Finite Group Databasebeta

← #13172234

Subgroups — #13172234

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723716C211yesmaximal, characteristic, complemented
2#11723600C211yesmaximal, characteristic
3#11723596C211yesmaximal, characteristic, complemented
4#11723594C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C211yesmaximal, characteristic
6C3×#63964C211yesmaximal, characteristic, complemented
7C3×#63959C211yesmaximal, characteristic
8#11723033C211yesmaximal, characteristic, complemented
9#11723022C211yesmaximal, characteristic, complemented
10#11723019C211yesmaximal, characteristic, complemented
11#11722969C211yesmaximal, characteristic, complemented
12#11722943C211yesmaximal, characteristic, complemented
13#11722941C211yesmaximal, characteristic, complemented
14Dic3×#627C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595273—31nomaximal
17#10594841—31nomaximal
18#10594134—31nomaximal
19C2×C32×#67C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25#88864C2211yescharacteristic
26C3×#3757C2211yescharacteristic
27C3×#3757C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88815C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88813C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64145—31no—
55#64135—31no—
56#64088—31no—
57C3×#936—31no—
58C3×D4×Dic3—31no—
59C3×C4×#67—31no—
60C3×#924—31no—
61C3×#885—31no—
62C3×#878—31no—
63Dic3×#67D311yescharacteristic
64#63964—31no—
65#63964D311yescharacteristic, complemented
66#63959—31no—
67#63959—31no—
68#63959—61no—
69#63959D311yescharacteristic
70#63956—31no—
71#63956—31no—
72#63956—31no—
73#63956—31no—
74#63956—31no—
75#63956—31no—
76#63956—31no—
77#63956—61no—
78#63955—31no—
79#63955—31no—
80#63955—31no—
81#63955—61no—
82#63918—31no—
83C4×#627—31no—
84#63887—31no—
85#63878—31no—
86#63866—31no—
87#63862—31no—
88#63862—31no—
89#63861—31no—
90#63858—31no—
91#63856—31no—
92#63844—31no—
93#63843—31no—
94#63843—31no—
95Dic3×Dic6—31no—
96Dic3×Dic6—31no—
97#63841—31no—
98#63839—31no—
99#63838—31no—
100#63838—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C32×#67—22no—
113C2×C32×Dic3—22no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119#6293—22no—
120C3×#627—22no—
121C3×#627—22no—
122C3×D3×Dic3—22no—
123#5671—91no—
124#5641—91no—
125#5542—91no—
126C2×C32×D4—31no—
127C22×C32×C4—31no—
128C2×#634—31no—
129C2×C3×#67—21no—
130C2×C3×#67C2×D311yescharacteristic
131C2×C3×#67C2×D311yescharacteristic
132C22×C3×Dic3—21no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3C2×D311yescharacteristic
135C22×C3×Dic3C2×D311yescharacteristic
136C2×C3×C4×D3—31no—
137C2×C3×Dic6—31no—
138C2×C3×Dic6—31no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—31no—
141C2×#627—31no—
142C2×#627—31no—
143C2×#627—61no—
144C2×#627C2×D311yescharacteristic
145C2×#627C2×D311yescharacteristic
146C2×D3×Dic3C2×D311yescharacteristic
147C32×C22⋊C4—31no—
148#3757—31no—
149#3757—31no—
150#3757—31no—
151#3757—31no—
152#3757—31no—
153#3757—61no—
154#3757—61no—
155#3757—61no—
156#3757—121no—
157#3757C2×D311yescharacteristic
158#3757C2×D311yescharacteristic
159#3757C2×D311yescharacteristic
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)—31no—
