Finite Group Databasebeta

← #13172240

Subgroups — #13172240

Order 1728.

998 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723716C211yesmaximal, characteristic
2#11723597C211yesmaximal, characteristic
3#11723596C211yesmaximal, characteristic
4#11723594C211yesmaximal, characteristic
5C3×#63964C211yesmaximal, characteristic
6C3×#63964C211yesmaximal, characteristic
7C3×#63956C211yesmaximal, characteristic
8#11723032C211yesmaximal, characteristic, complemented
9#11723018C211yesmaximal, characteristic, complemented
10#11723017C211yesmaximal, characteristic, complemented
11#11723013C211yesmaximal, characteristic, complemented
12#11723013C211yesmaximal, characteristic, complemented
13#11723011C211yesmaximal, characteristic, complemented
14#11722941C211yesmaximal, characteristic, complemented
15#11722940C211yesmaximal, characteristic, complemented
16#10594826—31nomaximal
17#10594028—31nomaximal
18#10594027—31nomaximal
19C22×C32×Dic3C2211yescharacteristic
20C2×C3×#627C2211yescharacteristic
21C2×C3×#627C2211yescharacteristic
22#88864C2211yescharacteristic
23C3×#3757C2211yescharacteristic
24C3×#3757C2211yescharacteristic
25C3×#3757C2211yescharacteristic
26C32×#217C2211yescharacteristic
27C32×#217C2211yescharacteristic
28#88815C2211yescharacteristic
29#88815C2211yescharacteristic
30#88815C2211yescharacteristic
31#88813C2211yescharacteristic
32#88807C2211yescharacteristic
33#88807C2211yescharacteristic
34#88806C2211yescharacteristic
35#88806C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×Dic3⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64135—31no—
55#64088—31no—
56#64088—31no—
57C3×#924—31no—
58C3×#924—31no—
59C3×#879—31no—
60C3×#879—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63964D311yescharacteristic
64#63964D311yescharacteristic
65#63956—31no—
66#63956—31no—
67#63956—31no—
68#63956—31no—
69#63956—31no—
70#63956—31no—
71#63956—31no—
72#63956—61no—
73#63956—61no—
74#63956D311yescharacteristic
75#63955—31no—
76#63955—31no—
77#63955—61no—
78#63873—31no—
79#63872—31no—
80#63872—31no—
81#63870—31no—
82#63869—31no—
83#63867—31no—
84#63847—31no—
85#63846—31no—
86#63846—31no—
87#63846—31no—
88#63845—31no—
89#63845—31no—
90#63845—31no—
91#63845—31no—
92#63845—31no—
93#63845—31no—
94#63843—31no—
95#63843—31no—
96#63843—31no—
97Dic3×Dic6—31no—
98#63839—31no—
99#63839—31no—
100#63838—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C3×#627—22no—
119C3×#627—22no—
120#5701—91no—
121#5625—91no—
122#5625—91no—
123C22×C32×C4—31no—
124C22×C3×Dic3—21no—
125C22×C3×Dic3C2×D311yescharacteristic
126C22×C3×Dic3C2×D311yescharacteristic
127C2×C3×Dic6—31no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6—31no—
130C2×C3×Dic6—31no—
131C2×#627C2×D311yescharacteristic
132C2×#627C2×D311yescharacteristic
133C32×C22⋊C4—31no—
