Finite Group Databasebeta

← #13178730

Subgroups — #13178730

Order 1728.

1122 conjugacy classes of subgroups.

The subgroup lattice has 762 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
4C4⋊#6296C211yesmaximal, characteristic, complemented
5#11723696C211yesmaximal, characteristic
6#11723692C212yesmaximal, complemented
7#11723691C211yesmaximal, characteristic, complemented
8#11723690C212yesmaximal, complemented
9#11723676C212yesmaximal, complemented
10#11723673C211yesmaximal, characteristic, complemented
11#11723672C212yesmaximal, complemented
12#10595396—31nomaximal
13#10595395—31nomaximal
14#10595346—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×#6296C2212yes—
19C2×#6295C2212yes—
20C2×#6294C2212yes—
21C3×#3752C2212yes—
22C3×#3752C2212yes—
23C3×#3752C2212yes—
24C3×C4⋊(C3⋊Dic3)C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2212yes—
28C3×C4×C3⋊Dic3C2212yes—
29C3×C4×C3⋊Dic3C2211yescharacteristic
30C3×C4×C3⋊Dic3C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2212yes—
34#88814C2211yescharacteristic
35#88814C2212yes—
36#88814C2211yescharacteristic
37#88814C2212yes—
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#63919—31no—
51#63918—31no—
52#63918—31no—
53#63916—31no—
54#63915—32no—
55#63909—31no—
56#63908—31no—
57#63899—32no—
58#63898—31no—
59#63895—32no—
60#63894—31no—
61#63893—32no—
62Dic3×D12—31no—
63#63891—32no—
64#63890—32no—
65#63874—31no—
66#63868—32no—
67#63862—32no—
68#63859—32no—
69#63855—31no—
70#63855—31no—
71#63854—32no—
72#63852—32no—
73#63852—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⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C3×C4⋊(C3⋊D3)—22no—
87C3×C4×C3⋊D3—22no—
88#6296—42no—
89#6295—42no—
90#6294—42no—
91#5682—91no—
92#5643—91no—
93#5582—91no—
94C2×C32×Q8—21no—
95C2×C32×Q8—21no—
96C2×C32×Q8—21no—
97C2×C32×Q8—41no—
98C2×C32×Q8C2×D311yescharacteristic
99C2×C32×Q8C2×D311yescharacteristic
100C2×C32×Q8C2×D311yescharacteristic
101C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
102C2×C4×C3⋊D3C2×D311yescharacteristic
103C2×C3×D12—31no—
104C2×C3×D12—31no—
105C2×C3×D12—61no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—61no—
109C2×#627—32no—
110C2×#627—32no—
111C2×#627—32no—
112C2×#626—32no—
113C2×#626—32no—
114C2×#625—32no—
115C2×#624—32no—
116C2×D3×Dic3—32no—
117C2×D3×Dic3—32no—
118#3752C2×D312yes—
119#3752C2×D312yes—
120#3752C2×D312yes—
121C4⋊(C3⋊Dic3)C2×D312yes—
122C4⋊(C3⋊Dic3)C2×D311yescharacteristic
123C4⋊(C3⋊Dic3)C2×D311yescharacteristic
124#3750C2×D312yes—
125C4×C3⋊Dic3C2×D311yescharacteristic
126C4×C3⋊Dic3C2×D311yescharacteristic
127C4×C3⋊Dic3C2×D312yes—
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—32no—
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—62no—
135C3×(C2×D3)⋊C4—62no—
136C3×(C2×D3)⋊C4—62no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—61no—
144C3×C4⋊Dic3—62no—
145C3×C4⋊Dic3—61no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—62no—
149C3×C4×Dic3—32no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—61no—
156C3×C4×Dic3—62no—
157C3×C4×Dic3—61no—
158#3724—32no—
159#3724—31no—
160#3724—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167#3722—31no—
168#3722—32no—
169#3722—32no—
170#3722—31no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—32no—
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—22no—