162C4⋊(C3⋊Dic3)—31no—
163#3750—31no—
164#3750—31no—
165C4×C3⋊Dic3—31no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C3×#217—21no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—31no—
177C3×#217—31no—
178C3×#217—31no—
179C3×#217—61no—
180C3×#217—61no—
181C3×#217—61no—
182C3×#217C2×D311yescharacteristic
183C3×#217C2×D311yescharacteristic
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×C4×Dic3—31no—
196C3×C4×Dic3—31no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199#3724—31no—
200#3724—31no—
201#3724—31no—
202#3724—31no—
203#3724—31no—
204#3724—61no—
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—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
227(C2×D3)⋊Dic3—31no—
228(C2×D3)⋊Dic3—31no—
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—61no—
232(C2×D3)⋊Dic3—61no—
233(C2×D3)⋊Dic3C2×D311yescharacteristic
234(C2×D3)⋊Dic3C2×D311yescharacteristic
235(C2×D3)⋊Dic3C2×D311yescharacteristic
236Dic32—31no—
237Dic32—31no—
238Dic32—31no—
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—61no—
248Dic32—61no—
249Dic32—61no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33—21no—
254C22×C33—21no—
255C22×C33—21no—
256C22×C33C2411yescharacteristic
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
260C3⋊(C3⋊Dic3)—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3#4112yes—
272C32×Dic3#4112yes—
273C3×#124—91no—
274C3×C22⋊Q8—91no—
275C3×C4×D4—91no—
276#946—91no—
277Q8×Dic3—91no—
278Q8×Dic3—91no—
279#944—91no—
280#936—31no—
281#936—91no—
282#936—91no—
283#936—181no—
284D4×Dic3—31no—
285C4×#67—31no—
286#926—91no—
287#926—91no—
288#926—91no—
289#926—181no—
290#924—31no—
291#924—91no—
292#898—91no—
293#898—91no—
294#892—91no—
295#888—91no—
296#887—91no—
297#887—91no—
298#887—91no—
299#887—91no—
300#885—31no—
301#885—91no—
302#879—91no—
303#879—91no—
304#879—91no—
305#879—91no—
306#879—91no—
307#879—91no—
308#879—91no—
309#879—91no—
310#879—91no—
311#879—91no—
312#879—181no—
313#878—31no—
314#878—91no—
315#877—91no—
316#877—91no—
317#869—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C4×Dic6—91no—
321C23×C32—21no—
322C23×C32—21no—
323C23×C32—21no—
324C23×C32—31no—
325C23×C32—41no—
326C23×C32C22×D311yescharacteristic
327C23×C32C22×D311yescharacteristic
328C23×C32C22×D311yescharacteristic
329C22×C3×D3—21no—
330C22×C3×D3C22×D311yescharacteristic
331C22×C3×D3C22×D311yescharacteristic
332C32×D4—62no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—62no—
339C2×C3⋊Dic3—31no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—121no—
352C2×C3⋊Dic3—121no—
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359#634—62no—
360C3×#67—22no—
361C3×#67—22no—
362C3×#67—42no—
363C2×C3×Dic3—24no—
364C2×C3×Dic3—22no—
365C2×C3×Dic3—22no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—62no—
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C3×C4×D3—62no—
401C3×Dic6—62no—
402C3×Dic6—62no—
403C3×Dic6—62no—
404C3×Dic6—62no—
405#627—22no—
406#627—22no—
407#627—62no—
408#627—62no—
409#627—122no—
410D3×Dic3—22no—
411#556—271noSylow
412C2×C33—41no—
413C2×C33C2×#4111yescharacteristic
414C2×C33C2×#4111yescharacteristic
415C2×C332−1+411yescharacteristic
416C32×D3—41no—
417C2×C3×Q8—91no—
