Finite Group Databasebeta

← #13168510

Subgroups — #13168510

Order 1728.

1154 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723668C211yesmaximal, characteristic, complemented
2C4×#6291C211yesmaximal, characteristic
3#11723449C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63872C211yesmaximal, characteristic, complemented
7C3×#63857C211yesmaximal, characteristic, complemented
8#11723028C212yesmaximal, complemented
9#11723013C212yesmaximal, complemented
10#11722987C212yesmaximal
11#11722914C212yesmaximal, complemented
12#10594825—31nomaximal
13#10594553—31nomaximal
14#10594457—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6291C2211yescharacteristic
19C2×C3×D3×Dic3C2212yes—
20C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C3×C4×C3⋊Dic3C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24#88815C2212yes—
25#88813C2212yes—
26#88807C2211yescharacteristic
27Dic3⋊(C3⋊Dic3)C2212yes—
28#88804C2211yescharacteristic
29#88804C2212yes—
30#88804C2212yes—
31(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C4×#638—31no—
39#64106—31no—
40#64101—31no—
41C2×C3×C4⋊Dic3—31no—
42C3×#924—31no—
43C3×#897—31no—
44C3×D3×C4⋊C4—31no—
45C3×#890—31no—
46C3×#890—31no—
47#63966—32no—
48#63955—32no—
49C4×#626—31no—
50C4×#626—31no—
51C4×#626—61no—
52#63890—32no—
53D3×C4⋊Dic3D311yescharacteristic, complemented
54#63878—32no—
55#63872—32no—
56#63872D311yescharacteristic, complemented
57#63871—31no—
58#63871—31no—
59#63871—61no—
60#63857D311yescharacteristic, complemented
61#63850—32no—
62#63849—31no—
63#63849—31no—
64#63849—61no—
65#63848—32no—
66#63848—32no—
67#63848—32no—
68#63846—32no—
69#63845—32no—
70#63844—31no—
71#63843—31no—
72Dic3×Dic6—31no—
73#63841—32no—
74C22×C3⋊(C3⋊D3)C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C4×C3⋊(C3⋊D3)—22no—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C3×#634—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88#6291—22no—
89C3×D3×Dic3—24no—
90#5694—91no—
91#5642—91no—
92#5513—91no—
93C22×C32×C4—31no—
94C2×#638—31no—
95C2×C4×C3⋊D3—31no—
96C2×C4×C3⋊D3—31no—
97C2×C4×C3⋊D3—31no—
98C2×C4×C3⋊D3—61no—
99C2×C4×C3⋊D3—61no—
100C2×C4×C3⋊D3—61no—
101C2×C4×C3⋊D3—121no—
102C2×#634C2×D311yescharacteristic
103C22×C3×Dic3—32no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3C2×D311yescharacteristic
107C2×C3×C4×D3C2×D311yescharacteristic
108C2×C3×Dic6—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—61no—
111C2×#626—31no—
112C2×#626—31no—
113C2×#626—61no—
114C2×D3×Dic3C2×D312yes—
115C32×C4⋊C4—31no—
116C32×C4⋊C4—31no—
117#3757—31no—
118#3752—32no—
119#3752—31no—
120#3752—32no—
121C4⋊(C3⋊Dic3)—32no—
122C4⋊(C3⋊Dic3)C2×D311yescharacteristic
123#3750—31no—
124C4×C3⋊Dic3—32no—
125C4×C3⋊Dic3C2×D311yescharacteristic
126C3×#217—32no—
127C3×(C2×D3)⋊C4—32no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—31no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—32no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3—32no—
136C3×C4⋊Dic3—61no—
137C3×C4⋊Dic3C2×D311yescharacteristic
138C3×C4⋊Dic3C2×D311yescharacteristic
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×Dic3⋊C4—32no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—61no—
148#3724—32no—
149Dic3⋊Dic3—32no—
150Dic3⋊Dic3—32no—
151Dic3⋊Dic3—31no—
152Dic3⋊Dic3—32no—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—62no—
156Dic3⋊Dic3—61no—
157Dic3⋊Dic3C2×D312yes—
158Dic3⋊Dic3C2×D312yes—
159Dic3⋊Dic3C2×D312yes—
160Dic3⋊Dic3C2×D312yes—
161#3722—31no—
162#3722—31no—
163#3722—32no—
164#3722—32no—
165#3722—32no—
166#3722—32no—
167#3722—62no—
168#3722—62no—
169#3722—61no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—61no—
173(C2×D3)⋊Dic3C2×D312yes—
174Dic32—32no—
