Finite Group Databasebeta

← #13178143

Subgroups — #13178143

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64084C211yesmaximal, characteristic, complemented
2C3×#64081C211yesmaximal, characteristic, complemented
3C3×#64078C211yesmaximal, characteristic, complemented
4#11723696C211yesmaximal, characteristic
5#11723691C211yesmaximal, characteristic, complemented
6#11723690C212yesmaximal, complemented
7#11723688C212yesmaximal, complemented
8#11723675C212yesmaximal, complemented
9#11723674C211yesmaximal, characteristic, complemented
10#11723670C212yesmaximal, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10593961—31nomaximal
13#10593955—31nomaximal
14#10593877—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C3×#634C2212yes—
19C2×#6295C2212yes—
20C2×#6294C2212yes—
21C33×C42C2211yescharacteristic
22C3×#3752C2211yescharacteristic
23C3×#3752C2211yescharacteristic
24C3×#3752C2212yes—
25C3×#3752C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2212yes—
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88814C2212yes—
36#88814C2212yes—
37#88813C2212yes—
38#64084D311yescharacteristic, complemented
39#64081D311yescharacteristic, complemented
40#64078D311yescharacteristic, complemented
41C3×#875—31no—
42C3×#875—31no—
43C3×#875—61no—
44C3×#872—31no—
45C3×#872—31no—
46C3×#872—61no—
47C3×#869—31no—
48C3×#869—31no—
49C3×#869—61no—
50#63916—31no—
51#63913—32no—
52#63909—31no—
53#63908—31no—
54#63907—32no—
55#63907—32no—
56#63898—31no—
57#63896—32no—
58#63894—31no—
59Dic3×D12—31no—
60#63891—32no—
61#63890—32no—
62#63888—32no—
63#63887—32no—
64#63871—31no—
65#63861—32no—
66#63858—32no—
67#63857—31no—
68#63856—31no—
69#63854—32no—
70#63848—32no—
71#63844—31no—
72#63843—31no—
73Dic3×Dic6—31no—
74C22×C3×C3⋊D3C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2312yes—
85C3×C4⋊(C3⋊D3)—22no—
86C3×C4×C3⋊D3—22no—
87C3×#634—22no—
88C3×#634—42no—
89#6295—42no—
90#6294—42no—
91#5733—91no—
92#5682—91no—
93#5534—91no—
94C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×#634C2×D311yescharacteristic
97C2×#634C2×D312yes—
98C2×C3×D12—31no—
99C2×C3×D12—31no—
100C2×C3×D12—61no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—61no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—32no—
107C2×C3×Dic6—32no—
108C2×C3×Dic6—62no—
109C2×C3×Dic6—61no—
110C2×#626—32no—
111C2×#626—32no—
112C2×#625—32no—
113C2×#624—32no—
114C2×D3×Dic3—32no—
115C2×D3×Dic3—32no—
116C32×C42—21no—
117C32×C42—21no—
118C32×C42—21no—
119C32×C42—41no—
120C32×C42C2×D311yescharacteristic
121C32×C42C2×D311yescharacteristic
122C32×C42C2×D311yescharacteristic
123#3752C2×D311yescharacteristic
124#3752C2×D311yescharacteristic
125#3752C2×D312yes—
126#3752C2×D312yes—
127C4⋊(C3⋊Dic3)C2×D311yescharacteristic
128C4⋊(C3⋊Dic3)C2×D311yescharacteristic
129C4⋊(C3⋊Dic3)C2×D312yes—
130#3750C2×D311yescharacteristic
131#3750C2×D311yescharacteristic
132C4×C3⋊Dic3C2×D311yescharacteristic
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—61no—
142C3×(C2×D3)⋊C4—61no—
143C3×(C2×D3)⋊C4—62no—
144C3×(C2×D3)⋊C4—62no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—32no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—32no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—61no—
152C3×C4⋊Dic3—61no—
153C3×C4⋊Dic3—62no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4—31no—
156C3×Dic3⋊C4—31no—
157C3×Dic3⋊C4—31no—
158C3×Dic3⋊C4—61no—
159C3×Dic3⋊C4—61no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—61no—
