Finite Group Databasebeta

← #13169333

Subgroups — #13169333

Order 1728.

1006 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723668C211yesmaximal, characteristic
2#11723445C211yesmaximal, characteristic
3#11723401C211yesmaximal, characteristic
4#11723394C211yesmaximal, characteristic
5C3×#63845C211yesmaximal, characteristic
6C3×#63840C211yesmaximal, characteristic
7C3×#63838C211yesmaximal, characteristic
8#11723034C211yesmaximal, characteristic
9#11723017C211yesmaximal, characteristic
10#11723012C211yesmaximal, characteristic
11#11723011C211yesmaximal, characteristic
12#11722942C211yesmaximal, characteristic
13#11722940C211yesmaximal, characteristic
14#11722940C211yesmaximal, characteristic
15Dic3×#627C211yesmaximal, characteristic
16#10594322—31nomaximal
17#10594317—31nomaximal
18#10594314—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×C3×#627C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23#88857C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C32×Dic3⋊C4C2211yescharacteristic
27C32×Dic3⋊C4C2211yescharacteristic
28C32×Dic3⋊C4C2211yescharacteristic
29#88815C2211yescharacteristic
30#88815C2211yescharacteristic
31#88813C2211yescharacteristic
32#88813C2211yescharacteristic
33#88807C2211yescharacteristic
34#88807C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic32C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64099—31no—
55#64098—31no—
56#64097—31no—
57C3×#890—31no—
58C3×#889—31no—
59C3×#888—31no—
60C3×#888—31no—
61C3×#887—31no—
62C3×#887—31no—
63C4×#627—31no—
64C4×#627—31no—
65#63869—31no—
66#63869—31no—
67#63867—31no—
68#63867—31no—
69#63867—31no—
70#63867—31no—
71#63867—61no—
72#63847—31no—
73#63846—31no—
74#63846—31no—
75#63846—31no—
76#63846—31no—
77#63846—61no—
78#63845—31no—
79#63845—31no—
80#63845D311yescharacteristic
81#63844—31no—
82#63844—31no—
83#63843—31no—
84#63843—31no—
85#63843—31no—
86Dic3×Dic6—31no—
87Dic3×Dic6—31no—
88Dic3×Dic6—31no—
89Dic3×Dic6—31no—
90Dic3×Dic6—31no—
91#63840—31no—
92#63840D311yescharacteristic
93#63839—31no—
94#63839—31no—
95#63839—31no—
96#63839—31no—
97#63839—61no—
98#63838D311yescharacteristic
99#63837—31no—
100#63837—31no—
101#63837—31no—
102C2×C33×C4C2311yescharacteristic
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
111C3×#634—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6293—22no—
119C3×#627—22no—
120C3×#627Q814yescomplemented
121#5721—91no—
122#5685—91no—
123#5569—91no—
124C2×#634—31no—
125C2×#634C2×D311yescharacteristic
126C2×C3×Dic6—31no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6—31no—
130C2×C3×Dic6—31no—
131C2×C3×Dic6—31no—
132C2×C3×Dic6—61no—
133C2×#627—31no—
134C2×#627—31no—
135C2×#627—61no—
136C2×#627C2×D311yescharacteristic
137C2×#627C2×D311yescharacteristic
