Finite Group Databasebeta

← #13175850

Subgroups — #13175850

Order 1728.

1976 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6293C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
3#11723919C211yesmaximal, characteristic, complemented
4C3×#64090C211yesmaximal, characteristic
5C32×#878C211yesmaximal, characteristic, complemented
6#11723641C211yesmaximal, characteristic, complemented
7#11723626C211yesmaximal, characteristic
8Dic3×#638C211yesmaximal, characteristic
9#11723535C211yesmaximal, characteristic, complemented
10#11723502C211yesmaximal, characteristic, complemented
11#11723483C211yesmaximal, characteristic, complemented
12#11723418C211yesmaximal, characteristic, complemented
13#11723395C211yesmaximal, characteristic, complemented
14#11723393C211yesmaximal, characteristic, complemented
15#11723390C211yesmaximal, characteristic, complemented
16#10596103—31nomaximal
17#10594071—34nomaximal
18C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#6308C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic
25C2×#6293—24no—
26C2×#6293C2211yescharacteristic
27C2×#6293C2211yescharacteristic
28C2×#6293C2211yescharacteristic
29C2×#6293C2211yescharacteristic
30C2×#6293C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic
32C2×Dic3×C3⋊D3C2211yescharacteristic
33C3⋊D3×Dic6—24no—
34C33×C22⋊C4C2211yescharacteristic
35#88864C2211yescharacteristic
36C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
37#88857C2211yescharacteristic
38#88857C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×C4×C3⋊Dic3C2211yescharacteristic
42C32×#217C2211yescharacteristic
43C32×C4⋊Dic3C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46#88807C2211yescharacteristic
47#88807C2211yescharacteristic
48#88807C2211yescharacteristic
49#88806C2211yescharacteristic
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic
51#88803C2211yescharacteristic
52#88803C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×Q8×C3⋊D3—31no—
56C22×#634—31no—
57C22×#627—34no—
58C2×D3×Dic6—34no—
59C32×C22⋊Q8—31no—
60#64153—31no—
61C4×#638—31no—
62#64106—31no—
63#64105—31no—
64#64105—31no—
65#64097—31no—
66#64097—31no—
67#64096—31no—
68#64090—31no—
69#64090D311yescharacteristic
70#64087—31no—
71#64087—31no—
72#64087—34no—
73#64087—64no—
74C3×#67⋊C4—34no—
75C3×#878D314yescomplemented
76#67⋊Dic3—34no—
77Dic3×#67—34no—
78#63964—34no—
79#63918—34no—
80#63899—34no—
81#63893—34no—
82#63851—34no—
83#63840—34no—
84#63839—34no—
85#63837—34no—
86C23×C33C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C3⋊(C3⋊Dic3)—22no—
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95#6308—22no—
96C3×#638Q814yescomplemented
97C2×C3×C3⋊Dic3—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4×C3⋊D3—22no—
102C2×C32×Dic3—22no—
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C32×Dic6—22no—
108#6293—22no—
109#6293—22no—
110#6293—22no—
111#6293—22no—
112#6293D414yescomplemented
113Dic3×C3⋊D3—22no—
114Dic3×C3⋊D3—22no—
115#5632—94no—
116D4×Dic6—91no—
117C2×C32×Q8—31no—
118C22×C32×C4—31no—
119C2×#638C2×D311yescharacteristic
120C22×C3⋊Dic3—31no—
