Finite Group Databasebeta

← #13147929

Subgroups — #13147929

Order 1728.

914 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×#6189C211yesmaximal, characteristic, complemented
2C2×D3×Dic18C211yesmaximal, characteristic, complemented
3#11721724C211yesmaximal, characteristic, complemented
4C9×#67⋊C4C211yesmaximal, characteristic
5C3×#63440C211yesmaximal, characteristic, complemented
6#67⋊Dic9C211yesmaximal, characteristic
7#67×Dic9C211yesmaximal, characteristic
8#11721249C211yesmaximal, characteristic, complemented
9#11721026C211yesmaximal, characteristic, complemented
10#11721023C211yesmaximal, characteristic, complemented
11#11720970C211yesmaximal, characteristic, complemented
12#11720955C211yesmaximal, characteristic, complemented
13#11720905C211yesmaximal, characteristic, complemented
14#11720904C211yesmaximal, characteristic, complemented
15#11720900C211yesmaximal, characteristic, complemented
16#10594071—31nomaximal
17D4×Dic18—31nomaximal
18C22×C3⋊Dic9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C22×C9×Dic3C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×C3×Dic18C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic
26C2×D3×Dic9C2211yescharacteristic
27C2×#6189—24no—
28C2×#6189C2211yescharacteristic
29C2×#6189C2211yescharacteristic
30C2×#6189C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32C2×#6189C2211yescharacteristic
33D3×Dic18—24no—
34C3×C9×C22⋊C4C2211yescharacteristic
35#88551C2211yescharacteristic
36C4⋊(C3⋊Dic9)C2211yescharacteristic
37#88534C2211yescharacteristic
38#88534C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C4×C9×Dic3C2211yescharacteristic
43C3×C4⋊Dic9C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C22×#627—31no—
56C2×D3×Dic6—31no—
57#64087—31no—
58C3×#67⋊C4D311yescharacteristic
59C3×#878—31no—
60#67⋊Dic3—31no—
61Dic3×#67—31no—
62#63964—31no—
63#63918—31no—
64#63899—31no—
65#63893—31no—
66#63851—31no—
67#63840—31no—
68#63839—31no—
69#63837—31no—
70C22×Dic18—31no—
71C22×Dic18—31no—
72C4×D4×C9—31no—
73D4×Dic9—31no—
74D4×Dic9—31no—
75#63486—31no—
76#63486—31no—
77#63450—31no—
78#63450—31no—
79#63440—31no—
80#63440—31no—
81#63440—31no—
82#63440—61no—
83#63440D311yescharacteristic, complemented
84#63431—31no—
85C4×Dic18—31no—
86C23×C3×C9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3⋊Dic9—22no—
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95#6226—22no—
96C9×#67Q814yescomplemented
97C2×C9×Dic3—22no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9—22no—
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C4×D3×C9—22no—
107C3×Dic18—22no—
108D3×Dic9—22no—
109D3×Dic9—22no—
110#6189—22no—
111#6189—22no—
112#6189—22no—
113#6189—22no—
114#6189D414yescomplemented
115#5632—91no—
116D4×Dic6—91no—
117C22×C3⋊Dic3—31no—
118C2×#634—31no—
119C2×C3×#67C2×D311yescharacteristic
120C22×C3×Dic3—31no—
121C22×C3×Dic3C2×D311yescharacteristic
122C2×C3×C4×D3C2×D311yescharacteristic
123C2×C3×Dic6—31no—
124C2×#627—31no—
125C2×#627—31no—
126C2×#627—31no—
127C2×#627—31no—
128C2×#627—31no—
129C2×#627—64no—
130C2×D3×Dic3—31no—
131C2×D3×Dic3—31no—
132D3×Dic6—64no—
133C32×C22⋊C4C2×D311yescharacteristic
134#3757—31no—
135C4⋊(C3⋊Dic3)—31no—
136#3750—31no—
137#3750—31no—
138C3×#217—31no—
139C3×(C2×D3)⋊C4C2×D311yescharacteristic
140C3×C4⋊Dic3—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4C2×D311yescharacteristic
144C3×C4×Dic3C2×D311yescharacteristic
145#3724—31no—
146Dic3⋊Dic3—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152Dic32—31no—
