Finite Group Databasebeta

← #13168648

Subgroups — #13168648

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#11723668C211yesmaximal, characteristic, complemented
2#11723536C211yesmaximal, characteristic, complemented
3C4×D3×C3⋊Dic3C211yesmaximal, characteristic
4#11723451C211yesmaximal, characteristic, complemented
5C3×#63857C211yesmaximal, characteristic
6C3×#63856C211yesmaximal, characteristic
7C3×#63843C211yesmaximal, characteristic, complemented
8#11723016C212yesmaximal, complemented
9#11722980C212yesmaximal
10#11722943C212yesmaximal, complemented
11#11722916C212yesmaximal
12#10595367—31nomaximal
13#10594810—31nomaximal
14#10594385—31nomaximal
15C2×C3×#634C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6293C2212yes—
19C2×D3×C3⋊Dic3C2211yescharacteristic
20C2×D3×C3⋊Dic3C2211yescharacteristic
21C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25#88815C2212yes—
26#88813C2212yes—
27#88806C2212yes—
28#88806C2212yes—
29#88806C2212yes—
30Dic3×C3⋊Dic3C2211yescharacteristic
31Dic3×C3⋊Dic3C2211yescharacteristic
32C3×#3724C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×Dic32C2212yes—
38#64153—31no—
39C2×C4×C3⋊Dic3—31no—
40#64097—31no—
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×#924—31no—
44C3×#924—31no—
45C3×#897—31no—
46C3×#887—31no—
47#63982—32no—
48#63957—32no—
49#63919—31no—
50#63919—31no—
51#63919—61no—
52#63899—32no—
53#63896—32no—
54#63877—32no—
55#63877—32no—
56C4×D3×Dic3—31no—
57C4×D3×Dic3—31no—
58C4×D3×Dic3—61no—
59#63873—31no—
60#63873—31no—
61#63873—61no—
62#63870—32no—
63#63857D311yescharacteristic
64#63856D311yescharacteristic
65#63847—32no—
66#63847—32no—
67#63844—31no—
68#63844—32no—
69#63843—31no—
70#63843D311yescharacteristic, complemented
71Dic3×Dic6—31no—
72#63838—32no—
73#63837—32no—
74C22×C32×D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×#634—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—22no—
87C32×Dic6—22no—
88#6293—24no—
89D3×C3⋊Dic3—22no—
90D3×C3⋊Dic3Q814yescomplemented
91#5622—91no—
92#5622—91no—
93#5578—91no—
94C2×C32×Q8—31no—
95C22×C32×C4—31no—
96C22×C3⋊Dic3—31no—
97C22×C3⋊Dic3—31no—
98C2×#634—32no—
99C2×#634C2×D311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2×D311yescharacteristic
102C2×C3×C4×D3C2×D311yescharacteristic
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—
119C4⋊(C3⋊Dic3)C2×D311yescharacteristic
120#3750—32no—
121#3750—32no—
122#3750—32no—
123C4×C3⋊Dic3—31no—
124C4×C3⋊Dic3—31no—
125C4×C3⋊Dic3—31no—
126C4×C3⋊Dic3—31no—
127C4×C3⋊Dic3—31no—
128C4×C3⋊Dic3—61no—
129C4×C3⋊Dic3—61no—
130C4×C3⋊Dic3—61no—
131C4×C3⋊Dic3—121no—
132C4×C3⋊Dic3C2×D311yescharacteristic
133C3×#217—32no—
134C3×#217—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—61no—
143C3×C4⋊Dic3C2×D311yescharacteristic
144C3×C4⋊Dic3C2×D311yescharacteristic
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—32no—
152C3×C4×Dic3—32no—
153C3×C4×Dic3—61no—
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(C2×D3)⋊Dic3C2×D312yes—
170(C2×D3)⋊Dic3C2×D312yes—
171Dic32—32no—
172Dic32—32no—
173Dic32—32no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—61no—
179Dic32—61no—
180Dic32C2×D312yes—
181C22×C33C2411yescharacteristic
182C2×C32×D3—21no—
183C2×C32×D3—21no—
184C2×C32×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—
191C3×C3⋊Dic3C2×Q812yes—
192C32×Dic3—21no—
193C32×Dic3—22no—
194C32×Dic3—22no—
195C3×C22⋊Q8—91no—
196C3×C22⋊Q8—91no—
197C3×C4×Q8—91no—
198#946—31no—
199Q8×Dic3—31no—
200Q8×Dic3—91no—
201#944—91no—
202#944—91no—
203#944—91no—
204#944—181no—
205#924—31no—
206#924—31no—
207C2×C4×Dic3—91no—
208C2×C4×Dic3—91no—
209C2×C4×Dic3—181no—
210#897—31no—
211#896—92no—
212#889—92no—
213#889—92no—
214#889—92no—
215#888—91no—
216#888—91no—
217#888—91no—
218#888—181no—
219#887—31no—
220#887—92no—
221#887—92no—
222#887—91no—
223#878—92no—
224#878—92no—
225#877—92no—
226#877—92no—
227#872—92no—
228C42×D3—91no—
229C4×Dic6—92no—
230C4×Dic6—91no—
231C23×C32—31no—