121C22×C3⋊Dic3—34no—
122C22×C3⋊Dic3—64no—
123C22×C3⋊Dic3C2×D311yescharacteristic
124Q8×C3⋊D3—64no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3C2×D311yescharacteristic
128C2×#634—31no—
129C2×#634—31no—
130C2×#634—34no—
131C2×#634—31no—
132C2×#634—31no—
133C2×#634—31no—
134C2×#634—31no—
135C2×#634—64no—
136C2×#634—64no—
137C2×C3×#67—34no—
138C22×C3×Dic3—34no—
139C22×C3×Dic3C2×D314yes—
140C2×C3×C4×D3—34no—
141C2×C3×Dic6C2×D314yes—
142C2×#627—34no—
143C2×#627—34no—
144C2×#627—34no—
145C2×#627—34no—
146C2×#627—34no—
147C2×#627—616no—
148C2×D3×Dic3—34no—
149C2×D3×Dic3—34no—
150D3×Dic6—616no—
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154C32×C22⋊C4—24no—
155C32×C22⋊C4—31no—
156C32×C22⋊C4C2×D314yes—
157C32×C22⋊C4C2×D311yescharacteristic
158#3757—31no—
159#3757—34no—
160#3757—64no—
161#3752—31no—
162#3752—31no—
163#3752C2×D311yescharacteristic
164C4⋊(C3⋊Dic3)—31no—
165C4⋊(C3⋊Dic3)—34no—
166C4⋊(C3⋊Dic3)—31no—
167C4⋊(C3⋊Dic3)—64no—
168#3750—31no—
169#3750—31no—
170#3750—34no—
171#3750—34no—
172#3750—31no—
173#3750—31no—
174#3750—31no—
175#3750—31no—
176#3750—64no—
177#3750—64no—
178#3750C2×D311yescharacteristic
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3—31no—
181C4×C3⋊Dic3C2×D311yescharacteristic
182C3×#217C2×D314yes—
183C3×(C2×D3)⋊C4—34no—
184C3×C4⋊Dic3C2×D314yes—
185C3×Dic3⋊C4—34no—
186C3×Dic3⋊C4C2×D314yes—
187C3×Dic3⋊C4C2×D314yes—
188C3×C4×Dic3—34no—
189#3724—34no—
190Dic3⋊Dic3—34no—
191Dic3⋊Dic3—34no—
192Dic3⋊Dic3—34no—
193Dic3⋊Dic3—34no—
194(C2×D3)⋊Dic3—34no—
195(C2×D3)⋊Dic3—34no—
196Dic32—34no—
197Dic32—34no—
198C22×C33—21no—
199C22×C33—21no—
200C22×C33C2×Q812yescomplemented
201C22×C33C2411yescharacteristic
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3C2×Q812yescomplemented
205C33×C4—21no—
206C33×C4—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)—21no—
209C3⋊(C3⋊Dic3)—21no—
210C3⋊(C3⋊Dic3)C2×D412yes—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3C2×D412yes—
213C3×C3⋊Dic3C2×Q812yescomplemented
214C32×Dic3—21no—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3C2×D412yes—
218C2×D3×Q8—94no—
219C22×Dic6—94no—
220C22×Dic6—91no—
221C22×Dic6—91no—
222C3×C22⋊Q8—34no—
223C3×C4×D4—91no—
224#944—94no—
225D4×Dic3—91no—
226D4×Dic3—91no—
227C4×#67—94no—
228#924—91no—
229#924—91no—
230#897—94no—
231#896—94no—
232#896—94no—
233#888—94no—
234#888—94no—
235#888—91no—
236#888—91no—
237#887—94no—
238#67⋊C4—34no—
239#67⋊C4—94no—
240#878—94no—
241#878—94no—
242#878—91no—
243#878—91no—
244#878—91no—
245#878—184no—
246#878C3⋊D311yescharacteristic, complemented
247#869—91no—
248C4×Dic6—91no—
249C23×C32—24no—
250C23×C32C22×D314yes—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—34no—
254C32×Q8—62no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—62no—
262C2×C32×C4C22×D314yes—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266#638Dic614yescomplemented
267C2×C3⋊Dic3—22no—
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—34no—
273C2×C3⋊Dic3—34no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—34no—
276C2×C3⋊Dic3—64no—
277C2×C3⋊Dic3—64no—