134C32×C22⋊C4—31no—
135#3757—31no—
136#3757—31no—
137#3757—31no—
138#3757—61no—
139#3757—61no—
140#3757—61no—
141#3757—121no—
142#3757C2×D311yescharacteristic
143#3757C2×D311yescharacteristic
144#3757C2×D311yescharacteristic
145C4⋊(C3⋊Dic3)—31no—
146C4⋊(C3⋊Dic3)—31no—
147C4⋊(C3⋊Dic3)—31no—
148C4⋊(C3⋊Dic3)—31no—
149#3750—31no—
150#3750—31no—
151#3750—31no—
152#3750—31no—
153C4×C3⋊Dic3—31no—
154C4×C3⋊Dic3—31no—
155C4×C3⋊Dic3—31no—
156C4×C3⋊Dic3—31no—
157C3×#217—21no—
158C3×#217—21no—
159C3×#217—31no—
160C3×#217—31no—
161C3×#217—31no—
162C3×#217—31no—
163C3×#217—31no—
164C3×#217—31no—
165C3×#217—61no—
166C3×#217—61no—
167C3×#217—61no—
168C3×#217C2×D311yescharacteristic
169C3×#217C2×D311yescharacteristic
170C3×#217C2×D311yescharacteristic
171C3×#217C2×D311yescharacteristic
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4—31no—
180C3×Dic3⋊C4—31no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×C4×Dic3—31no—
191C3×C4×Dic3—31no—
192#3724—31no—
193#3724—31no—
194#3724—31no—
195#3724—31no—
196#3724—31no—
197#3724—31no—
198#3724—31no—
199#3724—61no—
200#3724—61no—
201#3724C2×D311yescharacteristic
202#3724C2×D311yescharacteristic
203#3724C2×D311yescharacteristic
204Dic3⋊Dic3—31no—
205Dic3⋊Dic3—31no—
206Dic3⋊Dic3—31no—
207Dic3⋊Dic3—31no—
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic32—31no—
235Dic32—31no—
236Dic32—31no—
237Dic32—31no—
238Dic32—31no—
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—61no—
246Dic32—61no—
247Dic32—61no—
248Dic32—61no—
249Dic32C2×D311yescharacteristic
250C22×C33—21no—
251C22×C33—21no—
252C22×C33—21no—
253C22×C33C2411yescharacteristic
254C3⋊(C3⋊Dic3)—21no—
255C3⋊(C3⋊Dic3)—21no—
256C3×C3⋊Dic3—21no—
257C3×C3⋊Dic3—21no—
258C3×C3⋊Dic3—21no—
259C3×C3⋊Dic3—21no—
260C3×C3⋊Dic3—21no—
261C3×C3⋊Dic3—21no—
262C32×Dic3—21no—
263C32×Dic3—21no—
264C32×Dic3—21no—
265C32×Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3#4112yes—
268C3×#126—91no—
269C3×C22⋊Q8—91no—
270C3×C22⋊Q8—91no—
271Q8×Dic3—91no—
272Q8×Dic3—91no—
273#944—91no—
274#944—91no—
275#926—91no—
276#926—91no—
277#926—181no—
278#924—31no—
279#924—31no—
280#890—91no—
281#890—91no—
282#890—91no—
283#890—91no—
284#890—91no—
285#890—91no—
286#890—91no—
287#889—91no—
288#889—91no—
289#889—91no—
290#889—91no—
291#889—91no—
292#889—91no—
293#889—91no—
294#888—91no—
295#887—91no—
296#887—91no—
297#887—91no—
298#879—31no—
299#879—31no—
300#879—91no—
301#879—91no—
302#879—91no—
303#879—91no—
304#879—91no—
305#879—91no—
306#879—91no—
307#879—91no—
308#879—91no—
309#879—181no—
310#879—181no—
311#878—31no—
312#878—31no—
313#877—91no—
314#870—91no—
315C4×Dic6—91no—
316C23×C32—21no—
317C23×C32—21no—
318C23×C32—21no—
319C23×C32—41no—
320C23×C32C22×D311yescharacteristic
321C23×C32C22×D311yescharacteristic
322C23×C32C22×D311yescharacteristic
