Finite Group Databasebeta

← #13168652

Subgroups — #13168652

Order 1728.

1162 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic
2#11723536C211yesmaximal, characteristic, complemented
3C4×Dic3×C3⋊D3C211yesmaximal, characteristic
4#11723451C211yesmaximal, characteristic, complemented
5C3×#63871C211yesmaximal, characteristic
6C3×#63844C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11723016C212yesmaximal, complemented
9#11722983C212yesmaximal
10#11722942C212yesmaximal, complemented
11#11722919C212yesmaximal
12#10595367—31nomaximal
13#10594385—31nomaximal
14#10593882—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6293C2212yes—
19C2×Dic3×C3⋊D3C2211yescharacteristic
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25#88815C2212yes—
26#88814C2212yes—
27#88806C2212yes—
28#88806C2212yes—
29#88806C2212yes—
30Dic3×C3⋊Dic3C2211yescharacteristic
31Dic3×C3⋊Dic3C2211yescharacteristic
32C3×#3724C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×#3722C2212yes—
36C3×Dic32C2212yes—
37C3×Dic32C2212yes—
38#64153—31no—
39#64097—31no—
40C42×C3⋊D3—31no—
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×#897—31no—
44C3×#887—31no—
45C3×C4×Dic6—31no—
46C3×C4×Dic6—31no—
47#63919—31no—
48#63919—31no—
49#63919—61no—
50C4×#627—32no—
51#63899—32no—
52#63896—32no—
53#63877—32no—
54#63877—32no—
55C4×D3×Dic3—31no—
56C4×D3×Dic3—31no—
57C4×D3×Dic3—61no—
58#63874—32no—
59#63873—31no—
60#63873—31no—
61#63873—61no—
62#63871—31no—
63#63871D311yescharacteristic
64#63870—32no—
65#63865—32no—
66#63857—31no—
67#63856—31no—
68#63847—32no—
69#63847—32no—
70#63844—32no—
71#63844D311yescharacteristic, complemented
72Dic3×Dic6D311yescharacteristic, complemented
73#63837—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4×C3⋊D3—22no—
82C3×#634—22no—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×Dic6—22no—
88#6293—24no—
89Dic3×C3⋊D3—22no—
90Dic3×C3⋊D3Q814yescomplemented
91#5622—91no—
92#5578—91no—
93#5578—91no—
94C2×C32×Q8—31no—
95C2×C4×C3⋊D3—31no—
96C2×C4×C3⋊D3—31no—
97C2×C4×C3⋊D3C2×D311yescharacteristic
98C2×#634—32no—
99C2×#634C2×D311yescharacteristic
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—61no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—61no—
107C2×C3×Dic6C2×D311yescharacteristic
108C2×C3×Dic6C2×D311yescharacteristic
109C2×#627—32no—
110C2×#627—32no—
111C2×#627—62no—
112C2×D3×Dic3—31no—
113C2×D3×Dic3—31no—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—31no—
116C2×D3×Dic3—61no—
117C2×D3×Dic3—61no—
118C32×C4⋊C4—31no—
119C32×C42—31no—
120C4⋊(C3⋊Dic3)C2×D311yescharacteristic
121#3750—32no—
122#3750—32no—
123#3750—32no—
124C4×C3⋊Dic3—31no—
125C4×C3⋊Dic3—31no—
126C4×C3⋊Dic3—31no—
127C4×C3⋊Dic3—31no—
128C4×C3⋊Dic3—31no—
129C4×C3⋊Dic3—61no—
130C4×C3⋊Dic3—61no—
131C4×C3⋊Dic3—61no—
132C4×C3⋊Dic3—121no—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3—61no—
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D311yescharacteristic
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×C4×Dic3—21no—
148C3×C4×Dic3—32no—
149C3×C4×Dic3—32no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—32no—
152C3×C4×Dic3C2×D311yescharacteristic
153C3×C4×Dic3C2×D311yescharacteristic
154#3724—32no—
155#3724—32no—
156#3724—32no—
157#3724—32no—
158#3724—32no—
159#3724—32no—
160#3724—32no—
161#3724—62no—
162#3724—62no—
163#3724—62no—