278C2×C3⋊Dic3—64no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—62no—
281C2×C3⋊Dic3—68no—
282C2×C3⋊Dic3—128no—
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C4×C3⋊D3—22no—
287C4×C3⋊D3—62no—
288C4×C3⋊D3—62no—
289#634—34no—
290#634—62no—
291#634—62no—
292#634—62no—
293#634—62no—
294#634—62no—
295#634—68no—
296#634—128no—
297C3×#67—316no—
298C2×C3×Dic3—28no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—68no—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D314yes—
305C2×C3×Dic3C22×D314yes—
306C2×C3×Dic3C22×D314yes—
307C3×C4×D3—68no—
308C3×Dic6—28no—
309#627—316no—
310#627—68no—
311#627—68no—
312#627—68no—
313#627—68no—
314D3×Dic3—68no—
315D3×Dic3—68no—
316D4×Q8—271noSylow
317C2×C33—22no—
318C2×C33C22×D411yescharacteristic
319C2×C33C22×Q811yescharacteristic
320C2×C332−1+411yescharacteristic
321C3×C3⋊D3—22no—
322C2×C3×Q8—34no—
323C2×C3×D4—91no—
324C22×C3×C4—34no—
325C22×C3×C4—91no—
326C22×C3×C4—91no—
327C2×#67—34no—
328C22×Dic3—34no—
329C22×Dic3—94no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333C22×Dic3—184no—
334C22×Dic3C2×C3⋊D311yescharacteristic
335D3×Q8—1816no—
336C2×C4×D3—34no—
337C2×C4×D3—94no—
338C2×C4×D3—94no—
339C2×Dic6—94no—
340C2×Dic6—91no—
341C2×Dic6—94no—
342C2×Dic6—94no—
343C2×Dic6—94no—
344C2×Dic6—94no—
345C2×Dic6—94no—
346C2×Dic6—91no—
347C2×Dic6—91no—
348C2×Dic6—91no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—184no—
352C2×Dic6—184no—
353C2×Dic6—184no—
354C2×Dic6—1816no—
355C2×Dic6C2×C3⋊D311yescharacteristic
356C3×C4⋊C4—34no—
357C3×C4⋊C4—34no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—24no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4D3214yes—
364C3×C22⋊C4C2×C3⋊D311yescharacteristic
365C3×C42—91no—
366#217—94no—
367#217—91no—
368#217—91no—
369#217—91no—
370#217—184no—
371#217C2×C3⋊D311yescharacteristic
372(C2×D3)⋊C4—34no—
373(C2×D3)⋊C4—94no—
374(C2×D3)⋊C4—94no—
375C4⋊Dic3—94no—
376C4⋊Dic3—94no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380C4⋊Dic3—91no—
381C4⋊Dic3—184no—
382C4⋊Dic3C2×C3⋊D311yescharacteristic
383Dic3⋊C4—34no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—94no—
387Dic3⋊C4—94no—
388Dic3⋊C4—94no—
389Dic3⋊C4—94no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—184no—
395Dic3⋊C4—184no—
396Dic3⋊C4C2×C3⋊D311yescharacteristic
397Dic3⋊C4C2×C3⋊D311yescharacteristic
398C4×Dic3—34no—
399C4×Dic3—94no—
400C4×Dic3—94no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—24no—
406C22×C32—28no—
407C22×C32—24no—
408C22×C32—24no—
409C22×C32—44no—
410C22×C32—44no—
411C22×C32C2×Dic612yescomplemented
412C22×C32D3×Q818yescomplemented
413C22×C32C23×D314yes—
414C22×C32C23×D311yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3C2×Dic612yescomplemented
418C2×C3×D3—38no—
419C2×C3×D3—64no—
420C2×C3×D3—64no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—24no—
424C32×C4—24no—
425C32×C4—32no—
426C32×C4—44no—
427C32×C4—44no—
428C32×C4—61no—
429C32×C4—61no—
430C32×C4—61no—
431C3⋊Dic3—21no—
432C3⋊Dic3—32no—
433C3⋊Dic3—38no—
434C3⋊Dic3—68no—
435C3⋊Dic3—61no—
436C3⋊Dic3—61no—
437C3⋊Dic3—61no—
438C3⋊Dic3—64no—
439C3⋊Dic3—64no—