186C33×C4—22no—
187C33×C4#4112yes—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×#124—91no—
196C3×C22⋊Q8—91no—
197C3×C4×Q8—91no—
198#947—31no—
199#947—31no—
200#947—61no—
201#946—31no—
202#946—31no—
203#946—61no—
204Q8×Dic3—31no—
205Q8×Dic3—31no—
206Q8×Dic3—61no—
207#938—91no—
208D4×Dic3—91no—
209#930—91no—
210#926—91no—
211#898—92no—
212#897—92no—
213#896—92no—
214#895—91no—
215#894—92no—
216#893—91no—
217#888—91no—
218#888—91no—
219#886—92no—
220#885—92no—
221#885—92no—
222#883—92no—
223#879—92no—
224#878—92no—
225#876—92no—
226#875—92no—
227C4×D12—91no—
228#872—91no—
229#872—91no—
230#869—91no—
231C22×C3⋊D3C22×D312yes—
232C22×C3⋊D3C22×D311yescharacteristic
233C22×C3×D3—32no—
234C22×C3×D3—32no—
235C22×C3×D3—31no—
236C22×C3×D3—31no—
237C22×C3×D3—61no—
238C22×C3×D3—62no—
239C32×Q8—22no—
240C32×Q8—24no—
241C32×Q8—22no—
242C32×Q8—22no—
243C32×Q8—42no—
244C32×Q8—42no—
245C32×Q8—44no—
246C2×C32×C4—22no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—22no—
251C2×C32×C4—22no—
252C2×C32×C4—41no—
253C2×C32×C4—42no—
254C2×C32×C4C22×D312yes—
255C2×C32×C4C22×D312yes—
256C2×C32×C4C22×D312yes—
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D312yes—
267C4⋊(C3⋊D3)—22no—
268C4×C3⋊D3—22no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—62no—
290C3×D12—62no—
291C3×D12—62no—
292C3×D12—122no—
293C3×C4×D3—62no—
294C3×C4×D3—62no—
295C3×C4×D3—122no—
296#627—122no—
297#627—122no—
298#627—122no—
299#626—122no—
300#626—122no—
301#625—122no—
302#624—122no—
303D3×Dic3—122no—
304D3×Dic3—122no—
305#542—271noSylow
306C2×C33C2×#4111yescharacteristic
307C2×C33H(5,𝔽2)11yescharacteristic
308C2×C332−1+411yescharacteristic
309C3×C3⋊D3—41no—
310C3×C3⋊D3—42no—
311C2×C3×Q8—21no—
312C2×C3×Q8—21no—
313C2×C3×Q8—21no—
314C2×C3×Q8—41no—
315C2×C3×Q8D3211yescharacteristic
316C2×C3×Q8D3211yescharacteristic
317C2×C3×Q8D3211yescharacteristic
318C2×C3×D4—91no—
319C22×C3×C4—91no—
320C2×#67—92no—
321C2×#67—92no—
322C22×Dic3—92no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—92no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—92no—
331C2×C4×D3—92no—
332C2×Dic6—92no—
333C2×Dic6—92no—
334C2×Dic6—92no—
335C3×C4⋊C4—91no—
336C3×C4⋊C4—91no—
337C3×C4⋊C4—92no—
338C3×C4⋊C4—92no—
339C3×C22⋊C4—92no—
340C3×C22⋊C4—92no—
341C3×C22⋊C4—92no—
342C3×C42—91no—
343C3×C42—91no—
344C3×C42—92no—
345#217—92no—
346#217—92no—
347#217—91no—
348#217—91no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—32no—
351(C2×D3)⋊C4—32no—
352(C2×D3)⋊C4—32no—
353(C2×D3)⋊C4—32no—
354(C2×D3)⋊C4—32no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—92no—
363(C2×D3)⋊C4—92no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—32no—
370C4⋊Dic3—32no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—62no—
374C4⋊Dic3—61no—
375C4⋊Dic3—92no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378Dic3⋊C4—32no—
379Dic3⋊C4—32no—
380Dic3⋊C4—62no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—92no—
386Dic3⋊C4—92no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—32no—
390C4×Dic3—32no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—61no—
394C4×Dic3—62no—
395C4×Dic3—61no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—41no—
400C22×C32C23×D311yescharacteristic
401C22×C32C23×D311yescharacteristic
402C22×C32C23×D311yescharacteristic
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—21no—