138C32×C4⋊C4—31no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4—31no—
141C4⋊(C3⋊Dic3)—31no—
142C4⋊(C3⋊Dic3)—31no—
143C4⋊(C3⋊Dic3)—31no—
144C4⋊(C3⋊Dic3)—31no—
145C4⋊(C3⋊Dic3)C2×D311yescharacteristic
146#3750—31no—
147#3750—31no—
148#3750—31no—
149#3750—31no—
150#3750—31no—
151#3750—31no—
152#3750—31no—
153#3750—31no—
154#3750—61no—
155#3750—61no—
156#3750—61no—
157#3750—121no—
158C4×C3⋊Dic3—31no—
159C4×C3⋊Dic3—31no—
160C4×C3⋊Dic3C2×D311yescharacteristic
161C3×C4⋊Dic3—31no—
162C3×C4⋊Dic3—31no—
163C3×C4⋊Dic3—31no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—31no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—61no—
168C3×Dic3⋊C4—21no—
169C3×Dic3⋊C4—21no—
170C3×Dic3⋊C4—21no—
171C3×Dic3⋊C4—31no—
172C3×Dic3⋊C4—31no—
173C3×Dic3⋊C4—31no—
174C3×Dic3⋊C4—31no—
175C3×Dic3⋊C4—31no—
176C3×Dic3⋊C4—31no—
177C3×Dic3⋊C4—31no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4C2×D311yescharacteristic
180C3×Dic3⋊C4C2×D311yescharacteristic
181C3×Dic3⋊C4C2×D311yescharacteristic
182C3×Dic3⋊C4C2×D311yescharacteristic
183C3×Dic3⋊C4C2×D311yescharacteristic
184C3×Dic3⋊C4C2×D311yescharacteristic
185C3×C4×Dic3—31no—
186C3×C4×Dic3—31no—
187C3×C4×Dic3—31no—
188C3×C4×Dic3—31no—
189C3×C4×Dic3—31no—
190C3×C4×Dic3—31no—
191C3×C4×Dic3—31no—
192C3×C4×Dic3—31no—
193C3×C4×Dic3—31no—
194C3×C4×Dic3—31no—
195C3×C4×Dic3—61no—
196#3724—31no—
197#3724—31no—
198#3724—31no—
199#3724—31no—
200#3724—31no—
201#3724—31no—
202#3724—61no—
203#3724—61no—
204#3724C2×D311yescharacteristic
205#3724C2×D311yescharacteristic
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—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
235Dic32—31no—
236Dic32—31no—
237Dic32—31no—
238Dic32—31no—
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—61no—
246Dic32—61no—
247Dic32C2×D311yescharacteristic
248Dic32C2×D311yescharacteristic
249Dic32C2×D311yescharacteristic
250Dic32C2×D311yescharacteristic
251C22×C33C2411yescharacteristic
252C33×C4—21no—
253C3⋊(C3⋊Dic3)—21no—
254C3⋊(C3⋊Dic3)—21no—
255C3×C3⋊Dic3—21no—
256C3×C3⋊Dic3—21no—
257C3×C3⋊Dic3—21no—
258C3×C3⋊Dic3—21no—
259C3×C3⋊Dic3C2×Q812yes—
260C3×C3⋊Dic3#4112yes—
261C32×Dic3—21no—
262C32×Dic3—21no—
263C32×Dic3—21no—
264C32×Dic3—21no—
265C32×Dic3C2×Q812yes—
266C32×Dic3C2×Q812yes—
267C3×C4⋊Q8—91no—
268C3×#125—91no—
269C3×C4×Q8—91no—
270Q8×Dic3—91no—
271Q8×Dic3—91no—
272Q8×Dic3—91no—
273Q8×Dic3—91no—
274#944—91no—
275#944—91no—
276#890—31no—
277#890—91no—
278#890—91no—
279#890—91no—
280#890—91no—
281#890—91no—
282#890—181no—
283#889—31no—
284#889—91no—
285#889—91no—
286#889—91no—
287#889—91no—
288#889—91no—
289#889—91no—
290#889—91no—
291#889—181no—
292#888—31no—
293#888—31no—
294#888—91no—
295#888—91no—
296#888—91no—
297#888—91no—
298#888—181no—
299#887—31no—