440C3⋊Dic3—64no—
441C3⋊Dic3—124no—
442C3⋊Dic3—124no—
443C3⋊Dic3—124no—
444C3⋊Dic3C2×Dic612yescomplemented
445C3⋊Dic3D3×D412yes—
446C3×Dic3—24no—
447C3×Dic3—24no—
448C3×Dic3—24no—
449C3×Dic3—38no—
450C3×Dic3—38no—
451C3×Dic3—64no—
452C3×Dic3D3×D418yes—
453C22×Q8—271no—
454C22×Q8—271no—
455C4⋊Q8—271no—
456C4⋊Q8—271no—
457C4⋊Q8—271no—
458C22⋊Q8—31no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464C4×Q8—271no—
465C4×D4—91no—
466C4×D4—271no—
467C4×D4—271no—
468C33D4×Q811yescharacteristic, complemented, Sylow
469C23×C3—24no—
470C23×C3—91no—
471C23×C3C2×D3214yes—
472C23×C3C22×C3⋊D311yescharacteristic
473C22×D3—34no—
474C3×Q8—68no—
475C3×D4—94no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—34no—
479C2×C3×C4—34no—
480C2×C3×C4—34no—
481C2×C3×C4—34no—
482C2×C3×C4—68no—
483C2×C3×C4—91no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—182no—
487C2×C3×C4—182no—
488C2×C3×C4C2×D3214yes—
489C2×C3×C4C2×D3214yes—
490C2×C3×C4C22×C3⋊D311yescharacteristic
491C2×C3×C4C22×C3⋊D311yescharacteristic
492#67—316no—
493C2×Dic3—22no—
494C2×Dic3—34no—
495C2×Dic3—34no—
496C2×Dic3—34no—
497C2×Dic3—68no—
498C2×Dic3—94no—
499C2×Dic3—91no—
500C2×Dic3—94no—
501C2×Dic3—94no—
502C2×Dic3—94no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—184no—
507C2×Dic3—184no—
508C2×Dic3—184no—
509C2×Dic3—184no—
510C2×Dic3—182no—
511C2×Dic3—182no—
512C2×Dic3—188no—
513C2×Dic3—182no—
514C2×Dic3—368no—
515C2×Dic3C22×C3⋊D311yescharacteristic
516C2×Dic3C22×C3⋊D311yescharacteristic
517C2×Dic3C22×C3⋊D311yescharacteristic
518C2×Dic3C22×C3⋊D311yescharacteristic
519C4×D3—68no—
520C4×D3—188no—
521C4×D3—188no—
522Dic6—22no—
523Dic6—916no—
524Dic6—94no—
525Dic6—182no—
526Dic6—182no—
527Dic6—182no—
528Dic6—188no—
529Dic6—188no—
530Dic6—188no—
531Dic6—188no—
532Dic6—182no—
533Dic6—188no—
534Dic6—182no—
535Dic6—368no—
536C2×C32—22no—
537C2×C32—24no—
538C2×C32—24no—
539C2×C32—24no—
540C2×C32—28no—
541C2×C32—48no—
542C2×C32C22×Dic611yescharacteristic
543C2×C32C2×D3×D414yes—
544C2×C32C2×D3×D411yescharacteristic
545C2×C32C2×D3×Q814yes—
546C2×C32#101014yes—
547C2×C32#101011yescharacteristic
548C3⋊D3—22no—
549C3×D3—68no—
550C2×Q8—31no—
551C2×Q8—271no—
552C2×Q8—271no—
553C2×Q8—271no—
554C2×Q8—271no—
555C2×Q8—271no—
556C2×Q8—271no—
557C2×Q8—544no—
558C2×Q8—544no—
559C2×D4—91no—
560C22×C4—31no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—91no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C4⋊C4—271no—
576C4⋊C4—271no—
577C4⋊C4—271no—
578C22⋊C4—31no—
579C22⋊C4—91no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4D3×C3⋊D311yescharacteristic
584C42—91no—
585C42—271no—
586C42—271no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—24no—
592C22×C3—28no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—92no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3D3×Dic618yescomplemented
599C22×C3Q8×C3⋊D312yescomplemented
600C22×C3C22×D3214yes—
601C22×C3C23×C3⋊D311yescharacteristic
602C2×D3—38no—
603C2×D3—64no—
604C2×D3—64no—
605C3×C4—24no—
606C3×C4—24no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—38no—
610C3×C4—44no—
611C3×C4—44no—