153Dic32—31no—
154C2×D4×C9—31no—
155C22×C4×C9—31no—
156C22×C4×C9—31no—
157C22×Dic9—31no—
158C22×Dic9—31no—
159C22×Dic9—31no—
160C22×Dic9—61no—
161C22×Dic9C2×D311yescharacteristic
162C2×Dic18—31no—
163C2×Dic18—31no—
164C2×Dic18—31no—
165C2×Dic18—31no—
166C2×Dic18—31no—
167C2×Dic18—31no—
168C2×Dic18—64no—
169C2×Dic18—64no—
170C2×Dic18—61no—
171C2×Dic18C2×D311yescharacteristic
172C9×C4⋊C4—31no—
173C9×C22⋊C4—21no—
174C9×C22⋊C4—31no—
175C9×C22⋊C4C2×D311yescharacteristic
176C42×C9—31no—
177#3676—31no—
178#3676—31no—
179#3676—31no—
180#3676—61no—
181#3676C2×D311yescharacteristic
182C4⋊Dic9—31no—
183C4⋊Dic9—31no—
184C4⋊Dic9—31no—
185C4⋊Dic9—31no—
186C4⋊Dic9—61no—
187C4⋊Dic9C2×D311yescharacteristic
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—61no—
193Dic9⋊C4—61no—
194Dic9⋊C4C2×D311yescharacteristic
195Dic9⋊C4C2×D311yescharacteristic
196C4×Dic9—31no—
197C4×Dic9—31no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9C2×Q812yescomplemented
201C22×C3×C9C2411yescharacteristic
202C2×D3×C9—21no—
203C2×D3×C9—21no—
204C2×D3×C9C2×Q812yescomplemented
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C3⋊Dic9—21no—
210C3⋊Dic9C2×D412yes—
211C9×Dic3—21no—
212C9×Dic3C2×D412yes—
213C9×Dic3C2×Q812yescomplemented
214C3×Dic9—21no—
215C3×Dic9—21no—
216C3×Dic9—21no—
217C3×Dic9C2×D412yes—
218C2×D3×Q8—91no—
219C22×Dic6—91no—
220C22×Dic6—91no—
221C22×Dic6—91no—
222C3×C22⋊Q8—91no—
223C3×C4×D4—31no—
224#944—91no—
225D4×Dic3—91no—
226D4×Dic3—91no—
227C4×#67—91no—
228#924—91no—
229#924—91no—
230#897—91no—
231#896—91no—
232#896—91no—
233#888—91no—
234#888—91no—
235#888—91no—
236#888—91no—
237#887—91no—
238#67⋊C4—91no—
239#67⋊C4D911yescharacteristic
240#878—31no—
241#878—91no—
242#878—91no—
243#878—91no—
244#878—91no—
245#878—91no—
246#878—181no—
247#869—91no—
248C4×Dic6—91no—
249C23×C32C22×D311yescharacteristic
250C22×C3×D3C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—62no—
258#634—62no—
259C3×#67Dic614yes—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—62no—
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×C4×D3—22no—
270C3×Dic6—62no—
271#627—34no—
272#627—62no—
273#627—62no—
274#627—62no—
275#627—62no—
276D3×Dic3—62no—
277D3×Dic3—62no—
278C23×C9—21no—
279C23×C9—31no—
280C23×C9C22×D311yescharacteristic
281D4×C9—34no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—62no—
288C2×C4×C9—62no—
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291C2×Dic9—22no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—62no—
301C2×Dic9—62no—
302C2×Dic9—62no—
303C2×Dic9—122no—
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C2×Dic9C22×D311yescharacteristic
308Dic18—22no—
309Dic18—34no—
310Dic18—62no—
311Dic18—62no—
312Dic18—62no—
313Dic18—62no—
314Dic18—62no—
315Dic18—122no—
316D4×Q8—271noSylow
317C2×C3×C9—22no—
318C2×C3×C9C22×D411yescharacteristic
319C2×C3×C9C22×Q811yescharacteristic
320C2×C3×C92−1+411yescharacteristic
321D3×C9—22no—
322C2×C3×Q8—91no—
323C2×C3×D4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—91no—
327C2×#67C2×D911yescharacteristic
328C22×Dic3—31no—
329C22×Dic3—91no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333C22×Dic3—181no—
334C22×Dic3C2×D911yescharacteristic
335D3×Q8—184no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3C2×D911yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—91no—
341C2×Dic6—91no—
342C2×Dic6—91no—
343C2×Dic6—91no—
344C2×Dic6—91no—
345C2×Dic6—91no—
346C2×Dic6—91no—
347C2×Dic6—91no—
348C2×Dic6—91no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—91no—