175Dic32—32no—
176Dic32—32no—
177Dic32—32no—
178Dic32—32no—
179Dic32—62no—
180C22×C33C2411yescharacteristic
181C2×C3⋊(C3⋊D3)—21no—
182C2×C3⋊(C3⋊D3)—21no—
183C2×C3⋊(C3⋊D3)—21no—
184C2×C32×D3—21no—
185C2×C32×D3—21no—
186C2×C32×D3#4112yes—
187C33×C4#4112yes—
188C3⋊(C3⋊Dic3)—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—21no—
193C32×Dic3—22no—
194C32×Dic3—21no—
195C32×Dic3—22no—
196C3×#125—91no—
197C3×C22⋊Q8—91no—
198C2×C3×C4⋊C4—91no—
199#946—91no—
200Q8×Dic3—91no—
201#929—92no—
202C4×#67—91no—
203C4×#67—91no—
204C4×#67—181no—
205#926—92no—
206C2×C4⋊Dic3—31no—
207#924—31no—
208#898—92no—
209#898—92no—
210#898—92no—
211#897—31no—
212#897—91no—
213#897—91no—
214#897—181no—
215#894—92no—
216#892—91no—
217#892—91no—
218#892—92no—
219#892—91no—
220#892—181no—
221D3×C4⋊C4—31no—
222#890—31no—
223#890—31no—
224#890—92no—
225#890—92no—
226#889—92no—
227#887—91no—
228#886—92no—
229#877—92no—
230C4×D12—91no—
231C4×Dic6—91no—
232C23×C32—31no—
233C22×C3⋊D3—31no—
234C22×C3⋊D3—31no—
235C22×C3⋊D3—31no—
236C22×C3⋊D3—61no—
237C22×C3⋊D3—61no—
238C22×C3⋊D3—61no—
239C22×C3⋊D3—121no—
240C22×C3×D3—21no—
241C22×C3×D3C22×D311yescharacteristic
242C22×C3×D3C22×D311yescharacteristic
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—31no—
247C2×C32×C4—32no—
248C2×C32×C4—32no—
249C2×C32×C4—41no—
250C2×C32×C4—62no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254#638—62no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—61no—
259C2×C3⋊Dic3—61no—
260C2×C3⋊Dic3—61no—
261C2×C3⋊Dic3—121no—
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D312yes—
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D311yescharacteristic
266C4×C3⋊D3—62no—
267C4×C3⋊D3—64no—
268C4×C3⋊D3—62no—
269C4×C3⋊D3—62no—
270C4×C3⋊D3—122no—
271C4×C3⋊D3—122no—
272C4×C3⋊D3—124no—
273#634—22no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—64no—
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D312yes—
295C2×C3×Dic3C22×D312yes—
296C3×C4×D3—22no—
297C3×C4×D3—22no—
298C3×C4×D3—42no—
299C3×C4×D3—64no—
300C3×Dic6—62no—
301C3×Dic6—62no—
302C3×Dic6—122no—
303#626—64no—
304#626—62no—
305#626—62no—
306D3×Dic3—24no—
307#552—271noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C332−1+411yescharacteristic
311C3⋊(C3⋊D3)—41no—
312C32×D3—22no—
313C2×C3×Q8—91no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—92no—
318C2×#67—91no—
319C2×#67—91no—
320C2×#67—181no—
321C22×Dic3—32no—
322C2×D12—91no—
323C2×C4×D3—32no—
324C2×C4×D3—91no—
325C2×C4×D3—91no—
326C2×C4×D3—91no—
327C2×C4×D3—181no—
328C2×C4×D3—181no—
329C2×C4×D3—181no—
330C2×C4×D3—361no—
331C2×C4×D3D3211yescharacteristic
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—92no—
342C3×C4⋊C4—92no—
343C3×C4⋊C4—92no—
344C3×C4⋊C4—92no—
345C3×C4⋊C4—91no—
346C3×C22⋊C4—92no—
347C3×C42—91no—
348#217—32no—
349#217—91no—
350#217—91no—
351#217—181no—
352(C2×D3)⋊C4—32no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—92no—
355(C2×D3)⋊C4—92no—
356(C2×D3)⋊C4—92no—
357(C2×D3)⋊C4—91no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—92no—
362(C2×D3)⋊C4—92no—
363(C2×D3)⋊C4—182no—
364(C2×D3)⋊C4—182no—
365(C2×D3)⋊C4—181no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—32no—
369C4⋊Dic3—32no—
370C4⋊Dic3—32no—
371C4⋊Dic3—32no—
372C4⋊Dic3—61no—
373C4⋊Dic3—92no—
374C4⋊Dic3—92no—
375C4⋊Dic3—92no—
376C4⋊Dic3—91no—
377C4⋊Dic3—182no—
378C4⋊Dic3D3211yescharacteristic
379C4⋊Dic3D3211yescharacteristic
380Dic3⋊C4—32no—
381Dic3⋊C4—32no—
382Dic3⋊C4—32no—
383Dic3⋊C4—32no—
384Dic3⋊C4—92no—
385Dic3⋊C4—92no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—92no—
389Dic3⋊C4—181no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—92no—
394C4×Dic3—92no—
395C4×Dic3—92no—