300#887—31no—
301#887—91no—
302#887—91no—
303#887—91no—
304#887—91no—
305#870—91no—
306#870—91no—
307#870—91no—
308C4×Dic6—91no—
309C4×Dic6—91no—
310C4×Dic6—91no—
311C4×Dic6—91no—
312C4×Dic6—91no—
313C4×Dic6—91no—
314C4×Dic6—91no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—21no—
318C2×C32×C4—31no—
319C2×C32×C4—31no—
320C2×C32×C4—31no—
321C2×C32×C4—31no—
322C2×C32×C4—31no—
323C2×C32×C4—31no—
324C2×C32×C4—41no—
325C2×C32×C4C22×D311yescharacteristic
326C2×C32×C4C22×D311yescharacteristic
327C2×C32×C4C22×D311yescharacteristic
328C2×C3⋊Dic3—31no—
329C2×C3⋊Dic3—31no—
330C2×C3⋊Dic3—31no—
331C2×C3⋊Dic3—31no—
332C2×C3⋊Dic3—31no—
333C2×C3⋊Dic3—31no—
334C2×C3⋊Dic3—61no—
335C2×C3⋊Dic3—61no—
336C2×C3⋊Dic3—61no—
337C2×C3⋊Dic3—61no—
338C2×C3⋊Dic3—61no—
339C2×C3⋊Dic3—61no—
340C2×C3⋊Dic3—121no—
341C2×C3⋊Dic3—121no—
342C2×C3⋊Dic3C22×D311yescharacteristic
343C2×C3⋊Dic3C22×D311yescharacteristic
344C2×C3⋊Dic3C22×D311yescharacteristic
345C2×C3⋊Dic3C22×D311yescharacteristic
346C2×C3⋊Dic3C22×D311yescharacteristic
347C2×C3⋊Dic3C22×D311yescharacteristic
348#634—22no—
349#634—62no—
350C2×C3×Dic3—21no—
351C2×C3×Dic3—21no—
352C2×C3×Dic3—21no—
353C2×C3×Dic3—21no—
354C2×C3×Dic3—21no—
355C2×C3×Dic3—21no—
356C2×C3×Dic3—31no—
357C2×C3×Dic3—31no—
358C2×C3×Dic3—31no—
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—61no—
369C2×C3×Dic3—61no—
370C2×C3×Dic3—61no—
371C2×C3×Dic3—61no—
372C2×C3×Dic3—61no—
373C2×C3×Dic3—61no—
374C2×C3×Dic3C22×D311yescharacteristic
375C2×C3×Dic3C22×D311yescharacteristic
376C2×C3×Dic3C22×D311yescharacteristic
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
386C3×Dic6—34no—
387C3×Dic6—34no—
388C3×Dic6—62no—
389C3×Dic6—62no—
390C3×Dic6—62no—
391C3×Dic6—62no—
392C3×Dic6—122no—
393#627—22no—
394#627—62no—
395#627—62no—
396#627—122no—
397#627Dic614yescomplemented
398#557—271noSylow
399C2×C33C22×Q811yescharacteristic
400C2×C33C2×#4111yescharacteristic
401C2×C332−1+411yescharacteristic
402C2×C3×Q8—91no—
403C2×C3×Q8—91no—
404C2×C3×Q8—91no—
405C2×Dic6—31no—
406C2×Dic6—31no—
407C2×Dic6—31no—
408C2×Dic6—31no—
409C2×Dic6—31no—
410C2×Dic6—31no—
411C2×Dic6—61no—
412C2×Dic6—91no—
413C2×Dic6—91no—
414C2×Dic6—91no—
415C2×Dic6—181no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—31no—
419C3×C4⋊C4—31no—
420C3×C4⋊C4—31no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—61no—
423C3×C4⋊C4—61no—
424C3×C4⋊C4—61no—
425C3×C4⋊C4—91no—
426C3×C4⋊C4—91no—
427C3×C4⋊C4—91no—
428C3×C4⋊C4—91no—
429C3×C4⋊C4—91no—
430C3×C4⋊C4—91no—
431C3×C4⋊C4—91no—
432C3×C42—91no—
433C3×C42—91no—
434C3×C42—91no—
435C3×C42—91no—
436C3×C42—91no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—31no—
443C4⋊Dic3—61no—
444C4⋊Dic3—91no—
445C4⋊Dic3—91no—
446C4⋊Dic3—91no—
447C4⋊Dic3—91no—
448C4⋊Dic3—91no—
