Finite Group Databasebeta

← #13168710

Subgroups — #13168710

Order 1728.

1172 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723668C211yesmaximal, characteristic, complemented
2#11723535C211yesmaximal, characteristic, complemented
3D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4#11723425C211yesmaximal, characteristic, complemented
5C3×C4×#625C211yesmaximal, characteristic
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63857C211yesmaximal, characteristic, complemented
8#11723017C212yesmaximal, complemented
9#11722980C212yesmaximal, complemented
10#11722971C212yesmaximal, complemented
11#11722924C212yesmaximal
12#10594993—31nomaximal
13#10594988—31nomaximal
14#10594532—31nomaximal
15C2×C3×#634C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6293C2212yes—
19C2×D3×C3⋊Dic3C2212yes—
20C2×C3×#625C2211yescharacteristic
21C2×C3×D3×Dic3C2212yes—
22C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26#88815C2212yes—
27#88813C2212yes—
28#88807C2212yes—
29#88806C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31(C2×D3)⋊(C3⋊Dic3)C2212yes—
32C3×#3724C2211yescharacteristic
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×C4⋊(C3⋊Dic3)—31no—
39#64133—31no—
40#64097—31no—
41C3×C4×#67—31no—
42C3×C4×#67—31no—
43C2×C3×C4⋊Dic3—31no—
44C3×#924—31no—
45C3×#897—31no—
46C3×D3×C4⋊C4—31no—
47#63982—32no—
48#67⋊Dic3—32no—
49Dic3×#67—32no—
50#63964—32no—
51#63918—31no—
52#63918—31no—
53#63918—61no—
54C4×#625D311yescharacteristic
55#63899—32no—
56#63896—32no—
57#63893—32no—
58D3×C4⋊Dic3—31no—
59D3×C4⋊Dic3—31no—
60D3×C4⋊Dic3—61no—
61D3×C4⋊Dic3D311yescharacteristic, complemented
62#63879—32no—
63#63857—32no—
64#63857D311yescharacteristic, complemented
65#63856—31no—
66#63856—31no—
67#63856—61no—
68#63847—32no—
69#63846—32no—
70#63845—32no—
71#63844—31no—
72#63843—31no—
73Dic3×Dic6—31no—
74C22×C32×D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×#634—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—22no—
87C32×C4×D3—22no—
88#6293—42no—
89D3×C3⋊Dic3—42no—
90C3×#625Q814yescomplemented
91C3×D3×Dic3—42no—
92#5635—91no—
93#5543—91no—
94#5511—91no—
95C22×C32×C4—31no—
96C22×C32×C4—31no—
97C22×C3⋊Dic3—32no—
98C2×#634—32no—
99C2×#634C2×D311yescharacteristic
100C2×C3×#67—31no—
101C2×C3×#67—31no—
102C22×C3×Dic3—32no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3C2×D311yescharacteristic
107C2×C3×C4×D3C2×D311yescharacteristic
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×Dic6—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—61no—
113C2×#627—32no—
114C2×#627—32no—
115C2×#627—62no—
116C2×#625C2×D311yescharacteristic
117C2×D3×Dic3—32no—
118C2×D3×Dic3—32no—
119C2×D3×Dic3—62no—
120C2×D3×Dic3C2×D312yes—
121C32×C4⋊C4—31no—
122#3757—32no—
123C4⋊(C3⋊Dic3)—31no—
124C4⋊(C3⋊Dic3)—31no—
125C4⋊(C3⋊Dic3)—31no—
126C4⋊(C3⋊Dic3)—32no—
127C4⋊(C3⋊Dic3)—61no—
128C4⋊(C3⋊Dic3)—61no—
129C4⋊(C3⋊Dic3)—61no—
130C4⋊(C3⋊Dic3)—121no—
131C4⋊(C3⋊Dic3)C2×D311yescharacteristic
132#3750—32no—
133#3750—32no—
134C4×C3⋊Dic3C2×D311yescharacteristic
135C3×#217—32no—
136C3×#217—31no—
137C3×#217—31no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3—32no—
145C3×C4⋊Dic3—32no—
146C3×C4⋊Dic3—61no—
147C3×C4⋊Dic3C2×D311yescharacteristic
148C3×C4⋊Dic3C2×D311yescharacteristic
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—31no—
152C3×Dic3⋊C4—31no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—61no—
156#3724—32no—
157#3724—32no—
158#3724—32no—
159#3724—62no—
160#3724C2×D311yescharacteristic
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—62no—
168Dic3⋊Dic3—62no—
169Dic3⋊Dic3C2×D312yes—