163#3724—32no—
164#3724—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169#3722—32no—
170#3722—32no—
171#3722—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178Dic32—32no—
179Dic32—32no—
180Dic32—32no—
181C22×C33C2411yescharacteristic
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3—22no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—22no—
188C33×C4—21no—
189C33×C4—21no—
190C33×C4#4112yes—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—22no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3—21no—
197C3×C4⋊Q8—91no—
198C3×#124—91no—
199C3×#117—91no—
200#947—92no—
201#946—92no—
202#946—91no—
203Q8×Dic3—91no—
204#938—91no—
205D4×Dic3—91no—
206#930—91no—
207#924—91no—
208#898—92no—
209#898—92no—
210#897—91no—
211#896—92no—
212#895—91no—
213#894—92no—
214#893—91no—
215#887—91no—
216#886—92no—
217#885—92no—
218#885—92no—
219#883—92no—
220#879—92no—
221#878—92no—
222#875—31no—
223#875—31no—
224#875—61no—
225C4×D12—91no—
226#872—31no—
227#872—31no—
228#872—61no—
229#869—31no—
230#869—31no—
231#869—61no—
232C4×Dic6—91no—
233C22×C3⋊D3C22×D312yes—
234C22×C3⋊D3C22×D311yescharacteristic
235C22×C3×D3—32no—
236C22×C3×D3—32no—
237C22×C3×D3—31no—
238C22×C3×D3—31no—
239C22×C3×D3—61no—
240C22×C3×D3—62no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—41no—
251C2×C32×C4—41no—
252C2×C32×C4—41no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D312yes—
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D312yes—
267C2×C3⋊Dic3C22×D311yescharacteristic
268C4⋊(C3⋊D3)—22no—
269C4×C3⋊D3—22no—
270#634—22no—
271#634—42no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—62no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—62no—
290C3×D12—62no—
291C3×D12—62no—
292C3×D12—122no—
293C3×C4×D3—64no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—122no—
299C3×Dic6—122no—
300C3×Dic6—122no—
301C3×Dic6—124no—
302#626—122no—
303#626—122no—
304#625—122no—
305#624—122no—
306D3×Dic3—122no—
307D3×Dic3—122no—
308#542—271noSylow
309C2×C33C2×#4111yescharacteristic
310C2×C33H(5,𝔽2)11yescharacteristic
311C2×C332−1+411yescharacteristic
312C3×C3⋊D3—41no—
313C3×C3⋊D3—42no—
314C2×C3×Q8—91no—
315C2×C3×Q8—92no—
316C2×C3×D4—91no—
317C22×C3×C4—91no—
318C2×#67—92no—
319C2×#67—92no—
320C22×Dic3—92no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12—92no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—92no—
329C2×C4×D3—92no—
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—32no—
333C2×Dic6—32no—
334C2×Dic6—62no—
335C2×Dic6—61no—
336C3×C4⋊C4—91no—
337C3×C4⋊C4—91no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C22⋊C4—92no—
342C3×C22⋊C4—92no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—41no—
349C3×C42—91no—
350C3×C42D3211yescharacteristic
351C3×C42D3211yescharacteristic
352C3×C42D3211yescharacteristic
353#217—92no—
354#217—92no—
355#217—92no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—32no—
361(C2×D3)⋊C4—32no—
362(C2×D3)⋊C4—32no—
363(C2×D3)⋊C4—32no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—92no—
370(C2×D3)⋊C4—92no—
371(C2×D3)⋊C4—92no—
372(C2×D3)⋊C4—92no—
373(C2×D3)⋊C4—92no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—32no—
377C4⋊Dic3—32no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—62no—
383C4⋊Dic3—92no—
384C4⋊Dic3—92no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—92no—
392Dic3⋊C4—92no—
393Dic3⋊C4—92no—
394Dic3⋊C4—92no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—92no—