449C4⋊Dic3—91no—
450C4⋊Dic3—91no—
451C4⋊Dic3—91no—
452C4⋊Dic3—91no—
453C4⋊Dic3—91no—
454C4⋊Dic3—91no—
455C4⋊Dic3—91no—
456C4⋊Dic3—91no—
457C4⋊Dic3—181no—
458C4⋊Dic3—181no—
459C4⋊Dic3—181no—
460C4⋊Dic3—181no—
461Dic3⋊C4—31no—
462Dic3⋊C4—31no—
463Dic3⋊C4—31no—
464Dic3⋊C4—31no—
465Dic3⋊C4—31no—
466Dic3⋊C4—31no—
467Dic3⋊C4—31no—
468Dic3⋊C4—31no—
469Dic3⋊C4—91no—
470Dic3⋊C4—91no—
471Dic3⋊C4—91no—
472Dic3⋊C4—91no—
473Dic3⋊C4—91no—
474Dic3⋊C4—91no—
475Dic3⋊C4—91no—
476Dic3⋊C4—91no—
477Dic3⋊C4—91no—
478Dic3⋊C4—91no—
479Dic3⋊C4—91no—
480Dic3⋊C4—91no—
481Dic3⋊C4—91no—
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—181no—
493Dic3⋊C4—181no—
494Dic3⋊C4—181no—
495Dic3⋊C4—181no—
496Dic3⋊C4—181no—
497Dic3⋊C4—181no—
498Dic3⋊C4—181no—
499Dic3⋊C4—181no—
500Dic3⋊C4—361no—
501Dic3⋊C4D3211yescharacteristic
502Dic3⋊C4D3211yescharacteristic
503Dic3⋊C4D3211yescharacteristic
504C4×Dic3—31no—
505C4×Dic3—31no—
506C4×Dic3—31no—
507C4×Dic3—31no—
508C4×Dic3—31no—
509C4×Dic3—31no—
510C4×Dic3—31no—
511C4×Dic3—31no—
512C4×Dic3—31no—
513C4×Dic3—31no—
514C4×Dic3—61no—
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—91no—
524C4×Dic3—91no—
525C4×Dic3—91no—
526C4×Dic3—91no—
527C4×Dic3—181no—
528C4×Dic3—181no—
529C22×C32—21no—
530C22×C32—21no—
531C22×C32—21no—
532C22×C32—41no—
533C22×C32C23×D311yescharacteristic
534C22×C32C23×D311yescharacteristic
535C22×C32C23×D311yescharacteristic
536C32×C4—21no—
537C32×C4—21no—
538C32×C4—21no—
539C32×C4—32no—
540C32×C4—32no—
541C32×C4—41no—
542C32×C4—41no—
543C32×C4—41no—
544C32×C4—61no—
545C32×C4—61no—
546C32×C4—61no—
547C32×C4—61no—
548C32×C4—81no—
549C3⋊Dic3—21no—
550C3⋊Dic3—21no—
551C3⋊Dic3—21no—
552C3⋊Dic3—21no—
553C3⋊Dic3—61no—
554C3⋊Dic3—62no—
555C3⋊Dic3—61no—
556C3⋊Dic3—61no—
557C3⋊Dic3—61no—
558C3⋊Dic3—61no—
559C3⋊Dic3—61no—
560C3⋊Dic3—121no—
561C3⋊Dic3—121no—
562C3⋊Dic3—122no—
563C3⋊Dic3—121no—
564C3⋊Dic3—121no—
565C3⋊Dic3—121no—
566C3⋊Dic3—241no—
567C3⋊Dic3C2×Dic612yes—
568C3⋊Dic3#23712yes—
569C3×Dic3—21no—
570C3×Dic3—21no—
571C3×Dic3—21no—
572C3×Dic3—21no—
573C3×Dic3—21no—
574C3×Dic3—21no—
575C3×Dic3—21no—
576C3×Dic3—21no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—32no—
580C3×Dic3—32no—
581C3×Dic3—32no—
582C3×Dic3—32no—
583C3×Dic3—41no—
584C3×Dic3—41no—
585C3×Dic3—41no—
586C3×Dic3—41no—
587C3×Dic3—62no—
588C3×Dic3—62no—
589C3×Dic3—61no—
590C3×Dic3—61no—
591C3×Dic3—61no—
592C3×Dic3—61no—
593C3×Dic3—61no—
594C3×Dic3—61no—
595C3×Dic3—61no—
596C3×Dic3—61no—
597C3×Dic3—121no—
598C3×Dic3—121no—
599C3×Dic3—121no—
600C3×Dic3—121no—
601C3×Dic3C2×Dic612yes—
602C3×Dic3C2×Dic612yes—
603C3×Dic3D3×Q812yes—
604C3×Dic3D3×Q812yes—
605C4⋊Q8—91no—
606C4⋊Q8—271no—
607C4⋊Q8—271no—
608#125—91no—
609#125—271no—
610#125—271no—
611#125—271no—
612#125—271no—