170Dic3⋊Dic3C2×D312yes—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—62no—
174(C2×D3)⋊Dic3C2×D311yescharacteristic
175(C2×D3)⋊Dic3C2×D312yes—
176(C2×D3)⋊Dic3C2×D311yescharacteristic
177Dic32—32no—
178Dic32—32no—
179Dic32—32no—
180C22×C33C2411yescharacteristic
181C2×C32×D3—21no—
182C2×C32×D3—21no—
183C2×C32×D3—21no—
184C2×C32×D3—21no—
185C2×C32×D3C2×Q812yes—
186C2×C32×D3C2×Q812yes—
187C33×C4#4112yes—
188C3⋊(C3⋊Dic3)—22no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3C2×Q812yes—
193C32×Dic3—21no—
194C32×Dic3—21no—
195C32×Dic3—22no—
196C3×C22⋊Q8—91no—
197C3×C4×D4—91no—
198C2×C3×C4⋊C4—91no—
199#946—91no—
200Q8×Dic3—91no—
201D4×Dic3—92no—
202C4×#67—31no—
203C4×#67—31no—
204C4×#67—92no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—91no—
207C2×C4⋊Dic3—91no—
208C2×C4⋊Dic3—181no—
209#924—31no—
210#924—92no—
211#924—91no—
212#924—91no—
213#924—181no—
214#897—31no—
215#897—92no—
216#896—92no—
217D3×C4⋊C4—31no—
218D3×C4⋊C4—91no—
219#890—92no—
220#889—92no—
221#889—92no—
222#888—91no—
223#888—91no—
224#888—181no—
225#887—91no—
226#67⋊C4—92no—
227#878—92no—
228#878—92no—
229#878—92no—
230#869—91no—
231C4×Dic6—91no—
232C23×C32—31no—
233C23×C32—31no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3C22×D311yescharacteristic
237C22×C3×D3C22×D311yescharacteristic
238C22×C3×D3C22×D311yescharacteristic
239C22×C3×D3C22×D311yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—31no—
244C2×C32×C4—31no—
245C2×C32×C4—32no—
246C2×C32×C4—41no—
247C2×C32×C4—62no—
248C2×C32×C4—62no—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—32no—
254C2×C3⋊Dic3—32no—
255C2×C3⋊Dic3—62no—
256C2×C3⋊Dic3—62no—
257C2×C3⋊Dic3—62no—
258C2×C3⋊Dic3—122no—
259C2×C3⋊Dic3—122no—
260C2×C3⋊Dic3C22×D312yes—
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264#634—22no—
265#634—122no—
266C3×#67—34no—
267C3×#67—34no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—122no—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D311yescharacteristic
290C3×C4×D3—24no—
291C3×C4×D3—22no—
292C3×C4×D3—22no—
293C3×C4×D3—22no—
294C3×C4×D3—22no—
295C3×C4×D3—42no—
296C3×C4×D3—122no—
297C3×Dic6—62no—
298C3×Dic6—62no—
299C3×Dic6—122no—
300#627—122no—
301#627—122no—
302#627—124no—
303#625Dic614yescomplemented
304D3×Dic3—42no—
305D3×Dic3—122no—
306D3×Dic3—122no—
307D3×Dic3—124no—
308#554—271noSylow
309C2×C33C22×Q811yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C2×C33H(5,𝔽2)11yescharacteristic
312C32×D3—22no—
313C32×D3—22no—
314C2×C3×Q8—91no—
315C2×C3×D4—91no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—92no—
323C2×#67—31no—
324C2×#67—31no—
325C22×Dic3—32no—
326C22×Dic3—92no—
327C22×Dic3—92no—
328C22×Dic3—182no—
329C2×C4×D3—32no—
330C2×C4×D3—92no—
331C2×C4×D3D3211yescharacteristic
332C2×C4×D3D3211yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—92no—
337C2×Dic6—92no—
338C2×Dic6—92no—
339C2×Dic6—182no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—92no—
344C3×C4⋊C4—92no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4—92no—
350C3×C42—91no—
351#217—31no—
352#217—32no—
353#217—31no—
354#217—92no—
355#217—92no—
356#217—182no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—92no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—32no—
364C4⋊Dic3—32no—
365C4⋊Dic3—61no—
366C4⋊Dic3—92no—
367C4⋊Dic3—92no—
368C4⋊Dic3—92no—
369C4⋊Dic3—91no—
370C4⋊Dic3—91no—
371C4⋊Dic3—91no—
372C4⋊Dic3—92no—
373C4⋊Dic3—182no—
374C4⋊Dic3—181no—
375C4⋊Dic3—181no—
376C4⋊Dic3—181no—
377C4⋊Dic3—361no—
378C4⋊Dic3D3211yescharacteristic
379Dic3⋊C4—32no—
380Dic3⋊C4—32no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—92no—