352C2×Dic6—181no—
353C2×Dic6—184no—
354C2×Dic6—184no—
355C2×Dic6—184no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4C2×D911yescharacteristic
364C3×C22⋊C4D3211yescharacteristic
365C3×C42—31no—
366#217—31no—
367#217—91no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—181no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4C2×D911yescharacteristic
375C4⋊Dic3—31no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382C4⋊Dic3—181no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—181no—
396Dic3⋊C4—181no—
397Dic3⋊C4C2×D911yescharacteristic
398C4×Dic3—91no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3C2×D911yescharacteristic
403C22×C32—21no—
404C22×C32—21no—
405C22×C32C2×Dic612yes—
406C22×C32C23×D311yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3C2×Dic612yes—
410C32×C4—21no—
411C32×C4—21no—
412C3⋊Dic3—32no—
413C3⋊Dic3—61no—
414C3⋊Dic3—61no—
415C3⋊Dic3—61no—
416C3×Dic3—21no—
417C3×Dic3—32no—
418C3×Dic3—61no—
419C3×Dic3—61no—
420C3×Dic3—61no—
421C3×Dic3C2×Dic612yes—
422C3×Dic3D3×D412yes—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—22no—
427C22×C9—32no—
428C22×C9—41no—
429C22×C9—41no—
430C22×C9—61no—
431C22×C9—61no—
432C22×C9D3×Q812yescomplemented
433C22×C9C23×D311yescharacteristic
434C4×C9—21no—
435C4×C9—21no—
436C4×C9—32no—
437C4×C9—32no—
438C4×C9—41no—
439C4×C9—41no—
440C4×C9—61no—
441Dic9—21no—
442Dic9—21no—
443Dic9—21no—
444Dic9—32no—
445Dic9—62no—
446Dic9—61no—
447Dic9—61no—
448Dic9—61no—
449Dic9—121no—
450Dic9—121no—
451Dic9—121no—
452Dic9D3×D412yes—
453C22×Q8—271no—
454C22×Q8—271no—
455C4⋊Q8—271no—
456C4⋊Q8—271no—
457C4⋊Q8—271no—
458C22⋊Q8—91no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464C4×Q8—271no—
465C4×D4—31no—
466C4×D4—271no—
467C4×D4—271no—
468C3×C9D4×Q811yescharacteristic, complemented, Sylow
469C23×C3—21no—
470C23×C3—31no—
471C23×C3C22×D911yescharacteristic
472C23×C3C2×D3211yescharacteristic
473C22×D3C22×D911yescharacteristic
474C3×Q8—182no—
475C3×D4—34no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—62no—
482C2×C3×C4—62no—
483C2×C3×C4—91no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—91no—
487C2×C3×C4—182no—
488C2×C3×C4C22×D911yescharacteristic
489C2×C3×C4C22×D911yescharacteristic
490C2×C3×C4C2×D3211yescharacteristic
491C2×C3×C4C2×D3211yescharacteristic
492#67Dic1814yescomplemented
493C2×Dic3—22no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—62no—
499C2×Dic3—91no—
500C2×Dic3—91no—
501C2×Dic3—91no—
502C2×Dic3—91no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—181no—
508C2×Dic3—181no—
509C2×Dic3—181no—
510C2×Dic3—181no—
511C2×Dic3—182no—
512C2×Dic3—182no—
513C2×Dic3—182no—
514C2×Dic3—182no—
515C2×Dic3—362no—
516C2×Dic3C22×D911yescharacteristic
517C2×Dic3C22×D911yescharacteristic
518C2×Dic3C22×D911yescharacteristic
519C4×D3—22no—
520C4×D3—182no—
521C4×D3—182no—
522Dic6—62no—
523Dic6—94no—
524Dic6—94no—
525Dic6—182no—
526Dic6—182no—
527Dic6—182no—
528Dic6—182no—
529Dic6—182no—
530Dic6—182no—
531Dic6—182no—
532Dic6—182no—
533Dic6—182no—
534Dic6—182no—
535Dic6—362no—
536C2×C32—22no—
537C2×C32C22×Dic611yescharacteristic
538C2×C32C2×D3×D411yescharacteristic
539C2×C32#101011yescharacteristic
540C3×D3—22no—
541C2×C9—22no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—21no—
545C2×C9—42no—
546C2×C9—62no—
547C2×C9C2×D3×D411yescharacteristic
548C2×C9C2×D3×Q811yescharacteristic
549C2×C9#101011yescharacteristic
550C2×Q8—91no—