613#125—271no—
614C4×Q8—91no—
615C4×Q8—271no—
616C4×Q8—271no—
617C4×Q8—271no—
618C4×Q8—271no—
619C4×Q8—271no—
620C33#55711yescharacteristic, complemented, Sylow
621C3×Q8—94no—
622C3×Q8—182no—
623C3×Q8—182no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—31no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—31no—
639C2×C3×C4—41no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—91no—
647C2×C3×C4—91no—
648C2×C3×C4—91no—
649C2×C3×C4—91no—
650C2×C3×C4—91no—
651C2×C3×C4—91no—
652C2×C3×C4C2×D3211yescharacteristic
653C2×C3×C4C2×D3211yescharacteristic
654C2×C3×C4C2×D3211yescharacteristic
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—31no—
660C2×Dic3—31no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—91no—
674C2×Dic3—91no—
675C2×Dic3—91no—
676C2×Dic3—91no—
677C2×Dic3—91no—
678C2×Dic3—91no—
679C2×Dic3—181no—
680C2×Dic3—181no—
681C2×Dic3—181no—
682C2×Dic3—181no—
683C2×Dic3—181no—
684C2×Dic3—181no—
685C2×Dic3—361no—
686C2×Dic3—361no—
687C2×Dic3C2×D3211yescharacteristic
688C2×Dic3C2×D3211yescharacteristic
689C2×Dic3C2×D3211yescharacteristic
690C2×Dic3C2×D3211yescharacteristic
691C2×Dic3C2×D3211yescharacteristic
692C2×Dic3C2×D3211yescharacteristic
693Dic6—34no—
694Dic6—34no—
695Dic6—62no—
696Dic6—62no—
697Dic6—62no—
698Dic6—62no—
699Dic6—122no—
700Dic6—182no—
701Dic6—182no—
702Dic6—182no—
703Dic6—362no—
704C2×C32—21no—
705C2×C32—21no—
706C2×C32—21no—
707C2×C32—21no—
708C2×C32—21no—
709C2×C32—21no—
710C2×C32—21no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—41no—
714C2×C32—41no—
715C2×C32—41no—
716C2×C32C22×Dic611yescharacteristic
717C2×C32C2×#23711yescharacteristic
718C2×C32C2×D3×Q811yescharacteristic
719C2×C32C2×D3×Q811yescharacteristic
720C2×C32#100711yescharacteristic
721C2×C32#100711yescharacteristic
722C2×C32D3×#4111yescharacteristic
723C2×C32D3×#4111yescharacteristic
724C2×C32#101011yescharacteristic
725C2×Q8—91no—
726C2×Q8—91no—
727C2×Q8—91no—
728C2×Q8—271no—
729C4⋊C4—31no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—91no—
733C4⋊C4—91no—
734C4⋊C4—91no—
735C4⋊C4—91no—
736C4⋊C4—91no—
737C4⋊C4—91no—
738C4⋊C4—91no—
739C4⋊C4—271no—
740C4⋊C4—271no—
741C4⋊C4—271no—
742C4⋊C4—271no—
743C4⋊C4—271no—
744C4⋊C4—271no—
745C4⋊C4—271no—
746C4⋊C4—271no—
747C4⋊C4—271no—
748C4⋊C4—271no—
749C4⋊C4—271no—
750C4⋊C4—271no—
751C42—91no—
752C42—91no—
753C42—91no—
754C42—91no—
755C42—91no—
756C42—271no—
757C42—271no—
758C42—271no—
759C42—271no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—41no—
764C22×C3C22×D3211yescharacteristic
765C22×C3C22×D3211yescharacteristic
766C22×C3C22×D3211yescharacteristic
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—32no—
771C3×C4—32no—
772C3×C4—32no—
773C3×C4—32no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—81no—