396C4×Dic3—92no—
397C4×Dic3—92no—
398C4×Dic3—92no—
399C4×Dic3—182no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—32no—
404C22×C32—41no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32C23×D311yescharacteristic
408C22×C32C23×D311yescharacteristic
409C22×C32C23×D311yescharacteristic
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—62no—
414C2×C3⋊D3—62no—
415C2×C3⋊D3—62no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—121no—
423C2×C3⋊D3—121no—
424C2×C3⋊D3—121no—
425C2×C3⋊D3—121no—
426C2×C3⋊D3—121no—
427C2×C3⋊D3—121no—
428C2×C3⋊D3—122no—
429C2×C3⋊D3—122no—
430C2×C3⋊D3—122no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—22no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3#23712yes—
439C2×C3×D3#23912yes—
440C32×C4—22no—
441C32×C4—22no—
442C32×C4—22no—
443C32×C4—42no—
444C32×C4—62no—
445C32×C4—61no—
446C32×C4—62no—
447C32×C4#23512yes—
448C32×C4#23712yes—
449C32×C4#23912yes—
450C3⋊Dic3—21no—
451C3⋊Dic3—22no—
452C3⋊Dic3—22no—
453C3⋊Dic3—21no—
454C3⋊Dic3—61no—
455C3⋊Dic3—62no—
456C3⋊Dic3—61no—
457C3⋊Dic3—61no—
458C3⋊Dic3—121no—
459C3⋊Dic3—121no—
460C3⋊Dic3—122no—
461C3×Dic3—21no—
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—41no—
468C3×Dic3—42no—
469C3×Dic3—42no—
470C3×Dic3—62no—
471C3×Dic3—62no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3—62no—
475C3×Dic3—62no—
476C3×Dic3—61no—
477C3×Dic3—62no—
478C3×Dic3—61no—
479C3×Dic3—122no—
480C3×Dic3—121no—
481C3×Dic3—122no—
482#126—272no—
483#125—91no—
484#125—272no—
485#123—272no—
486C22⋊Q8—91no—
487C22⋊Q8—271no—
488C4×Q8—271no—
489C4×D4—271no—
490#117—272no—
491#117—271no—
492C2×C4⋊C4—91no—
493C33#55211yescharacteristic, complemented, Sylow
494C23×C3—31no—
495C23×C3—31no—
496C23×C3—61no—
497C22×D3—91no—
498C22×D3—91no—
499C22×D3—91no—
500C22×D3—181no—
501C22×D3—181no—
502C22×D3—181no—
503C22×D3—361no—
504C22×D3C2×D3211yescharacteristic
505C3×Q8—182no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—31no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—62no—
517C2×C3×C4—61no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—92no—
522C2×C3×C4—91no—
523C2×C3×C4—92no—
524C2×C3×C4—91no—
525C2×C3×C4—122no—
526C2×C3×C4—184no—
527C2×C3×C4C2×D3211yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C2×D3211yescharacteristic
530#67—182no—
531#67—182no—
532#67—184no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—64no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—91no—
549C2×Dic3—181no—
550C2×Dic3—181no—
551C2×Dic3—181no—
552C2×Dic3—361no—
553C2×Dic3C2×D3212yes—
554C2×Dic3C2×D3211yescharacteristic
555C2×Dic3C2×D3212yes—
556D12—182no—
557C4×D3—22no—
558C4×D3—64no—
559C4×D3—184no—
560C4×D3—182no—
561C4×D3—182no—
562C4×D3—182no—
563C4×D3—362no—
564C4×D3—362no—
565C4×D3—364no—
566Dic6—62no—
567Dic6—62no—
568Dic6—122no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—41no—
579C2×C32—41no—
580C2×C32—41no—
581C2×C32—62no—
582C2×C32C2×#23511yescharacteristic
583C2×C32C2×#23711yescharacteristic
584C2×C32C2×#23711yescharacteristic
585C2×C32C2×#23911yescharacteristic
586C2×C32C2×#23911yescharacteristic
587C2×C32#100711yescharacteristic
588C2×C32D3×#4111yescharacteristic
589C2×C32#101011yescharacteristic
590C2×C32#101011yescharacteristic
591C3⋊D3—122no—
592C3⋊D3—122no—
593C3⋊D3—122no—
594C3⋊D3—124no—
595C3⋊D3—121no—
596C3⋊D3—121no—
597C3⋊D3—121no—
598C3×D3—22no—
599C3×D3—22no—
600C3×D3—42no—
601C2×Q8—91no—
602C2×D4—271no—
603C22×C4—31no—
604C22×C4—92no—
605C22×C4—271no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—92no—
609C4⋊C4—92no—
610C4⋊C4—92no—
611C4⋊C4—92no—
612C4⋊C4—91no—
613C4⋊C4—272no—
614C4⋊C4—271no—
615C4⋊C4—272no—
616C22⋊C4—92no—
617C22⋊C4—272no—
618C22⋊C4—271no—