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—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—91no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C4⋊C4—31no—
567C4⋊C4—91no—
568C4⋊C4—91no—
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×D911yescharacteristic
584C42—31no—
585C42—271no—
586C42—271no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—22no—
592C22×C3—21no—
593C22×C3—32no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3C2×Dic1812yescomplemented
599C22×C3C23×D911yescharacteristic
600C22×C3D3×Dic612yes—
601C22×C3C22×D3211yescharacteristic
602C2×D3—21no—
603C2×D3—21no—
604C2×D3C2×Dic1812yescomplemented
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—32no—
610C3×C4—32no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—61no—
614C3×C4—92no—
615C3×C4—181no—
616C3×C4—181no—
617C3×C4—181no—
618Dic3—21no—
619Dic3—32no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—92no—
624Dic3—92no—
625Dic3—182no—
626Dic3—181no—
627Dic3—181no—
628Dic3—181no—
629Dic3—181no—
630Dic3—181no—
631Dic3—181no—
632Dic3—361no—
633Dic3—361no—
634Dic3—361no—
635Dic3C2×Dic1812yescomplemented
636Dic3D4×D912yes—
637C32D4×Dic611yescharacteristic
638C9—21no—
639C9#563211yescharacteristic, complemented
640C23—31no—
641C23C2×D3×D911yescharacteristic
642Q8—182no—
643Q8—274no—
644Q8—542no—
645Q8—542no—
646Q8—542no—
647Q8—542no—
648Q8—542no—
649D4—34no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—91no—
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×D911yescharacteristic
668C2×C4C2×D3×D911yescharacteristic
669C2×C3—22no—
670C2×C3—22no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—42no—
675C2×C3—62no—
676C2×C3C22×Dic1811yescharacteristic
677C2×C3C2×D4×D911yescharacteristic
678C2×C3#6371611yescharacteristic
679C2×C3C2×D3×Dic611yescharacteristic
680C2×C3#6430911yescharacteristic
681C2×C3D32×D411yescharacteristic
682D3—22no—
683C22—21no—
684C22—21no—
685C22—32no—
686C22—61no—
687C22—61no—
688C22D3×Dic1812yescomplemented
689C22C22×D3×D911yescharacteristic
690C4—21no—
691C4—21no—
692C4—32no—
693C4—32no—
694C4—61no—
695C4—92no—
696C4—181no—
697C4—181no—
698C4—181no—
699C4—272no—
700C4—541no—
701C4—541no—
702C4—541no—
703C3—21no—
704C3D4×Dic1811yescharacteristic, complemented
705C3#1059407111yescharacteristic
706C2—22no—
707C2—62no—
708C2C2×D3×Dic1811yescharacteristic
709C2#1172249411yescharacteristic
710C2D3×D4×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×C3×#67C2×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9D4×Q8
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6189C2semidirect
2. C2×D3×Dic18C2semidirect
3. #11721724C2semidirect
5. C3×#63440C2semidirect
8. #11721249C2semidirect
9. #11721026C2semidirect
10. #11721023C2semidirect
11. #11720970C2semidirect
12. #11720955C2semidirect
13. #11720905C2semidirect
14. #11720904C2semidirect
15. #11720900C2semidirect
83. #63440D3semidirect
96. C9×#67Q8semidirect
114. #6189D4semidirect
200. C22×C3×C9C2×Q8semidirect
204. C2×D3×C9C2×Q8semidirect
213. C9×Dic3C2×Q8semidirect
432. C22×C9D3×Q8semidirect
468. C3×C9D4×Q8semidirect
492. #67Dic18semidirect
598. C22×C3C2×Dic18semidirect
604. C2×D3C2×Dic18semidirect
635. Dic3C2×Dic18semidirect
639. C9#5632semidirect
688. C22D3×Dic18semidirect
704. C3D4×Dic18semidirect

Maximal subgroups

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

subgroupindex
C22×#61892
C2×D3×Dic182
#117217242
C9×#67⋊C42
C3×#634402
#67⋊Dic92
#67×Dic92
#117212492
#117210262
#117210232
#117209702
#117209552
#117209052
#117209042
#117209002
#105940713
D4×Dic183