612C3×C4—64no—
613C3×C4—64no—
614C3×C4—64no—
615C3×C4—92no—
616C3×C4—92no—
617C3×C4—181no—
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—38no—
622Dic3—38no—
623Dic3—64no—
624Dic3—98no—
625Dic3—92no—
626Dic3—188no—
627Dic3—184no—
628Dic3—184no—
629Dic3—184no—
630Dic3—181no—
631Dic3—181no—
632Dic3—181no—
633Dic3—364no—
634Dic3—364no—
635Dic3—364no—
636Dic3D4×C3⋊D312yes—
637C32—24no—
638C32D4×Dic611yescharacteristic, complemented
639C32#563214yescomplemented
640C23—91no—
641C23C2×D3×C3⋊D311yescharacteristic
642Q8—62no—
643Q8—274no—
644Q8—542no—
645Q8—542no—
646Q8—542no—
647Q8—542no—
648Q8—542no—
649D4—94no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—62no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—182no—
659C2×C4—182no—
660C2×C4—271no—
661C2×C4—271no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—542no—
665C2×C4—542no—
666C2×C4—542no—
667C2×C4C2×D3×C3⋊D311yescharacteristic
668C2×C4C2×D3×C3⋊D311yescharacteristic
669C2×C3—22no—
670C2×C3—28no—
671C2×C3—24no—
672C2×C3—24no—
673C2×C3—24no—
674C2×C3—48no—
675C2×C3—182no—
676C2×C3C2×D3×Dic614yes—
677C2×C3#6430914yes—
678C2×C3D32×D414yes—
679C2×C3C2×D4×C3⋊D311yescharacteristic
680C2×C3C2×Q8×C3⋊D311yescharacteristic
681C2×C3#6436711yescharacteristic
682D3—68no—
683C22—21no—
684C22—21no—
685C22—92no—
686C22—181no—
687C22—181no—
688C22C3⋊D3×Dic612yescomplemented
689C22C22×D3×C3⋊D311yescharacteristic
690C4—21no—
691C4—21no—
692C4—32no—
693C4—61no—
694C4—61no—
695C4—61no—
696C4—92no—
697C4—92no—
698C4—181no—
699C4—272no—
700C4—541no—
701C4—541no—
702C4—541no—
703C3—24no—
704C3#1059407114yescomplemented
705C3#1059610311yescharacteristic, complemented
706C2—22no—
707C2—182no—
708C2C2×C3⋊D3×Dic611yescharacteristic
709C2#1172458211yescharacteristic
710C2D3×D4×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×C3×#638C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33D4×Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6293C2semidirect
2. C2×C3⋊D3×Dic6C2semidirect
3. #11723919C2semidirect
5. C32×#878C2semidirect
6. #11723641C2semidirect
9. #11723535C2semidirect
10. #11723502C2semidirect
11. #11723483C2semidirect
12. #11723418C2semidirect
13. #11723395C2semidirect
14. #11723393C2semidirect
15. #11723390C2semidirect
75. C3×#878D3semidirect
96. C3×#638Q8semidirect
112. #6293D4semidirect
200. C22×C33C2×Q8semidirect
204. C2×C3×C3⋊D3C2×Q8semidirect
213. C3×C3⋊Dic3C2×Q8semidirect
246. #878C3⋊D3semidirect
266. #638Dic6semidirect
411. C22×C32C2×Dic6semidirect
412. C22×C32D3×Q8semidirect
417. C2×C3⋊D3C2×Dic6semidirect
444. C3⋊Dic3C2×Dic6semidirect
468. C33D4×Q8semidirect
598. C22×C3D3×Dic6semidirect
599. C22×C3Q8×C3⋊D3semidirect
638. C32D4×Dic6semidirect
639. C32#5632semidirect
688. C22C3⋊D3×Dic6semidirect
704. C3#10594071semidirect
705. C3#10596103semidirect

Maximal subgroups

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

subgroupindex
C22×#62932
C2×C3⋊D3×Dic62
#117239192
C3×#640902
C32×#8782
#117236412
#117236262
Dic3×#6382
#117235352
#117235022
#117234832
#117234182
#117233952
#117233932
#117233902
#105961033
#105940713