399C4×Dic3—92no—
400C4×Dic3—92no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—41no—
405C22×C32C23×D311yescharacteristic
406C22×C32C23×D311yescharacteristic
407C22×C32C23×D311yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—22no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—22no—
414C2×C3×D3—62no—
415C2×C3×D3—62no—
416C2×C3×D3—61no—
417C2×C3×D3—62no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—62no—
421C2×C3×D3—62no—
422C2×C3×D3—61no—
423C2×C3×D3—62no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—62no—
427C2×C3×D3—121no—
428C2×C3×D3—121no—
429C2×C3×D3—122no—
430C2×C3×D3—122no—
431C2×C3×D3—122no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—22no—
435C32×C4—22no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—22no—
441C32×C4—22no—
442C32×C4—22no—
443C32×C4—42no—
444C32×C4—41no—
445C32×C4—41no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4—42no—
449C32×C4—42no—
450C32×C4#23512yes—
451C32×C4#23712yes—
452C32×C4#23912yes—
453C3⋊Dic3—21no—
454C3⋊Dic3—22no—
455C3⋊Dic3—22no—
456C3⋊Dic3—22no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—62no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466C3×Dic3—62no—
467C3×Dic3—61no—
468C3×Dic3—62no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—61no—
472C3×Dic3—122no—
473C3×Dic3—122no—
474C3×Dic3—122no—
475C3×Dic3—121no—
476C3×Dic3—121no—
477C4⋊Q8—91no—
478#126—272no—
479#124—91no—
480#124—272no—
481#123—272no—
482C22⋊Q8—272no—
483C22⋊Q8—271no—
484#121—271no—
485C4×Q8—271no—
486C4×D4—271no—
487#117—91no—
488C33#54211yescharacteristic, complemented, Sylow
489C23×C3—92no—
490C23×C3—91no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—32no—
494C22×D3—32no—
495C22×D3—61no—
496C22×D3—62no—
497C3×Q8—182no—
498C3×Q8—362no—
499C3×D4—182no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—91no—
513C2×C3×C4—92no—
514C2×C3×C4—92no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—92no—
518C2×C3×C4—182no—
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523C2×C3×C4C2×D3211yescharacteristic
524C2×C3×C4C2×D3211yescharacteristic
525C2×C3×C4C2×D3211yescharacteristic
526C2×C3×C4C2×D3211yescharacteristic
527C2×C3×C4C2×D3211yescharacteristic
528#67—362no—
529#67—362no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—62no—
548C2×Dic3—362no—
549D12—62no—
550D12—62no—
551D12—122no—
552D12—362no—
553C4×D3—64no—
554C4×D3—62no—
555C4×D3—62no—
556C4×D3—362no—
557C4×D3—362no—
558Dic6—62no—
559Dic6—62no—
560Dic6—122no—
561Dic6—122no—
562Dic6—122no—
563Dic6—124no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—41no—
574C2×C32—41no—
575C2×C32—41no—
576C2×C32C2×#23511yescharacteristic
577C2×C32C2×#23711yescharacteristic
578C2×C32#100411yescharacteristic
579C2×C32C2×#23911yescharacteristic
580C2×C32#100711yescharacteristic
581C2×C32#100911yescharacteristic
582C2×C32#100911yescharacteristic
583C2×C32#101011yescharacteristic
584C2×C32#101011yescharacteristic
585C3⋊D3—41no—
586C3⋊D3—42no—
587C3×D3—122no—
588C3×D3—121no—
589C3×D3—121no—
590C3×D3—122no—
591C3×D3—122no—
592C3×D3—242no—
593C2×Q8—91no—
594C2×Q8—92no—
595C2×D4—91no—
596C2×D4—272no—
597C22×C4—91no—
598C22×C4—272no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—92no—
604C4⋊C4—272no—
605C4⋊C4—272no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—92no—
609C22⋊C4—92no—
610C22⋊C4—272no—
611C22⋊C4—272no—
612C22⋊C4—272no—
613C42—91no—
614C42—272no—
615C42#111311yescharacteristic