418C2×C3×Q8—91no—
419C2×C3×D4—31no—
420C2×C3×D4—31no—
421C2×C3×D4—61no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—61no—
425C22×C3×C4—91no—
426C2×#67D3211yescharacteristic
427C22×Dic3—31no—
428C22×Dic3D3211yescharacteristic
429C2×C4×D3—31no—
430C2×Dic6—31no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—91no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—181no—
438C3×C4⋊C4—91no—
439C3×C4⋊C4—91no—
440C3×C4⋊C4—91no—
441C3×C4⋊C4—91no—
442C3×C22⋊C4—31no—
443C3×C22⋊C4—31no—
444C3×C22⋊C4—61no—
445C3×C22⋊C4—91no—
446C3×C22⋊C4—91no—
447C3×C22⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4—91no—
450C3×C22⋊C4—91no—
451C3×C42—91no—
452C3×C42—91no—
453#217—31no—
454#217—31no—
455#217—31no—
456#217—31no—
457#217—31no—
458#217—31no—
459#217—31no—
460#217—31no—
461#217—31no—
462#217—61no—
463#217—61no—
464#217—61no—
465#217—91no—
466#217—91no—
467#217—91no—
468#217—91no—
469#217—91no—
470#217—91no—
471#217—91no—
472#217—181no—
473#217—181no—
474#217—181no—
475#217—181no—
476#217—181no—
477#217—361no—
478#217D3211yescharacteristic
479(C2×D3)⋊C4—31no—
480(C2×D3)⋊C4—31no—
481(C2×D3)⋊C4—31no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497C4⋊Dic3—181no—
498C4⋊Dic3—181no—
499C4⋊Dic3—181no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—181no—
520Dic3⋊C4—181no—
521C4×Dic3—31no—
522C4×Dic3—31no—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—91no—
526C4×Dic3—91no—
527C4×Dic3—91no—
528C4×Dic3—91no—
529C4×Dic3—91no—
530C4×Dic3—91no—
531C4×Dic3—91no—
532C4×Dic3—91no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—181no—
541C4×Dic3—181no—
542C4×Dic3—181no—
543C4×Dic3—181no—
544C22×C32—21no—
545C22×C32—22no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—21no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32—21no—
557C22×C32—41no—
558C22×C32—41no—
559C22×C32—41no—
560C22×C32—42no—
561C22×C32—41no—
562C22×C32—41no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32—81no—
571C22×C32—81no—
572C22×C32C23×D311yescharacteristic
573C22×C32C23×D311yescharacteristic
574C22×C32C23×D311yescharacteristic
575C2×C3×D3—21no—
576C2×C3×D3—21no—
577C2×C3×D3—21no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—41no—
582C2×C3×D3—41no—
583C2×C3×D3—41no—
584C32×C4—32no—
585C32×C4—32no—
586C32×C4—61no—
587C32×C4—61no—
588C32×C4—61no—
589C3⋊Dic3—21no—
590C3⋊Dic3—21no—
591C3⋊Dic3—21no—
592C3⋊Dic3—21no—
593C3⋊Dic3—21no—
594C3⋊Dic3—21no—
595C3⋊Dic3—61no—
596C3⋊Dic3—61no—
597C3⋊Dic3—61no—
598C3⋊Dic3—61no—
599C3⋊Dic3—61no—
600C3⋊Dic3—61no—
601C3⋊Dic3—121no—
602C3⋊Dic3—121no—
603C3⋊Dic3—121no—
604C3⋊Dic3—121no—
605C3⋊Dic3—121no—
606C3⋊Dic3—121no—
607C3⋊Dic3—241no—
608C3⋊Dic3—241no—
609C3×Dic3—22no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—22no—
617C3×Dic3—22no—
618C3×Dic3—41no—
619C3×Dic3—41no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—121no—
633C3×Dic3—121no—
634C3×Dic3—121no—
635C3×Dic3—121no—
636C3×Dic3—121no—
637C3×Dic3—121no—
638C3×Dic3#23512yes—
639C3×Dic3#23712yes—
640C3×Dic3#23712yes—
641C3×Dic3#23712yes—
642C4⋊Q8—271no—
643#126—271no—
644#126—271no—
645#126—271no—
646#126—271no—
647#124—91no—
648#124—271no—
649C22⋊Q8—91no—
650C22⋊Q8—271no—
651C4×Q8—271no—