323C2×C32×C4—31no—
324C2×C32×C4—31no—
325C2×C32×C4—31no—
326C2×C32×C4—31no—
327C2×C32×C4—31no—
328C2×C32×C4—31no—
329C2×C32×C4—62no—
330C2×C3⋊Dic3—31no—
331C2×C3⋊Dic3—31no—
332C2×C3⋊Dic3—31no—
333C2×C3⋊Dic3—31no—
334C2×C3⋊Dic3—31no—
335C2×C3⋊Dic3—31no—
336C2×C3⋊Dic3—61no—
337C2×C3⋊Dic3—61no—
338C2×C3⋊Dic3—61no—
339C2×C3⋊Dic3—61no—
340C2×C3⋊Dic3—61no—
341C2×C3⋊Dic3—61no—
342C2×C3⋊Dic3—121no—
343C2×C3⋊Dic3—121no—
344C2×C3⋊Dic3C22×D311yescharacteristic
345C2×C3⋊Dic3C22×D311yescharacteristic
346C2×C3⋊Dic3C22×D311yescharacteristic
347C2×C3⋊Dic3C22×D311yescharacteristic
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350C2×C3×Dic3—24no—
351C2×C3×Dic3—22no—
352C2×C3×Dic3—22no—
353C2×C3×Dic3—21no—
354C2×C3×Dic3—21no—
355C2×C3×Dic3—21no—
356C2×C3×Dic3—21no—
357C2×C3×Dic3—21no—
358C2×C3×Dic3—21no—
359C2×C3×Dic3—31no—
360C2×C3×Dic3—31no—
361C2×C3×Dic3—31no—
362C2×C3×Dic3—31no—
363C2×C3×Dic3—31no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—61no—
372C2×C3×Dic3—61no—
373C2×C3×Dic3—61no—
374C2×C3×Dic3—61no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3C22×D311yescharacteristic
378C2×C3×Dic3C22×D311yescharacteristic
379C2×C3×Dic3C22×D311yescharacteristic
380C2×C3×Dic3C22×D311yescharacteristic
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C3×Dic6—62no—
390C3×Dic6—62no—
391C3×Dic6—62no—
392C3×Dic6—62no—
393#627—22no—
394#627—22no—
395#541—271noSylow
396C2×C33—41no—
397C2×C33C2×#4111yescharacteristic
398C2×C332−1+411yescharacteristic
399C2×C332−1+411yescharacteristic
400C2×C3×Q8—91no—
401C2×C3×Q8—91no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—61no—
405C22×Dic3D3211yescharacteristic
406C2×Dic6—31no—
407C2×Dic6—31no—
408C2×Dic6—31no—
409C2×Dic6—31no—
410C3×C4⋊C4—91no—
411C3×C4⋊C4—91no—
412C3×C4⋊C4—91no—
413C3×C4⋊C4—91no—
414C3×C4⋊C4—91no—
415C3×C4⋊C4—91no—
416C3×C4⋊C4—91no—
417C3×C4⋊C4—91no—
418C3×C4⋊C4—91no—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—91no—
426C3×C22⋊C4—91no—
427C3×C22⋊C4—91no—
428C3×C42—91no—
429#217—31no—
430#217—31no—
431#217—31no—
432#217—31no—
433#217—31no—
434#217—31no—
435#217—61no—
436#217—61no—
437#217—61no—
438#217—91no—
439#217—91no—
440#217—91no—
441#217—181no—
442#217—181no—
443#217—181no—
444#217—361no—
445#217D3211yescharacteristic
446#217D3211yescharacteristic
447C4⋊Dic3—31no—
448C4⋊Dic3—31no—
449C4⋊Dic3—31no—
450C4⋊Dic3—31no—
451C4⋊Dic3—31no—
452C4⋊Dic3—31no—
453C4⋊Dic3—91no—
454C4⋊Dic3—91no—
455C4⋊Dic3—91no—
456C4⋊Dic3—91no—
457C4⋊Dic3—91no—
458C4⋊Dic3—91no—
459C4⋊Dic3—91no—
460C4⋊Dic3—91no—
461C4⋊Dic3—91no—
462C4⋊Dic3—91no—
463C4⋊Dic3—91no—
464C4⋊Dic3—91no—
465C4⋊Dic3—91no—
466C4⋊Dic3—181no—
467C4⋊Dic3—181no—
468C4⋊Dic3—181no—
469C4⋊Dic3—181no—
470Dic3⋊C4—31no—
471Dic3⋊C4—31no—
472Dic3⋊C4—31no—
473Dic3⋊C4—31no—
474Dic3⋊C4—31no—
475Dic3⋊C4—31no—
476Dic3⋊C4—31no—