232C22×C3×D3—21no—
233C22×C3×D3C22×D311yescharacteristic
234C22×C3×D3C22×D311yescharacteristic
235C32×Q8—62no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—32no—
240C2×C32×C4—32no—
241C2×C32×C4—31no—
242C2×C32×C4—41no—
243C2×C32×C4—62no—
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—34no—
254C2×C3⋊Dic3—61no—
255C2×C3⋊Dic3—61no—
256C2×C3⋊Dic3—61no—
257C2×C3⋊Dic3—61no—
258C2×C3⋊Dic3—61no—
259C2×C3⋊Dic3—61no—
260C2×C3⋊Dic3—62no—
261C2×C3⋊Dic3—121no—
262C2×C3⋊Dic3—121no—
263C2×C3⋊Dic3C22×D312yes—
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D311yescharacteristic
267#634—22no—
268#634—64no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D312yes—
290C3×C4×D3—24no—
291C3×C4×D3—22no—
292C3×C4×D3—22no—
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
312C32×D3—22no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×Q8—91no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—61no—
320C22×Dic3—91no—
321C22×Dic3—91no—
322C22×Dic3—91no—
323C22×Dic3—91no—
324C22×Dic3—181no—
325C22×Dic3—181no—
326C2×C4×D3—91no—
327C2×C4×D3—91no—
328C2×C4×D3D3211yescharacteristic
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×C22⋊C4—92no—
346C3×C42—92no—
347C3×C42—91no—
348#217—32no—
349#217—32no—
350(C2×D3)⋊C4—32no—
351(C2×D3)⋊C4—32no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—32no—
355C4⋊Dic3—32no—
356C4⋊Dic3—61no—
357C4⋊Dic3—92no—
358C4⋊Dic3D3211yescharacteristic
359Dic3⋊C4—32no—
360Dic3⋊C4—32no—
361Dic3⋊C4—32no—
362Dic3⋊C4—32no—
363Dic3⋊C4—92no—
364Dic3⋊C4—92no—
365Dic3⋊C4—92no—
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—182no—
375Dic3⋊C4—182no—
376Dic3⋊C4—182no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—32no—
380C4×Dic3—32no—
381C4×Dic3—61no—
382C4×Dic3—92no—
383C4×Dic3—92no—
384C4×Dic3—92no—
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—91no—
394C4×Dic3—181no—
395C4×Dic3—181no—
396C4×Dic3—181no—
397C4×Dic3—181no—
398C4×Dic3—181no—
399C4×Dic3—361no—
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—22no—
411C2×C3×D3—22no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3D3×Q812yes—
418C2×C3×D3D3×Q812yes—
419C32×C4—22no—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—42no—
423C32×C4—61no—
424C32×C4—62no—
425C32×C4—62no—
426C32×C4#23512yes—
427C32×C4#23712yes—
428C32×C4#23712yes—
429C3⋊Dic3—21no—
430C3⋊Dic3—22no—
431C3⋊Dic3—22no—
432C3⋊Dic3—32no—
433C3⋊Dic3—32no—
434C3⋊Dic3—32no—
435C3⋊Dic3—32no—
436C3⋊Dic3—32no—
437C3⋊Dic3—32no—
438C3⋊Dic3—62no—
439C3⋊Dic3—62no—
440C3⋊Dic3—62no—
441C3⋊Dic3—62no—
442C3⋊Dic3—62no—
443C3⋊Dic3—62no—
444C3⋊Dic3—122no—
445C3⋊Dic3—122no—
446C3⋊Dic3D3×Q812yes—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—32no—
455C3×Dic3—32no—
456C3×Dic3—42no—
457C3×Dic3—42no—
458C3×Dic3—62no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—62no—
465C3×Dic3—62no—
466C3×Dic3—122no—
467C3×Dic3—122no—
468C4⋊Q8—271no—
469C4⋊Q8—271no—
470#125—272no—
471C22⋊Q8—91no—
472C22⋊Q8—91no—
473C22⋊Q8—272no—
474C4×Q8—91no—
475C4×Q8—272no—
476C4×Q8—271no—
477#117—272no—
478C2×C42—271no—
479C33#53311yescharacteristic, complemented, Sylow
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—61no—
483C22×D3C2×D3211yescharacteristic
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—32no—
492C2×C3×C4—32no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—41no—
498C2×C3×C4—61no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—64no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—91no—
505C2×C3×C4—92no—
506C2×C3×C4—91no—
507C2×C3×C4—92no—
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510C2×C3×C4C2×D3211yescharacteristic
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—32no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3—94no—
524C2×Dic3—94no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—184no—
532C2×Dic3—181no—
533C2×Dic3—181no—
534C2×Dic3—181no—
535C2×Dic3—181no—
536C2×Dic3—181no—
537C2×Dic3—181no—
538C2×Dic3—182no—