384Dic3⋊C4—92no—
385Dic3⋊C4—92no—
386Dic3⋊C4—92no—
387Dic3⋊C4—92no—
388Dic3⋊C4—92no—
389Dic3⋊C4—92no—
390Dic3⋊C4—92no—
391Dic3⋊C4—182no—
392Dic3⋊C4—182no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—92no—
397C4×Dic3—92no—
398C4×Dic3—92no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—32no—
403C22×C32—32no—
404C22×C32—41no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32—61no—
408C22×C32—61no—
409C22×C32C23×D311yescharacteristic
410C22×C32C23×D311yescharacteristic
411C22×C32C23×D311yescharacteristic
412C2×C3×D3—22no—
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3C2×Dic612yes—
427C2×C3×D3C2×Dic612yes—
428C2×C3×D3D3×Q812yes—
429C2×C3×D3D3×Q812yes—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—22no—
433C32×C4—42no—
434C32×C4—61no—
435C32×C4—61no—
436C32×C4—62no—
437C32×C4#23512yes—
438C32×C4#23712yes—
439C32×C4#23712yes—
440C3⋊Dic3—21no—
441C3⋊Dic3—22no—
442C3⋊Dic3—22no—
443C3⋊Dic3—62no—
444C3⋊Dic3—62no—
445C3⋊Dic3—62no—
446C3⋊Dic3—122no—
447C3⋊Dic3—122no—
448C3⋊Dic3—122no—
449C3⋊Dic3—242no—
450C3⋊Dic3C2×Dic612yes—
451C3×Dic3—22no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—32no—
459C3×Dic3—32no—
460C3×Dic3—42no—
461C3×Dic3—41no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—62no—
465C3×Dic3—62no—
466C3×Dic3—61no—
467C3×Dic3—62no—
468C3×Dic3—62no—
469C3×Dic3—61no—
470C3×Dic3—122no—
471C3×Dic3—122no—
472C4⋊Q8—271no—
473#125—272no—
474C22⋊Q8—91no—
475C22⋊Q8—272no—
476C22⋊Q8—272no—
477C22⋊Q8—271no—
478C4×Q8—271no—
479C4×D4—91no—
480C4×D4—272no—
481C2×C4⋊C4—91no—
482C2×C4⋊C4—271no—
483C33#55411yescharacteristic, complemented, Sylow
484C23×C3—31no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—61no—
489C23×C3—61no—
490C22×D3C2×D3211yescharacteristic
491C22×D3C2×D3211yescharacteristic
492C3×Q8—182no—
493C3×D4—94no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—32no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—32no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—62no—
507C2×C3×C4—64no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—91no—
513C2×C3×C4—92no—
514C2×C3×C4—92no—
515C2×C3×C4—91no—
516C2×C3×C4—122no—
517C2×C3×C4—362no—
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521#67—34no—
522#67—34no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—92no—
536C2×Dic3—92no—
537C2×Dic3—92no—
538C2×Dic3—122no—
539C2×Dic3—182no—
540C2×Dic3—182no—
541C2×Dic3—182no—
542C2×Dic3—362no—
543C2×Dic3—362no—
544C2×Dic3—362no—
545C2×Dic3—364no—
546C2×Dic3C2×D3211yescharacteristic
547C2×Dic3C2×D3211yescharacteristic
548C2×Dic3C2×D3212yes—
549C4×D3—22no—
550C4×D3—22no—
551C4×D3—122no—
552C4×D3—362no—
553Dic6—62no—
554Dic6—62no—
555Dic6—122no—
556Dic6—362no—
557Dic6—362no—
558Dic6—362no—
559Dic6—364no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—41no—
570C2×C32—41no—
571C2×C32—41no—
572C2×C32—62no—
573C2×C32—62no—
574C2×C32C22×Dic611yescharacteristic
575C2×C32C2×#23511yescharacteristic
576C2×C32C2×#23711yescharacteristic
577C2×C32C2×#23711yescharacteristic
578C2×C32#100411yescharacteristic
579C2×C32C2×D3×Q811yescharacteristic
580C2×C32C2×D3×Q811yescharacteristic
581C2×C32#100911yescharacteristic
582C2×C32#100911yescharacteristic
583C3×D3—24no—
584C3×D3—22no—
585C3×D3—22no—
586C3×D3—22no—
587C3×D3—22no—
588C3×D3—42no—
589C2×Q8—91no—
590C2×Q8—272no—
591C2×D4—91no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—92no—
595C22×C4—272no—
596C4⋊C4—31no—
597C4⋊C4—92no—
598C4⋊C4—91no—
599C4⋊C4—92no—
600C4⋊C4—91no—
601C4⋊C4—272no—
602C4⋊C4—272no—
603C4⋊C4—272no—
604C4⋊C4—272no—