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—41no—
620C22×C3—181no—
621C22×C3—182no—
622C22×C3—181no—
623C22×C3—182no—
624C22×C3—182no—
625C22×C3—181no—
626C22×C3C22×D3211yescharacteristic
627C22×C3C22×D3211yescharacteristic
628C22×C3C22×D3211yescharacteristic
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—61no—
634C2×D3—62no—
635C2×D3—61no—
636C2×D3—62no—
637C2×D3—61no—
638C2×D3—62no—
639C2×D3—61no—
640C2×D3—62no—
641C2×D3—61no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—122no—
645C2×D3—122no—
646C2×D3—122no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—181no—
666C3×C4—181no—
667C3×C4—182no—
668C3×C4—181no—
669C3×C4—182no—
670C3×C4—182no—
671C3×C4#379512yes—
672C3×C4#379612yes—
673C3×C4#379912yes—
674Dic3—62no—
675Dic3—62no—
676Dic3—61no—
677Dic3—62no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—62no—
682Dic3—62no—
683Dic3—62no—
684Dic3—62no—
685Dic3—61no—
686Dic3—61no—
687Dic3—122no—
688Dic3—122no—
689Dic3—122no—
690Dic3—121no—
691Dic3—121no—
692C32—21no—
693C32—21no—
694C32—21no—
695C32—41no—
696C32#553411yescharacteristic, complemented
697C32#568211yescharacteristic, complemented
698C32#573311yescharacteristic, complemented
699C23—91no—
700C23—92no—
701Q8—182no—
702Q8—362no—
703D4—182no—
704D4—1082no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—92no—
708C2×C4—92no—
709C2×C4—91no—
710C2×C4—92no—
711C2×C4—182no—
712C2×C4—1082no—
713C2×C4C2×#111311yescharacteristic
714C2×C4C2×#111311yescharacteristic
715C2×C4C2×#111311yescharacteristic
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—362no—
729C2×C3—361no—
730C2×C3C2×#379511yescharacteristic
731C2×C3C2×#379611yescharacteristic
732C2×C3#6429711yescharacteristic
733C2×C3#6429711yescharacteristic
734C2×C3#6429811yescharacteristic
735C2×C3C2×#379911yescharacteristic
736C2×C3#6430711yescharacteristic
737C2×C3#6430711yescharacteristic
738C2×C3#6430811yescharacteristic
739D3—122no—
740D3—121no—
741D3—122no—
742D3—121no—
743D3—122no—
744D3—242no—
745C22—181no—
746C22—182no—
747C22—181no—
748C22—182no—
749C22—182no—
750C22—181no—
751C22C22×#111311yescharacteristic
752C4—21no—
753C4—21no—
754C4—181no—
755C4—182no—
756C4—181no—
757C4—181no—
758C4—182no—
759C4—182no—
760C4#8904112yes—
761C3—21no—
762C3—21no—
763C3—21no—
764C3—41no—
765C3#1059387711yescharacteristic, complemented
766C3#1059395511yescharacteristic, complemented
767C3#1059396111yescharacteristic, complemented
768C2—361no—
769C2—362no—
770C2C2×#8904111yescharacteristic
771C2#1172461411yescharacteristic
772C2#1172461911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radical#11723696C2
hypercenterC42#1113
hypocenterC33#542
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C3×#64084C2semidirect
2. C3×#64081C2semidirect
3. C3×#64078C2semidirect
5. #11723691C2semidirect
6. #11723690C2semidirect
7. #11723688C2semidirect
8. #11723675C2semidirect
9. #11723674C2semidirect
10. #11723670C2semidirect
11. #11723668C2semidirect
38. #64084D3semidirect
39. #64081D3semidirect
40. #64078D3semidirect
488. C33#542semidirect
696. C32#5534semidirect
697. C32#5682semidirect
698. C32#5733semidirect
765. C3#10593877semidirect
766. C3#10593955semidirect
767. C3#10593961semidirect

Maximal subgroups

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

subgroupindex
C3×#640842
C3×#640812
C3×#640782
#117236962
#117236912
#117236902
#117236882
#117236752
#117236742
#117236702
#117236682
#105939613
#105939553
#105938773