539C2×Dic3—182no—
540C2×Dic3—184no—
541C2×Dic3—361no—
542C2×Dic3—361no—
543C2×Dic3C2×D3212yes—
544C2×Dic3C2×D3212yes—
545C2×Dic3C2×D3211yescharacteristic
546C4×D3—22no—
547C4×D3—94no—
548C4×D3—182no—
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×C32—62no—
570C2×C32C2×#23511yescharacteristic
571C2×C32C2×#23711yescharacteristic
572C2×C32C2×#23711yescharacteristic
573C2×C32C2×D3×Q811yescharacteristic
574C2×C32C2×D3×Q811yescharacteristic
575C2×C32C2×D3×Q811yescharacteristic
576C2×C32D3×#4111yescharacteristic
577C2×C32D3×#4111yescharacteristic
578C2×C32D3×#4111yescharacteristic
579C3×D3—24no—
580C3×D3—22no—
581C3×D3—22no—
582C2×Q8—31no—
583C2×Q8—91no—
584C2×Q8—272no—
585C22×C4—31no—
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—92no—
599C42—92no—
600C42—91no—
601C42—271no—
602C42—271no—
603C42—272no—
604C42—271no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—32no—
609C22×C3—32no—
610C22×C3—41no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3C22×D3211yescharacteristic
619C22×C3C22×D3211yescharacteristic
620C22×C3C22×D3211yescharacteristic
621C2×D3—21no—
622C2×D3—21no—
623C2×D3#379712yes—
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—42no—
628C3×C4—62no—
629C3×C4—61no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—61no—
634C3×C4—62no—
635C3×C4—92no—
636C3×C4—122no—
637C3×C4—122no—
638C3×C4—181no—
639C3×C4—182no—
640C3×C4—182no—
641C3×C4#379512yes—
642C3×C4#380412yes—
643C3×C4#380512yes—
644Dic3—22no—
645Dic3—22no—
646Dic3—21no—
647Dic3—32no—
648Dic3—32no—
649Dic3—62no—
650Dic3—62no—
651Dic3—62no—
652Dic3—62no—
653Dic3—61no—
654Dic3—62no—
655Dic3—61no—
656Dic3—62no—
657Dic3—92no—
658Dic3—92no—
659Dic3—92no—
660Dic3—92no—
661Dic3—92no—
662Dic3—92no—
663Dic3—122no—
664Dic3—122no—
665Dic3—182no—
666Dic3—182no—
667Dic3—182no—
668Dic3—182no—
669Dic3—182no—
670Dic3—182no—
671Dic3—362no—
672Dic3—362no—
673C32—21no—
674C32—21no—
675C32—21no—
676C32—41no—
677C32#557811yescharacteristic, complemented
678C32#562211yescharacteristic, complemented
679C32#562211yescharacteristic, complemented
680C23—31no—
681Q8—62no—
682Q8—182no—
683Q8—544no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—31no—
687C2×C4—62no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—92no—
691C2×C4—92no—
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—64no—
710C2×C3—62no—
711C2×C3—62no—
712C2×C3C2×#379511yescharacteristic
713C2×C3C2×#379711yescharacteristic
714C2×C3#6430611yescharacteristic
715C2×C3#6431211yescharacteristic
716C2×C3D32×Q811yescharacteristic
717C2×C3D32×Q811yescharacteristic
718C2×C3#6431911yescharacteristic
719C2×C3C2×#380411yescharacteristic
720C2×C3C2×#380511yescharacteristic
721D3—22no—
722C22—32no—
723C22—61no—
724C22—61no—
725C22C2×D3311yescharacteristic
726C4—62no—
727C4—61no—
728C4—62no—
729C4—92no—
730C4—181no—
731C4—182no—
732C4—182no—
733C4—272no—
734C4—272no—
735C4#8896112yes—
736C3—21no—
737C3—21no—
738C3—21no—
739C3—41no—
740C3#1059438511yescharacteristic, complemented
741C3#1059481011yescharacteristic, complemented
742C3#1059536711yescharacteristic, complemented
743C2—62no—
744C2D3×#379711yescharacteristic
745C2#1172437611yescharacteristic
746C2C2×#8896111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×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
1. #11723668C2semidirect
2. #11723536C2semidirect
4. #11723451C2semidirect
7. C3×#63843C2semidirect
8. #11723016C2semidirect
10. #11722943C2semidirect
70. #63843D3semidirect
90. D3×C3⋊Dic3Q8semidirect
479. C33#533semidirect
677. C32#5578semidirect
678. C32#5622semidirect
679. C32#5622semidirect
740. C3#10594385semidirect
741. C3#10594810semidirect
742. C3#10595367semidirect

Maximal subgroups

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

subgroupindex
#117236682
#117235362
C4×D3×C3⋊Dic32
#117234512
C3×#638572
C3×#638562
C3×#638432
#117230162
#117229802
#117229432
#117229162
#105953673
#105948103
#105943853