652C4×Q8—271no—
653C4×Q8—271no—
654C4×D4—91no—
655#117—271no—
656#117—271no—
657C33#55611yescharacteristic, complemented, Sylow
658C23×C3—21no—
659C23×C3—21no—
660C23×C3—21no—
661C23×C3—31no—
662C23×C3—31no—
663C23×C3—41no—
664C23×C3—61no—
665C23×C3C2×D3211yescharacteristic
666C23×C3C2×D3211yescharacteristic
667C23×C3C2×D3211yescharacteristic
668C22×D3C2×D3211yescharacteristic
669C3×Q8—182no—
670C3×Q8—182no—
671C3×D4—62no—
672C3×D4—62no—
673C3×D4—122no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—31no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—64no—
692C2×C3×C4—91no—
693C2×C3×C4—91no—
694C2×C3×C4—91no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—91no—
698C2×C3×C4—182no—
699#67—22no—
700C2×Dic3—22no—
701C2×Dic3—31no—
702C2×Dic3—31no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—62no—
720C2×Dic3—91no—
721C2×Dic3—91no—
722C2×Dic3—91no—
723C2×Dic3—91no—
724C2×Dic3—91no—
725C2×Dic3—91no—
726C2×Dic3—181no—
727C2×Dic3—181no—
728C2×Dic3—181no—
729C2×Dic3—181no—
730C2×Dic3—181no—
731C2×Dic3—181no—
732C2×Dic3—361no—
733C2×Dic3—361no—
734C2×Dic3C2×D3211yescharacteristic
735C2×Dic3C2×D3211yescharacteristic
736C2×Dic3C2×D3211yescharacteristic
737C2×Dic3C2×D3211yescharacteristic
738C2×Dic3C2×D3211yescharacteristic
739C4×D3—62no—
740Dic6—62no—
741Dic6—62no—
742Dic6—62no—
743Dic6—62no—
744Dic6—182no—
745Dic6—182no—
746Dic6—182no—
747Dic6—362no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—42no—
762C2×C32—41no—
763C2×C32—41no—
764C2×C32—81no—
765C2×C32—81no—
766C2×C32—82no—
767C2×C32—121no—
768C2×C32C2×#23511yescharacteristic
769C2×C32C2×#23711yescharacteristic
770C2×C32C2×#23711yescharacteristic
771C2×C32C2×#23711yescharacteristic
772C2×C32#100711yescharacteristic
773C2×C32D3×#4111yescharacteristic
774C2×C32D3×#4111yescharacteristic
775C2×C32#101011yescharacteristic
776C2×C32#101011yescharacteristic
777C3×D3—41no—
778C3×D3—41no—
779C3×D3—81no—
780C2×Q8—91no—
781C2×Q8—91no—
782C2×Q8—271no—
783C2×D4—31no—
784C22×C4—31no—
785C22×C4—91no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—271no—
791C4⋊C4—271no—
792C4⋊C4—271no—
793C4⋊C4—271no—
794C4⋊C4—271no—
795C4⋊C4—271no—
796C4⋊C4—271no—
797C4⋊C4—271no—
798C22⋊C4—31no—
799C22⋊C4—91no—
800C22⋊C4—91no—
801C22⋊C4—91no—
802C22⋊C4—91no—
803C22⋊C4—91no—
804C22⋊C4—91no—
805C22⋊C4—271no—
806C22⋊C4—271no—
807C22⋊C4—271no—
808C42—91no—
809C42—91no—
810C42—271no—
811C42—271no—
812C42—271no—
813C42—271no—
814C42—271no—
815C22×C3—22no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—42no—
837C22×C3—41no—
838C22×C3—61no—
839C22×C3—61no—
840C22×C3—61no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—81no—
845C22×C3—81no—
846C22×C3—121no—
847C22×C3—121no—
848C22×C3—121no—
849C22×C3C22×D3211yescharacteristic
850C22×C3C22×D3211yescharacteristic
851C22×C3C22×D3211yescharacteristic
852C2×D3—21no—
853C2×D3—21no—
854C2×D3—21no—
855C3×C4—32no—
856C3×C4—32no—
857C3×C4—32no—
858C3×C4—32no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4—62no—
862C3×C4—61no—
863C3×C4—61no—
864C3×C4—61no—
865C3×C4—61no—
866C3×C4—61no—
867C3×C4—61no—
868C3×C4—121no—
869C3×C4—121no—
870C3×C4—181no—
871C3×C4—181no—
872C3×C4—181no—
873C3×C4—181no—