477Dic3⋊C4—31no—
478Dic3⋊C4—31no—
479Dic3⋊C4—31no—
480Dic3⋊C4—31no—
481Dic3⋊C4—31no—
482Dic3⋊C4—91no—
483Dic3⋊C4—91no—
484Dic3⋊C4—91no—
485Dic3⋊C4—91no—
486Dic3⋊C4—91no—
487Dic3⋊C4—91no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495Dic3⋊C4—91no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—181no—
503Dic3⋊C4—181no—
504Dic3⋊C4—181no—
505Dic3⋊C4—181no—
506C4×Dic3—31no—
507C4×Dic3—31no—
508C4×Dic3—91no—
509C4×Dic3—91no—
510C4×Dic3—91no—
511C4×Dic3—91no—
512C4×Dic3—91no—
513C4×Dic3—91no—
514C4×Dic3—91no—
515C4×Dic3—91no—
516C4×Dic3—91no—
517C4×Dic3—91no—
518C4×Dic3—91no—
519C4×Dic3—91no—
520C4×Dic3—91no—
521C4×Dic3—91no—
522C4×Dic3—91no—
523C4×Dic3—181no—
524C4×Dic3—181no—
525C4×Dic3—181no—
526C4×Dic3—181no—
527C22×C32—21no—
528C22×C32—22no—
529C22×C32—21no—
530C22×C32—21no—
531C22×C32—21no—
532C22×C32—21no—
533C22×C32—21no—
534C22×C32—21no—
535C22×C32—21no—
536C22×C32—21no—
537C22×C32—21no—
538C22×C32—21no—
539C22×C32—21no—
540C22×C32—41no—
541C22×C32—41no—
542C22×C32—41no—
543C22×C32—42no—
544C22×C32—41no—
545C22×C32—41no—
546C22×C32—41no—
547C22×C32—41no—
548C22×C32—41no—
549C22×C32—41no—
550C22×C32—81no—
551C22×C32—81no—
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C32×C4—32no—
556C32×C4—61no—
557C32×C4—61no—
558C32×C4—61no—
559C32×C4—61no—
560C32×C4—61no—
561C3⋊Dic3—21no—
562C3⋊Dic3—21no—
563C3⋊Dic3—21no—
564C3⋊Dic3—21no—
565C3⋊Dic3—21no—
566C3⋊Dic3—21no—
567C3⋊Dic3—61no—
568C3⋊Dic3—61no—
569C3⋊Dic3—61no—
570C3⋊Dic3—61no—
571C3⋊Dic3—61no—
572C3⋊Dic3—61no—
573C3⋊Dic3—121no—
574C3⋊Dic3—121no—
575C3⋊Dic3—121no—
576C3⋊Dic3—121no—
577C3⋊Dic3—121no—
578C3⋊Dic3—121no—
579C3⋊Dic3—241no—
580C3⋊Dic3—241no—
581C3×Dic3—22no—
582C3×Dic3—21no—
583C3×Dic3—21no—
584C3×Dic3—21no—
585C3×Dic3—21no—
586C3×Dic3—21no—
587C3×Dic3—21no—
588C3×Dic3—21no—
589C3×Dic3—21no—
590C3×Dic3—21no—
591C3×Dic3—21no—
592C3×Dic3—22no—
593C3×Dic3—41no—
594C3×Dic3—41no—
595C3×Dic3—41no—
596C3×Dic3—41no—
597C3×Dic3—61no—
598C3×Dic3—61no—
599C3×Dic3—61no—
600C3×Dic3—61no—
601C3×Dic3—61no—
602C3×Dic3—61no—
603C3×Dic3—61no—
604C3×Dic3—61no—
605C3×Dic3—61no—
606C3×Dic3—61no—
607C3×Dic3—61no—
608C3×Dic3—61no—
609C3×Dic3—121no—
610C3×Dic3—121no—
611C3×Dic3—121no—
612C3×Dic3—121no—
613C3×Dic3—121no—
614C3×Dic3—121no—
615C3×Dic3#23712yes—
616C3×Dic3#23712yes—
617C4⋊Q8—271no—
618#126—91no—
619#126—271no—
620#126—271no—
621#126—271no—
622#125—271no—
623#125—271no—
624#125—271no—
625#125—271no—
626#125—271no—
627C22⋊Q8—91no—
628C22⋊Q8—91no—
629C4×Q8—271no—
630C4×Q8—271no—
631#117—271no—
632C33#54111yescharacteristic, complemented, Sylow
633C23×C3—21no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—41no—
637C23×C3C2×D3211yescharacteristic
638C23×C3C2×D3211yescharacteristic
639C23×C3C2×D3211yescharacteristic
640C3×Q8—182no—