788C3×C4—92no—
789C3×C4—92no—
790C3×C4—121no—
791C3×C4—121no—
792C3×C4—121no—
793C3×C4—121no—
794C3×C4—181no—
795C3×C4—181no—
796C3×C4—181no—
797C3×C4—181no—
798Dic3—21no—
799Dic3—21no—
800Dic3—21no—
801Dic3—21no—
802Dic3—32no—
803Dic3—32no—
804Dic3—32no—
805Dic3—32no—
806Dic3—62no—
807Dic3—62no—
808Dic3—61no—
809Dic3—61no—
810Dic3—61no—
811Dic3—61no—
812Dic3—61no—
813Dic3—61no—
814Dic3—61no—
815Dic3—61no—
816Dic3—121no—
817Dic3—121no—
818Dic3—121no—
819Dic3—121no—
820Dic3—182no—
821Dic3—181no—
822Dic3—181no—
823Dic3—181no—
824Dic3—181no—
825Dic3—181no—
826Dic3—181no—
827Dic3—361no—
828Dic3—361no—
829Dic3—361no—
830Dic3—361no—
831Dic3—361no—
832Dic3—362no—
833Dic3—721no—
834Dic3D3×Dic612yes—
835Dic3D3×Dic612yes—
836C32—21no—
837C32—21no—
838C32—21no—
839C32—41no—
840C32#556911yescharacteristic, complemented
841C32#568511yescharacteristic, complemented
842C32#572111yescharacteristic, complemented
843Q8—94no—
844Q8—182no—
845Q8—182no—
846Q8—542no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—91no—
854C2×C4—91no—
855C2×C4—91no—
856C2×C4—91no—
857C2×C4—91no—
858C2×C4—91no—
859C2×C4—271no—
860C2×C4—271no—
861C2×C4D3311yescharacteristic
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—41no—
874C2×C3C2×D3×Dic611yescharacteristic
875C2×C3C2×D3×Dic611yescharacteristic
876C2×C3#6429711yescharacteristic
877C2×C3D3×#23711yescharacteristic
878C2×C3D3×#23711yescharacteristic
879C2×C3#6431211yescharacteristic
880C2×C3#6431511yescharacteristic
881C2×C3#6431611yescharacteristic
882C2×C3D32×Q811yescharacteristic
883C22C2×D3311yescharacteristic
884C4—21no—
885C4—32no—
886C4—32no—
887C4—61no—
888C4—61no—
889C4—61no—
890C4—61no—
891C4—92no—
892C4—92no—
893C4—181no—
894C4—181no—
895C4—181no—
896C4—181no—
897C4—541no—
898C4—541no—
899C3—21no—
900C3—21no—
901C3—21no—
902C3—41no—
903C3#1059431411yescharacteristic, complemented
904C3#1059431711yescharacteristic, complemented
905C3#1059432211yescharacteristic, complemented
906C2D32×Dic611yescharacteristic
907C2#1172439711yescharacteristic
908C2#1172440811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, prime radical, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#557
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
120. C3×#627Q8semidirect
397. #627Dic6semidirect
620. C33#557semidirect
840. C32#5569semidirect
841. C32#5685semidirect
842. C32#5721semidirect
903. C3#10594314semidirect
904. C3#10594317semidirect
905. C3#10594322semidirect

Maximal subgroups

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

subgroupindex
#117236682
#117234452
#117234012
#117233942
C3×#638452
C3×#638402
C3×#638382
#117230342
#117230172
#117230122
#117230112
#117229422
#117229402
Dic3×#6272
#105943223
#105943173
#105943143