164#3724C2×D312yes—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3C2×D312yes—
168Dic3⋊Dic3C2×D312yes—
169#3722—32no—
170#3722C2×D312yes—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173Dic32—31no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—61no—
178Dic32—61no—
179Dic32C2×D312yes—
180Dic32C2×D312yes—
181C22×C33C2411yescharacteristic
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3C2×Q812yes—
185C33×C4#4112yes—
186C3⋊(C3⋊Dic3)C2×Q812yes—
187C3⋊(C3⋊Dic3)#4112yes—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—22no—
191C32×Dic3—21no—
192C32×Dic3—22no—
193C32×Dic3—22no—
194C32×Dic3C2×Q812yes—
195C3×C22⋊Q8—91no—
196C3×C4×Q8—91no—
197C3×C4×Q8—91no—
198#946—31no—
199#946—91no—
200Q8×Dic3—31no—
201#944—91no—
202#944—91no—
203#944—91no—
204#944—181no—
205#924—91no—
206C2×C4×Dic3—91no—
207#897—31no—
208#897—91no—
209#896—92no—
210#896—92no—
211#889—92no—
212#889—92no—
213#889—92no—
214#888—91no—
215#888—91no—
216#888—91no—
217#888—181no—
218#887—31no—
219#887—92no—
220#878—92no—
221#877—92no—
222#872—92no—
223#872—92no—
224C42×D3—91no—
225C42×D3—91no—
226C42×D3—181no—
227C4×Dic6—31no—
228C4×Dic6—31no—
229C4×Dic6—92no—
230C4×Dic6—92no—
231C22×C3⋊D3C22×D311yescharacteristic
232C22×C3×D3—31no—
233C22×C3×D3—31no—
234C22×C3×D3—61no—
235C32×Q8—62no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—31no—
240C2×C32×C4—32no—
241C2×C32×C4—32no—
242C2×C32×C4—31no—
243C2×C32×C4—41no—
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—31no—
249C2×C3⋊Dic3—31no—
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—31no—
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—61no—
254C2×C3⋊Dic3—61no—
255C2×C3⋊Dic3—61no—
256C2×C3⋊Dic3—61no—
257C2×C3⋊Dic3—61no—
258C2×C3⋊Dic3—61no—
259C2×C3⋊Dic3—121no—
260C2×C3⋊Dic3—121no—
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D311yescharacteristic
264C4×C3⋊D3—22no—
265C4×C3⋊D3—34no—
266C4×C3⋊D3—62no—
267#634—22no—
268#634—64no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C3×C4×D3—64no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293C3×Dic6—22no—
294C3×Dic6—22no—
295C3×Dic6—42no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—122no—
299#627—64no—
300#627—64no—
301#627—124no—
302D3×Dic3—34no—
303D3×Dic3—34no—
304D3×Dic3—64no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307D3×Dic3—64no—
308#533—271noSylow
309C2×C33C22×Q811yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C3×C3⋊D3—22no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×Q8—91no—
317C22×C3×C4—91no—
318C22×Dic3—91no—
319C22×Dic3—91no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—91no—
324C2×C4×D3—91no—
325C2×C4×D3—91no—
326C2×C4×D3—91no—
327C2×C4×D3—181no—
328C2×C4×D3—181no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6—92no—
333C2×Dic6—92no—
334C2×Dic6—92no—
335C2×Dic6—182no—
336C2×Dic6D3211yescharacteristic
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—92no—
341C3×C4⋊C4—92no—
342C3×C4⋊C4—92no—
343C3×C4⋊C4—91no—
344C3×C22⋊C4—92no—
345C3×C42—31no—
346C3×C42—31no—
347C3×C42—61no—
348C3×C42—92no—
349C3×C42—92no—
350#217—92no—
351(C2×D3)⋊C4—32no—
352(C2×D3)⋊C4—32no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—92no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—32no—
358C4⋊Dic3—32no—
359C4⋊Dic3—61no—
360C4⋊Dic3—92no—
361C4⋊Dic3D3211yescharacteristic
362Dic3⋊C4—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—32no—
365Dic3⋊C4—32no—
