323C22×C3×C4—91no—
324C2×#67—92no—
325C2×#67—92no—
326C22×Dic3—92no—
327C22×Dic3—91no—
328C22×Dic3—91no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—61no—
332C2×D12—92no—
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—61no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—92no—
341C2×C4×D3—92no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—92no—
345C3×C4⋊C4—92no—
346C3×C22⋊C4—92no—
347C3×C22⋊C4—92no—
348C3×C22⋊C4—92no—
349C3×C42—91no—
350C3×C42—91no—
351C3×C42—92no—
352#217—92no—
353#217—92no—
354(C2×D3)⋊C4—32no—
355(C2×D3)⋊C4—32no—
356(C2×D3)⋊C4—32no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—32no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—92no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—92no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—32no—
371C4⋊Dic3—32no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—62no—
375C4⋊Dic3—61no—
376C4⋊Dic3—92no—
377C4⋊Dic3—92no—
378Dic3⋊C4—32no—
379Dic3⋊C4—32no—
380Dic3⋊C4—62no—
381Dic3⋊C4—92no—
382Dic3⋊C4—92no—
383Dic3⋊C4—92no—
384Dic3⋊C4—92no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—32no—
388C4×Dic3—32no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3—62no—
393C4×Dic3—61no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—91no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—41no—
404C22×C32C23×D311yescharacteristic
405C22×C32C23×D311yescharacteristic
406C22×C32C23×D311yescharacteristic
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—22no—
411C2×C3⋊D3—22no—
412C2×C3⋊D3#23912yes—
413C2×C3×D3—32no—
414C2×C3×D3—32no—
415C2×C3×D3—62no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—62no—
421C2×C3×D3—62no—
422C2×C3×D3—62no—
423C2×C3×D3—62no—
424C2×C3×D3—62no—
425C2×C3×D3—62no—
426C2×C3×D3—121no—
427C2×C3×D3—121no—
428C2×C3×D3—122no—
429C2×C3×D3—122no—
430C2×C3×D3—122no—
431C32×C4—22no—
432C32×C4—24no—
433C32×C4—22no—
434C32×C4—22no—
435C32×C4—22no—
436C32×C4—22no—
437C32×C4—22no—
438C32×C4—42no—
439C32×C4—42no—
440C32×C4—42no—
441C32×C4—44no—
442C32×C4#23512yes—
443C32×C4#23712yes—
444C32×C4#23712yes—
445C3⋊Dic3—21no—
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—22no—
450C3⋊Dic3—22no—
451C3⋊Dic3#23912yes—
452C3×Dic3—32no—
453C3×Dic3—32no—
454C3×Dic3—62no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—62no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—62no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—62no—
465C3×Dic3—61no—
466C3×Dic3—62no—
467C3×Dic3—121no—
468C3×Dic3—121no—
469C3×Dic3—122no—
470C3×Dic3—121no—
471C3×Dic3—121no—
472C3×Dic3—122no—
473#126—272no—
474#125—271no—
475#124—91no—
476#123—272no—
477C22⋊Q8—91no—
478#121—271no—
479C4×Q8—91no—
480C4×D4—272no—
481C4×D4—271no—
482#117—272no—
483C2×C42—271no—
484C33#52911yescharacteristic, complemented, Sylow
485C23×C3—91no—
486C23×C3—92no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—32no—
490C22×D3—32no—
491C22×D3—61no—
492C22×D3—62no—
493C3×Q8—24no—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—22no—
497C3×Q8—42no—
498C3×Q8—42no—
499C3×Q8—44no—
500C3×D4—182no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—42no—
508C2×C3×C4—41no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—92no—
515C2×C3×C4—92no—
516C2×C3×C4—182no—
517C2×C3×C4C2×D3212yes—
518C2×C3×C4C2×D3212yes—
519C2×C3×C4C2×D3212yes—
520C2×C3×C4C2×D3211yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523#67—184no—
524#67—184no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—62no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—62no—
546C2×Dic3—182no—
547C2×Dic3—184no—
548C2×Dic3—182no—
549D12—62no—
550D12—62no—
551D12—122no—
552D12—184no—
553C4×D3—62no—
554C4×D3—62no—
555C4×D3—122no—
556C4×D3—184no—
557C4×D3—182no—
558C4×D3—182no—
559C4×D3—184no—
560C4×D3—182no—
561C4×D3—182no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32—41no—
574C2×C32C2×#23511yescharacteristic
575C2×C32C2×#23711yescharacteristic
576C2×C32C2×#23711yescharacteristic
577C2×C32C2×#23911yescharacteristic
578C2×C32C2×#23911yescharacteristic