641C3×Q8—182no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—31no—
650C2×C3×C4—31no—
651C2×C3×C4—31no—
652C2×C3×C4—31no—
653C2×C3×C4—31no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—64no—
663C2×C3×C4—91no—
664C2×C3×C4—91no—
665C2×C3×C4—91no—
666C2×C3×C4—91no—
667C2×C3×C4—91no—
668C2×C3×C4—91no—
669C2×Dic3—22no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—31no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—91no—
689C2×Dic3—91no—
690C2×Dic3—91no—
691C2×Dic3—91no—
692C2×Dic3—91no—
693C2×Dic3—91no—
694C2×Dic3—181no—
695C2×Dic3—181no—
696C2×Dic3—181no—
697C2×Dic3—181no—
698C2×Dic3—181no—
699C2×Dic3—181no—
700C2×Dic3—361no—
701C2×Dic3—361no—
702C2×Dic3C2×D3211yescharacteristic
703C2×Dic3C2×D3211yescharacteristic
704C2×Dic3C2×D3211yescharacteristic
705C2×Dic3C2×D3211yescharacteristic
706C2×Dic3C2×D3211yescharacteristic
707C2×Dic3C2×D3211yescharacteristic
708Dic6—62no—
709Dic6—62no—
710Dic6—62no—
711Dic6—62no—
712C2×C32—21no—
713C2×C32—21no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—21no—
721C2×C32—41no—
722C2×C32—41no—
723C2×C32—41no—
724C2×C32—41no—
725C2×C32—42no—
726C2×C32—41no—
727C2×C32—41no—
728C2×C32—81no—
729C2×C32—81no—
730C2×C32—82no—
731C2×C32C2×#23711yescharacteristic
732C2×C32C2×#23711yescharacteristic
733C2×C32#100711yescharacteristic
734C2×C32#100711yescharacteristic
735C2×C32D3×#4111yescharacteristic
736C2×C32#101011yescharacteristic
737C2×C32#101011yescharacteristic
738C2×C32#101011yescharacteristic
739C2×C32#101011yescharacteristic
740C2×Q8—91no—
741C2×Q8—91no—
742C22×C4—31no—
743C4⋊C4—91no—
744C4⋊C4—91no—
745C4⋊C4—91no—
746C4⋊C4—91no—
747C4⋊C4—91no—
748C4⋊C4—91no—
749C4⋊C4—91no—
750C4⋊C4—91no—
751C4⋊C4—91no—
752C4⋊C4—271no—
753C4⋊C4—271no—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C4⋊C4—271no—
757C4⋊C4—271no—
758C4⋊C4—271no—
759C4⋊C4—271no—
760C4⋊C4—271no—
761C4⋊C4—271no—
762C4⋊C4—271no—
763C22⋊C4—31no—
764C22⋊C4—31no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—91no—
768C22⋊C4—271no—
769C42—91no—
770C42—271no—
771C42—271no—
772C42—271no—
773C42—271no—
774C42—271no—
775C22×C3—22no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—42no—
797C22×C3—41no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3C22×D3211yescharacteristic
801C22×C3C22×D3211yescharacteristic
802C22×C3C22×D3211yescharacteristic
803C3×C4—32no—
804C3×C4—32no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—61no—
808C3×C4—61no—
809C3×C4—61no—
810C3×C4—61no—
811C3×C4—61no—
812C3×C4—61no—
813C3×C4—61no—
814C3×C4—61no—
815C3×C4—61no—
816C3×C4—61no—
817C3×C4—121no—
818C3×C4—121no—
819C3×C4—121no—
820C3×C4—121no—
821C3×C4—181no—
822C3×C4—181no—
823C3×C4—181no—
824C3×C4—181no—
825C3×C4—181no—
826C3×C4—181no—
827Dic3—21no—
828Dic3—21no—
829Dic3—21no—
830Dic3—21no—
831Dic3—21no—
832Dic3—61no—
833Dic3—61no—