366Dic3⋊C4—92no—
367Dic3⋊C4—92no—
368Dic3⋊C4—92no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—182no—
378Dic3⋊C4—182no—
379Dic3⋊C4—182no—
380C4×Dic3—32no—
381C4×Dic3—32no—
382C4×Dic3—32no—
383C4×Dic3—32no—
384C4×Dic3—91no—
385C4×Dic3—91no—
386C4×Dic3—91no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—181no—
394C4×Dic3—181no—
395C4×Dic3—181no—
396C4×Dic3—181no—
397C4×Dic3—181no—
398C4×Dic3—361no—
399C4×Dic3D3211yescharacteristic
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⋊D3D3×Q812yes—
410C2×C3×D3—32no—
411C2×C3×D3—32no—
412C2×C3×D3—62no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C32×C4—22no—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—32no—
423C32×C4—42no—
424C32×C4—61no—
425C32×C4—62no—
426C32×C4—62no—
427C32×C4#23512yes—
428C32×C4#23512yes—
429C32×C4#23712yes—
430C3⋊Dic3—21no—
431C3⋊Dic3—22no—
432C3⋊Dic3—22no—
433C3⋊Dic3—32no—
434C3⋊Dic3—32no—
435C3⋊Dic3—32no—
436C3⋊Dic3—32no—
437C3⋊Dic3—32no—
438C3⋊Dic3—32no—
439C3⋊Dic3—62no—
440C3⋊Dic3—62no—
441C3⋊Dic3—62no—
442C3⋊Dic3—62no—
443C3⋊Dic3—62no—
444C3⋊Dic3—62no—
445C3⋊Dic3—122no—
446C3⋊Dic3—122no—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—42no—
456C3×Dic3—42no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—122no—
465C3×Dic3—122no—
466C3×Dic3D3×Q812yes—
467C3×Dic3D3×Q812yes—
468C4⋊Q8—271no—
469C4⋊Q8—271no—
470#125—272no—
471C22⋊Q8—91no—
472C22⋊Q8—272no—
473C22⋊Q8—271no—
474C4×Q8—91no—
475C4×Q8—91no—
476C4×Q8—272no—
477#117—272no—
478C2×C42—271no—
479C33#53311yescharacteristic, complemented, Sylow
480C23×C3—91no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C3×Q8—62no—
485C3×Q8—62no—
486C3×Q8—122no—
487C3×Q8—182no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—41no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—91no—
505C2×C3×C4—92no—
506C2×C3×C4—92no—
507C2×C3×C4—182no—
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510C2×C3×C4C2×D3211yescharacteristic
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—91no—
521C2×Dic3—91no—
522C2×Dic3—91no—
523C2×Dic3—91no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—94no—
527C2×Dic3—181no—
528C2×Dic3—181no—
529C2×Dic3—181no—
530C2×Dic3—181no—
531C2×Dic3—181no—
532C2×Dic3—181no—
533C2×Dic3—182no—
534C2×Dic3—361no—
535C2×Dic3—361no—
536C2×Dic3C2×D3212yes—
537C2×Dic3C2×D3212yes—
538C2×Dic3C2×D3211yescharacteristic
539C2×Dic3C2×D3211yescharacteristic
540C4×D3—64no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—94no—
544C4×D3—94no—
545C4×D3—184no—
546C4×D3—182no—
547C4×D3—182no—
548C4×D3—184no—
549Dic6—22no—
550Dic6—62no—
551Dic6—62no—
552Dic6—122no—
553Dic6—184no—
554Dic6—184no—
555Dic6—184no—
556Dic6—364no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—41no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32C2×#23511yescharacteristic
570C2×C32C2×#23511yescharacteristic
571C2×C32C2×#23711yescharacteristic
572C2×C32C2×D3×Q811yescharacteristic
573C2×C32C2×D3×Q811yescharacteristic
574C2×C32C2×D3×Q811yescharacteristic
575C2×C32D3×#4111yescharacteristic
576C2×C32D3×#4111yescharacteristic
577C2×C32D3×#4111yescharacteristic
578C3⋊D3—22no—
579C3×D3—64no—
580C3×D3—62no—
581C3×D3—62no—
582C2×Q8—31no—
583C2×Q8—91no—
584C2×Q8—272no—
585C22×C4—91no—
586C22×C4—271no—
587C22×C4—271no—
588C4⋊C4—31no—
589C4⋊C4—92no—
590C4⋊C4—92no—
591C4⋊C4—92no—
592C4⋊C4—91no—
593C4⋊C4—272no—
594C4⋊C4—272no—
595C4⋊C4—272no—