874C3×C4—181no—
875C3×C4—181no—
876Dic3—21no—
877Dic3—21no—
878Dic3—21no—
879Dic3—61no—
880Dic3—61no—
881Dic3—61no—
882Dic3—61no—
883Dic3—61no—
884Dic3—61no—
885Dic3—61no—
886Dic3—61no—
887Dic3—61no—
888Dic3—61no—
889Dic3—61no—
890Dic3—61no—
891Dic3—121no—
892Dic3—121no—
893Dic3—121no—
894Dic3—121no—
895Dic3—121no—
896Dic3—121no—
897Dic3—181no—
898Dic3—181no—
899Dic3—181no—
900Dic3—181no—
901Dic3—181no—
902Dic3—181no—
903Dic3—361no—
904Dic3—361no—
905Dic3—361no—
906Dic3—361no—
907Dic3—361no—
908Dic3—361no—
909Dic3—721no—
910Dic3—721no—
911Dic3#380412yes—
912Dic3#380512yes—
913C32—21no—
914C32—21no—
915C32—21no—
916C32—41no—
917C32#554211yescharacteristic, complemented
918C32#564111yescharacteristic, complemented
919C32#567111yescharacteristic, complemented
920C23—31no—
921C23D3311yescharacteristic
922Q8—182no—
923Q8—182no—
924Q8—542no—
925D4—62no—
926C2×C4—31no—
927C2×C4—31no—
928C2×C4—31no—
929C2×C4—31no—
930C2×C4—31no—
931C2×C4—62no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—91no—
936C2×C4—91no—
937C2×C4—91no—
938C2×C4—182no—
939C2×C4—271no—
940C2×C4—271no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—42no—
951C2×C3—41no—
952C2×C3—41no—
953C2×C3—41no—
954C2×C3—41no—
955C2×C3—41no—
956C2×C3—41no—
957C2×C3—81no—
958C2×C3—81no—
959C2×C3—82no—
960C2×C3—121no—
961C2×C3—121no—
962C2×C3—241no—
963C2×C3#6429711yescharacteristic
964C2×C3#6429711yescharacteristic
965C2×C3D3×#23511yescharacteristic
966C2×C3#6430911yescharacteristic
967C2×C3D3×#23711yescharacteristic
968C2×C3D3×#23711yescharacteristic
969C2×C3D3×#23711yescharacteristic
970C2×C3C2×#380411yescharacteristic
971C2×C3C2×#380511yescharacteristic
972D3—41no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—61no—
977C22—61no—
978C22—61no—
979C22C2×D3311yescharacteristic
980C4—32no—
981C4—32no—
982C4—61no—
983C4—61no—
984C4—61no—
985C4—181no—
986C4—181no—
987C4—181no—
988C4—181no—
989C4—181no—
990C4—181no—
991C4—541no—
992C4—541no—
993C3—21no—
994C3—21no—
995C3—21no—
996C3—41no—
997C3#1059413411yescharacteristic, complemented
998C3#1059484111yescharacteristic, complemented
999C3#1059527311yescharacteristic, complemented
1000C2—41no—
1001C2—121no—
1002C2D3×#380411yescharacteristic
1003C2D3×#380511yescharacteristic
1004C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC2×C32×#67C22
hypercenterC23D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723716C2semidirect
3. #11723596C2semidirect
4. #11723594C2semidirect
6. C3×#63964C2semidirect
8. #11723033C2semidirect
9. #11723022C2semidirect
10. #11723019C2semidirect
11. #11722969C2semidirect
12. #11722943C2semidirect
13. #11722941C2semidirect
14. Dic3×#627C2semidirect
15. #11722914C2semidirect
65. #63964D3semidirect
657. C33#556semidirect
917. C32#5542semidirect
918. C32#5641semidirect
919. C32#5671semidirect
997. C3#10594134semidirect
998. C3#10594841semidirect
999. C3#10595273semidirect

Maximal subgroups

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

subgroupindex
#117237162
#117236002
#117235962
#117235942
C3×Dic3×#672
C3×#639642
C3×#639592
#117230332
#117230222
#117230192
#117229692
#117229432
#117229412
Dic3×#6272
#117229142
#105952733
#105948413
#105941343