408C2×C3⋊D3—22no—
409C2×C3×D3—62no—
410C2×C3×D3—61no—
411C2×C3×D3—62no—
412C2×C3×D3—61no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—62no—
416C2×C3×D3—61no—
417C2×C3×D3—62no—
418C2×C3×D3—62no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—121no—
423C2×C3×D3—121no—
424C2×C3×D3—122no—
425C2×C3×D3—122no—
426C2×C3×D3—122no—
427C32×C4—22no—
428C32×C4—24no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—22no—
433C32×C4—22no—
434C32×C4—42no—
435C32×C4—42no—
436C32×C4—42no—
437C32×C4—44no—
438C32×C4#23512yes—
439C32×C4#23712yes—
440C32×C4#23712yes—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—22no—
445C3⋊Dic3—22no—
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3×Dic3—62no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C3×Dic3—61no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—62no—
456C3×Dic3—61no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3—62no—
460C3×Dic3—61no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—121no—
464C3×Dic3—121no—
465C3×Dic3—121no—
466C3×Dic3—122no—
467C3×Dic3—122no—
468C3×Dic3—121no—
469C4⋊Q8—271no—
470#126—272no—
471#124—91no—
472#124—272no—
473#123—272no—
474C22⋊Q8—91no—
475C22⋊Q8—272no—
476#121—271no—
477C4×Q8—91no—
478C4×D4—271no—
479#117—271no—
480C33#54211yescharacteristic, complemented, Sylow
481C23×C3—92no—
482C23×C3—91no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—32no—
486C22×D3—32no—
487C22×D3—61no—
488C22×D3—62no—
489C3×Q8—24no—
490C3×Q8—22no—
491C3×Q8—22no—
492C3×Q8—22no—
493C3×Q8—42no—
494C3×Q8—42no—
495C3×Q8—44no—
496C3×D4—182no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—42no—
504C2×C3×C4—41no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—91no—
508C2×C3×C4—92no—
509C2×C3×C4—91no—
510C2×C3×C4—92no—
511C2×C3×C4—91no—
512C2×C3×C4—182no—
513C2×C3×C4C2×D3212yes—
514C2×C3×C4C2×D3212yes—
515C2×C3×C4C2×D3212yes—
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519#67—362no—
520#67—362no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—32no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—32no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—62no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—62no—
542C2×Dic3—362no—
543D12—62no—
544D12—62no—
545D12—122no—
546D12—362no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—122no—
550C4×D3—362no—
551C4×D3—362no—
552Dic6—362no—
553Dic6—362no—
554Dic6—362no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—41no—
565C2×C32—41no—
566C2×C32—41no—
567C2×C32C2×#23511yescharacteristic
568C2×C32C2×#23711yescharacteristic
569C2×C32C2×#23711yescharacteristic
570C2×C32#100711yescharacteristic
571C2×C32#100711yescharacteristic
572C2×C32#100911yescharacteristic
573C2×C32#100911yescharacteristic
574C2×C32#100911yescharacteristic
575C2×C32#101011yescharacteristic
576C3⋊D3—41no—
577C3⋊D3—42no—
578C3×D3—122no—
579C3×D3—122no—
580C3×D3—121no—
581C3×D3—121no—
582C3×D3—122no—
583C3×D3—242no—
584C2×Q8—272no—
585C2×Q8#111311yescharacteristic
586C2×D4—91no—
587C2×D4—272no—
588C22×C4—91no—
589C22×C4—272no—
590C4⋊C4—91no—
591C4⋊C4—91no—
592C4⋊C4—92no—
593C4⋊C4—92no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—272no—
597C22⋊C4—92no—
598C22⋊C4—92no—
599C22⋊C4—92no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—272no—
603C22⋊C4—272no—
604C42—91no—
605C42—91no—