834Dic3—61no—
835Dic3—61no—
836Dic3—61no—
837Dic3—61no—
838Dic3—61no—
839Dic3—61no—
840Dic3—61no—
841Dic3—61no—
842Dic3—61no—
843Dic3—61no—
844Dic3—121no—
845Dic3—121no—
846Dic3—121no—
847Dic3—121no—
848Dic3—121no—
849Dic3—121no—
850Dic3—181no—
851Dic3—181no—
852Dic3—181no—
853Dic3—181no—
854Dic3—181no—
855Dic3—181no—
856Dic3—361no—
857Dic3—361no—
858Dic3—361no—
859Dic3—361no—
860Dic3—361no—
861Dic3—361no—
862Dic3—721no—
863Dic3—721no—
864Dic3#380512yes—
865C32—21no—
866C32—21no—
867C32—21no—
868C32—41no—
869C32#562511yescharacteristic, complemented
870C32#562511yescharacteristic, complemented
871C32#570111yescharacteristic, complemented
872C23D3311yescharacteristic
873Q8—182no—
874Q8—182no—
875C2×C4—31no—
876C2×C4—31no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—62no—
882C2×C4—91no—
883C2×C4—91no—
884C2×C4—91no—
885C2×C4—91no—
886C2×C4—91no—
887C2×C4—91no—
888C2×C4—271no—
889C2×C4—271no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—42no—
900C2×C3—41no—
901C2×C3—41no—
902C2×C3—41no—
903C2×C3—41no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—81no—
907C2×C3—81no—
908C2×C3—82no—
909C2×C3#6429711yescharacteristic
910C2×C3#6429711yescharacteristic
911C2×C3#6429711yescharacteristic
912C2×C3#6429711yescharacteristic
913C2×C3#6430911yescharacteristic
914C2×C3#6430911yescharacteristic
915C2×C3D3×#23711yescharacteristic
916C2×C3D3×#23711yescharacteristic
917C2×C3C2×#380511yescharacteristic
918C22—21no—
919C22—21no—
920C22—21no—
921C22C2×D3311yescharacteristic
922C4—32no—
923C4—61no—
924C4—61no—
925C4—61no—
926C4—61no—
927C4—61no—
928C4—181no—
929C4—181no—
930C4—181no—
931C4—181no—
932C4—181no—
933C4—181no—
934C4—541no—
935C4—541no—
936C3—21no—
937C3—21no—
938C3—21no—
939C3—41no—
940C3#1059402711yescharacteristic, complemented
941C3#1059402811yescharacteristic, complemented
942C3#1059482611yescharacteristic, complemented
943C2—41no—
944C2D3×#380511yescharacteristic
945C2#1172442611yescharacteristic
946C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
Fitting, prime radicalC23×C33C23
hypercenterC23D33
hypocenterC33#541
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
8. #11723032C2semidirect
9. #11723018C2semidirect
10. #11723017C2semidirect
11. #11723013C2semidirect
12. #11723013C2semidirect
13. #11723011C2semidirect
14. #11722941C2semidirect
15. #11722940C2semidirect
632. C33#541semidirect
869. C32#5625semidirect
870. C32#5625semidirect
871. C32#5701semidirect
940. C3#10594027semidirect
941. C3#10594028semidirect
942. C3#10594826semidirect

Maximal subgroups

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

subgroupindex
#117237162
#117235972
#117235962
#117235942
C3×#639642
C3×#639562
#117230322
#117230182
#117230172
#117230132
#117230112
#117229412
#117229402
#105948263
#105940283
#105940273