596C4⋊C4—272no—
597C22⋊C4—92no—
598C22⋊C4—272no—
599C42—31no—
600C42—92no—
601C42—92no—
602C42—271no—
603C42—271no—
604C42—271no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—41no—
609C22×C3—92no—
610C22×C3—181no—
611C22×C3—181no—
612C22×C3C22×D3211yescharacteristic
613C22×C3C22×D3211yescharacteristic
614C22×C3C22×D3211yescharacteristic
615C2×D3—32no—
616C2×D3—32no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—62no—
620C2×D3—61no—
621C2×D3—61no—
622C2×D3—61no—
623C2×D3—61no—
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—32no—
628C3×C4—32no—
629C3×C4—42no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—62no—
635C3×C4—61no—
636C3×C4—62no—
637C3×C4—61no—
638C3×C4—122no—
639C3×C4—122no—
640C3×C4—181no—
641C3×C4—182no—
642C3×C4—182no—
643C3×C4#379512yes—
644C3×C4#379812yes—
645C3×C4#380412yes—
646Dic3—21no—
647Dic3—22no—
648Dic3—22no—
649Dic3—62no—
650Dic3—62no—
651Dic3—61no—
652Dic3—62no—
653Dic3—62no—
654Dic3—62no—
655Dic3—61no—
656Dic3—92no—
657Dic3—92no—
658Dic3—92no—
659Dic3—92no—
660Dic3—92no—
661Dic3—92no—
662Dic3—122no—
663Dic3—122no—
664Dic3—182no—
665Dic3—182no—
666Dic3—182no—
667Dic3—182no—
668Dic3—182no—
669Dic3—182no—
670Dic3—362no—
671Dic3—362no—
672Dic3#379712yes—
673C32—21no—
674C32—21no—
675C32—21no—
676C32—41no—
677C32#557811yescharacteristic, complemented
678C32#557811yescharacteristic, complemented
679C32#562211yescharacteristic, complemented
680C23—91no—
681Q8—62no—
682Q8—182no—
683Q8—544no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—92no—
689C2×C4—92no—
690C2×C4—91no—
691C2×C4—182no—
692C2×C4—274no—
693C2×C4—271no—
694C2×C4—271no—
695C2×C4—542no—
696C2×C4D3311yescharacteristic
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—41no—
709C2×C3—182no—
710C2×C3C2×#379511yescharacteristic
711C2×C3C2×#379711yescharacteristic
712C2×C3C2×#379811yescharacteristic
713C2×C3#6430611yescharacteristic
714C2×C3#6431211yescharacteristic
715C2×C3D32×Q811yescharacteristic
716C2×C3D32×Q811yescharacteristic
717C2×C3#6431911yescharacteristic
718C2×C3C2×#380411yescharacteristic
719D3—64no—
720D3—62no—
721D3—62no—
722C22—92no—
723C22—181no—
724C22—181no—
725C22C2×D3311yescharacteristic
726C4—32no—
727C4—61no—
728C4—62no—
729C4—62no—
730C4—182no—
731C4—181no—
732C4—182no—
733C4—272no—
734C4—272no—
735C4#8896012yes—
736C3—21no—
737C3—21no—
738C3—21no—
739C3—41no—
740C3#1059388211yescharacteristic, complemented
741C3#1059438511yescharacteristic, complemented
742C3#1059536711yescharacteristic, complemented
743C2—182no—
744C2D3×#379711yescharacteristic
745C2#1172437611yescharacteristic
746C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×C4D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723536C2semidirect
4. #11723451C2semidirect
6. C3×#63844C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11723016C2semidirect
10. #11722942C2semidirect
71. #63844D3semidirect
72. Dic3×Dic6D3semidirect
90. Dic3×C3⋊D3Q8semidirect
479. C33#533semidirect
677. C32#5578semidirect
678. C32#5578semidirect
679. C32#5622semidirect
740. C3#10593882semidirect
741. C3#10594385semidirect
742. C3#10595367semidirect

Maximal subgroups

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

subgroupindex
#117236742
#117235362
C4×Dic3×C3⋊D32
#117234512
C3×#638712
C3×#638442
C3×Dic3×Dic62
#117230162
#117229832
#117229422
#117229192
#105953673
#105943853
#105938823