606C42—92no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—41no—
611C22×C3—181no—
612C22×C3—182no—
613C22×C3—182no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3—182no—
617C22×C3C22×D3211yescharacteristic
618C22×C3C22×D3211yescharacteristic
619C22×C3C22×D3211yescharacteristic
620C2×D3—62no—
621C2×D3—61no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—61no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—62no—
631C2×D3—61no—
632C2×D3—62no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—122no—
636C2×D3—122no—
637C2×D3—122no—
638C3×C4—24no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—44no—
648C3×C4—42no—
649C3×C4—181no—
650C3×C4—181no—
651C3×C4—181no—
652C3×C4—182no—
653C3×C4—182no—
654C3×C4—181no—
655C3×C4—181no—
656C3×C4#380412yes—
657C3×C4#380412yes—
658C3×C4#380512yes—
659Dic3—62no—
660Dic3—61no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—62no—
667Dic3—62no—
668Dic3—62no—
669Dic3—62no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—122no—
678Dic3—122no—
679Dic3—121no—
680C32—21no—
681C32—21no—
682C32—21no—
683C32—41no—
684C32#558211yescharacteristic, complemented
685C32#564311yescharacteristic, complemented
686C32#568211yescharacteristic, complemented
687C23—91no—
688C23—92no—
689Q8—22no—
690Q8—1082no—
691D4—182no—
692D4—1082no—
693C2×C4—91no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—92no—
698C2×C4—92no—
699C2×C4—91no—
700C2×C4—182no—
701C2×C4—1082no—
702C2×C4C2×#111312yes—
703C2×C4C2×#111311yescharacteristic
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—41no—
714C2×C3—41no—
715C2×C3—41no—
716C2×C3—362no—
717C2×C3—361no—
718C2×C3#6431511yescharacteristic
719C2×C3#6431511yescharacteristic
720C2×C3#6431611yescharacteristic
721C2×C3#6432011yescharacteristic
722C2×C3#6432011yescharacteristic
723C2×C3#6432011yescharacteristic
724C2×C3C2×#380411yescharacteristic
725C2×C3C2×#380411yescharacteristic
726C2×C3C2×#380511yescharacteristic
727D3—122no—
728D3—121no—
729D3—122no—
730D3—121no—
731D3—122no—
732D3—242no—
733C22—181no—
734C22—182no—
735C22—182no—
736C22—181no—
737C22—181no—
738C22—182no—
739C22C22×#111311yescharacteristic
740C4—22no—
741C4—181no—
742C4—181no—
743C4—181no—
744C4—182no—
745C4—182no—
746C4—181no—
747C4—181no—
748C4#8904612yes—
749C3—21no—
750C3—21no—
751C3—21no—
752C3—41no—
753C3#1059534611yescharacteristic, complemented
754C3#1059539511yescharacteristic, complemented
755C3#1059539611yescharacteristic, complemented
756C2—361no—
757C2—362no—
758C2#1172462411yescharacteristic
759C2#1172462711yescharacteristic
760C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radical#11723696C2
hypercenterC2×Q8#1113
hypocenterC33#542
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
4. C4⋊#6296C2semidirect
6. #11723692C2semidirect
7. #11723691C2semidirect
8. #11723690C2semidirect
9. #11723676C2semidirect
10. #11723673C2semidirect
11. #11723672C2semidirect
38. #64156D3semidirect
39. #64155D3semidirect
40. Q8×C3⋊Dic3D3semidirect
480. C33#542semidirect
684. C32#5582semidirect
685. C32#5643semidirect
686. C32#5682semidirect
753. C3#10595346semidirect
754. C3#10595395semidirect
755. C3#10595396semidirect

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
C4⋊#62962
#117236962
#117236922
#117236912
#117236902
#117236762
#117236732
#117236722
#105953963
#105953953
#105953463