579C2×C32D3×#4111yescharacteristic
580C2×C32D3×#4111yescharacteristic
581C2×C32D3×#4111yescharacteristic
582C2×C32D3×#4111yescharacteristic
583C3⋊D3—22no—
584C3⋊D3—42no—
585C3×D3—62no—
586C3×D3—62no—
587C3×D3—122no—
588C3×D3—122no—
589C3×D3—122no—
590C3×D3—242no—
591C2×Q8#111311yescharacteristic
592C2×D4—91no—
593C2×D4—272no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—272no—
598C4⋊C4—92no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—92no—
602C4⋊C4—272no—
603C4⋊C4—272no—
604C22⋊C4—92no—
605C22⋊C4—92no—
606C22⋊C4—92no—
607C22⋊C4—272no—
608C22⋊C4—272no—
609C42—91no—
610C42—91no—
611C42—92no—
612C42—271no—
613C42—271no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—41no—
618C22×C3—92no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—182no—
622C22×C3—182no—
623C22×C3—182no—
624C22×C3C22×D3211yescharacteristic
625C22×C3C22×D3211yescharacteristic
626C22×C3C22×D3211yescharacteristic
627C2×D3—32no—
628C2×D3—32no—
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—122no—
643C2×D3—122no—
644C2×D3—122no—
645C3×C4—24no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—44no—
655C3×C4—42no—
656C3×C4—92no—
657C3×C4—181no—
658C3×C4—181no—
659C3×C4—181no—
660C3×C4—182no—
661C3×C4—182no—
662C3×C4—181no—
663C3×C4#380412yes—
664C3×C4#380412yes—
665C3×C4#380512yes—
666Dic3—32no—
667Dic3—32no—
668Dic3—62no—
669Dic3—61no—
670Dic3—61no—
671Dic3—62no—
672Dic3—61no—
673Dic3—62no—
674Dic3—61no—
675Dic3—62no—
676Dic3—61no—
677Dic3—61no—
678Dic3—62no—
679Dic3—61no—
680Dic3—61no—
681Dic3—121no—
682Dic3—121no—
683Dic3—122no—
684Dic3—121no—
685Dic3—121no—
686Dic3—122no—
687C32—21no—
688C32—21no—
689C32—21no—
690C32—41no—
691C32#558011yescharacteristic, complemented
692C32#562411yescharacteristic, complemented
693C32#568011yescharacteristic, complemented
694C23—91no—
695C23—92no—
696Q8—22no—
697D4—182no—
698D4—544no—
699C2×C4—91no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—92no—
704C2×C4—91no—
705C2×C4—92no—
706C2×C4—182no—
707C2×C4—542no—
708C2×C4—544no—
709C2×C4—542no—
710C2×C4C2×#111312yes—
711C2×C4C2×#111311yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—41no—
722C2×C3—41no—
723C2×C3—41no—
724C2×C3—182no—
725C2×C3—362no—
726C2×C3D3×#23911yescharacteristic
727C2×C3D3×#23911yescharacteristic
728C2×C3D3×#23911yescharacteristic
729C2×C3D3×#23911yescharacteristic
730C2×C3#6431911yescharacteristic
731C2×C3#6431911yescharacteristic
732C2×C3C2×#380411yescharacteristic
733C2×C3C2×#380411yescharacteristic
734C2×C3C2×#380511yescharacteristic
735D3—62no—
736D3—62no—
737D3—122no—
738D3—122no—
739D3—122no—
740D3—242no—
741C22—92no—
742C22—181no—
743C22—181no—
744C22—182no—
745C22—182no—
746C22—182no—
747C22C22×#111311yescharacteristic
748C4—22no—
749C4—92no—
750C4—181no—
751C4—182no—
752C4—181no—
753C4—181no—
754C4—182no—
755C4—181no—
756C4#8904612yes—
757C3—21no—
758C3—21no—
759C3—21no—
760C3—41no—
761C3#1059537611yescharacteristic, complemented
762C3#1059537711yescharacteristic, complemented
763C3#1059538211yescharacteristic, complemented
764C2—182no—
765C2—362no—
766C2#1172462611yescharacteristic
767C2#1172462611yescharacteristic
768C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radical#11723696C2
hypercenterC2×Q8#1113
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#64156C2semidirect
2. C3×#64155C2semidirect
3. C3×Q8×C3⋊Dic3C2semidirect
5. #11723691C2semidirect
6. #11723690C2semidirect
7. #11723685C2semidirect
8. #11723683C2semidirect
9. C4×#6294C2semidirect
10. #11723680C2semidirect
11. #11723675C2semidirect
38. #64156D3semidirect
39. #64155D3semidirect
40. Q8×C3⋊Dic3D3semidirect
484. C33#529semidirect
691. C32#5580semidirect
692. C32#5624semidirect
693. C32#5680semidirect
761. C3#10595376semidirect
762. C3#10595377semidirect
763. C3#10595382semidirect

Maximal subgroups

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

subgroupindex
C3×#641562
C3×#641552
C3×Q8×C3⋊Dic32
#117236962
#117236912
#117236902
#117236852
#117236832
C4×#62942
#117236802
#117236752
#105953823
#105953773
#105953763