605C4⋊C4—271no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—92no—
609C22⋊C4—272no—
610C42—91no—
611C42—272no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—32no—
617C22×C3—32no—
618C22×C3—32no—
619C22×C3—41no—
620C22×C3—62no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—62no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3C22×D3211yescharacteristic
635C22×C3C22×D3211yescharacteristic
636C22×C3C22×D3211yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3D3×Dic612yes—
642C2×D3D3×Dic612yes—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—42no—
647C3×C4—62no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—62no—
651C3×C4—62no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—92no—
655C3×C4—122no—
656C3×C4—121no—
657C3×C4—182no—
658C3×C4—181no—
659C3×C4—182no—
660C3×C4#379512yes—
661C3×C4#380412yes—
662C3×C4#380512yes—
663Dic3—22no—
664Dic3—21no—
665Dic3—21no—
666Dic3—32no—
667Dic3—32no—
668Dic3—62no—
669Dic3—62no—
670Dic3—62no—
671Dic3—61no—
672Dic3—62no—
673Dic3—61no—
674Dic3—62no—
675Dic3—62no—
676Dic3—122no—
677Dic3—122no—
678Dic3—182no—
679Dic3—182no—
680Dic3—182no—
681Dic3—362no—
682Dic3—362no—
683Dic3—362no—
684Dic3—722no—
685C32—21no—
686C32—21no—
687C32—21no—
688C32—41no—
689C32#551111yescharacteristic, complemented
690C32#554311yescharacteristic, complemented
691C32#563511yescharacteristic, complemented
692C23—31no—
693C23—31no—
694Q8—182no—
695Q8—1082no—
696D4—94no—
697C2×C4—32no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—92no—
705C2×C4—92no—
706C2×C4—272no—
707C2×C4—362no—
708C2×C4—1082no—
709C2×C4D3311yescharacteristic
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—41no—
720C2×C3—41no—
721C2×C3—41no—
722C2×C3—64no—
723C2×C3—62no—
724C2×C3—62no—
725C2×C3—62no—
726C2×C3—62no—
727C2×C3—122no—
728C2×C3C2×D3×Dic611yescharacteristic
729C2×C3C2×D3×Dic611yescharacteristic
730C2×C3C2×#379511yescharacteristic
731C2×C3#6430711yescharacteristic
732C2×C3#6430811yescharacteristic
733C2×C3#6431411yescharacteristic
734C2×C3D32×Q811yescharacteristic
735C2×C3C2×#380411yescharacteristic
736C2×C3C2×#380511yescharacteristic
737D3—22no—
738D3—22no—
739C22—32no—
740C22—32no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22C2×D3311yescharacteristic
746C4—62no—
747C4—61no—
748C4—61no—
749C4—92no—
750C4—182no—
751C4—181no—
752C4—182no—
753C4—542no—
754C4#8896112yes—
755C3—21no—
756C3—21no—
757C3—21no—
758C3—41no—
759C3#1059453211yescharacteristic, complemented
760C3#1059498811yescharacteristic, complemented
761C3#1059499311yescharacteristic, complemented
762C2—62no—
763C2—62no—
764C2D32×Dic611yescharacteristic
765C2#1172438411yescharacteristic
766C2C2×#8896111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#625C22
hypercenterC2×C4D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723668C2semidirect
2. #11723535C2semidirect
3. D3×C4⋊(C3⋊Dic3)C2semidirect
4. #11723425C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63857C2semidirect
8. #11723017C2semidirect
9. #11722980C2semidirect
10. #11722971C2semidirect
61. D3×C4⋊Dic3D3semidirect
64. #63857D3semidirect
90. C3×#625Q8semidirect
303. #625Dic6semidirect
483. C33#554semidirect
689. C32#5511semidirect
690. C32#5543semidirect
691. C32#5635semidirect
759. C3#10594532semidirect
760. C3#10594988semidirect
761. C3#10594993semidirect

Maximal subgroups

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

subgroupindex
#117236682
#117235352
D3×C4⋊(C3⋊Dic3)2
#117234252
C3×C4×#6252
C3×D3×C4⋊Dic32
C3×#638572
#117230172
#117229802
#117229712
#117229242
#105949933
#105949883
#105945323