619C22⋊C4—272no—
620C22⋊C4—271no—
621C42—91no—
622C42—272no—
623C42—272no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—32no—
629C22×C3—41no—
630C22×C3—62no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3C22×D3211yescharacteristic
638C22×C3C22×D3211yescharacteristic
639C22×C3C22×D3211yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—182no—
643C2×D3—182no—
644C2×D3—182no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—361no—
655C2×D3—361no—
656C2×D3—361no—
657C2×D3—361no—
658C2×D3—361no—
659C2×D3—361no—
660C2×D3—362no—
661C2×D3—362no—
662C2×D3—362no—
663C2×D3#379612yes—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—42no—
668C3×C4—62no—
669C3×C4—61no—
670C3×C4—62no—
671C3×C4—61no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—121no—
675C3×C4—122no—
676C3×C4—122no—
677C3×C4—181no—
678C3×C4—181no—
679C3×C4—182no—
680C3×C4—182no—
681C3×C4#379612yes—
682C3×C4#379912yes—
683C3×C4#380412yes—
684Dic3—22no—
685Dic3—22no—
686Dic3—21no—
687Dic3—62no—
688Dic3—62no—
689Dic3—62no—
690Dic3—61no—
691Dic3—62no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—62no—
696Dic3—122no—
697Dic3—122no—
698Dic3—121no—
699Dic3—182no—
700Dic3—181no—
701Dic3—181no—
702Dic3—181no—
703Dic3—361no—
704Dic3—361no—
705Dic3—362no—
706C32—21no—
707C32—21no—
708C32—21no—
709C32—41no—
710C32#551311yescharacteristic, complemented
711C32#564211yescharacteristic, complemented
712C32#569411yescharacteristic, complemented
713C23—31no—
714C23—271no—
715Q8—182no—
716D4—542no—
717C2×C4—32no—
718C2×C4—32no—
719C2×C4—31no—
720C2×C4—62no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—92no—
724C2×C4—92no—
725C2×C4—184no—
726C2×C4—271no—
727C2×C4—542no—
728C2×C4D3311yescharacteristic
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—41no—
739C2×C3—41no—
740C2×C3—41no—
741C2×C3—62no—
742C2×C3—62no—
743C2×C3—122no—
744C2×C3C2×#379611yescharacteristic
745C2×C3C2×#379611yescharacteristic
746C2×C3#6429711yescharacteristic
747C2×C3C2×#379911yescharacteristic
748C2×C3#6430911yescharacteristic
749C2×C3D3×#23711yescharacteristic
750C2×C3#6431511yescharacteristic
751C2×C3D3×#23911yescharacteristic
752C2×C3C2×#380411yescharacteristic
753D3—22no—
754D3—362no—
755D3—362no—
756D3—362no—
757D3—364no—
758D3—361no—
759D3—361no—
760D3—361no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—541no—
765C22—541no—
766C22—541no—
767C22C2×D3311yescharacteristic
768C4—62no—
769C4—62no—
770C4—61no—
771C4—182no—
772C4—181no—
773C4—181no—
774C4—182no—
775C4—541no—
776C4#8896212yes—
777C3—21no—
778C3—21no—
779C3—21no—
780C3—41no—
781C3#1059445711yescharacteristic, complemented
782C3#1059455311yescharacteristic, complemented
783C3#1059482511yescharacteristic, complemented
784C2—62no—
785C2—1081no—
786C2D3×#379611yescharacteristic
787C2#1172439311yescharacteristic
788C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6291C22
hypercenterC2×C4D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723668C2semidirect
3. #11723449C2semidirect
4. #11723413C2semidirect
5. C3×D3×C4⋊Dic3C2semidirect
6. C3×#63872C2semidirect
7. C3×#63857C2semidirect
8. #11723028C2semidirect
9. #11723013C2semidirect
11. #11722914C2semidirect
53. D3×C4⋊Dic3D3semidirect
56. #63872D3semidirect
60. #63857D3semidirect
493. C33#552semidirect
710. C32#5513semidirect
711. C32#5642semidirect
712. C32#5694semidirect
781. C3#10594457semidirect
782. C3#10594553semidirect
783. C3#10594825semidirect

Maximal subgroups

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

subgroupindex
#117236682
C4×#62912
#117234492
#117234132
C3×D3×C4⋊Dic32
C3×#638722
C3×#638572
#117230282
#117230132
#117229872
#117229142
#105948253
#105945533
#105944573