Finite Group Databasebeta

← #13148140

Subgroups — #13148140

Order 1728.

970 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88658C211yesmaximal, characteristic, complemented
2C2×#88635C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C3×#63445C211yesmaximal, characteristic, complemented
5C9×#878C211yesmaximal, characteristic, complemented
6#11721275C211yesmaximal, characteristic, complemented
7#11721271C211yesmaximal, characteristic, complemented
8#11721240C211yesmaximal, characteristic, complemented
9#11721000C211yesmaximal, characteristic, complemented
10#11720997C211yesmaximal, characteristic, complemented
11#11720995C211yesmaximal, characteristic, complemented
12#11720988C211yesmaximal, characteristic, complemented
13#11720978C211yesmaximal, characteristic, complemented
14D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#11720903C211yesmaximal, characteristic, complemented
16#10594064—31nomaximal
17#10589733—31nomaximal
18C2×#6233C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C9×Dic6C2211yescharacteristic
26C2×#6192C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31#88658—24no—
32C2×Dic3×D9C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C2×#6189C2211yescharacteristic
35#88635—24no—
36C3×C9×C22⋊C4C2211yescharacteristic
37#88536C2211yescharacteristic
38#88534C2211yescharacteristic
39C9×#217C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C9×C4⋊Dic3C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic
44C9×Dic3⋊C4C2211yescharacteristic
45C3×C4⋊Dic9C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52#88442C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3804—31no—
56C2×#3799—31no—
57#64093—31no—
58C3×#883—31no—
59C3×#878D311yescharacteristic
60#63975—31no—
61#63971—31no—
62#63952—31no—
63#63900—31no—
64#63897—31no—
65#63895—31no—
66#63890—31no—
67#63881—31no—
68D3×Dic3⋊C4—31no—
69#63839—31no—
70C2×#3701—31no—
71C2×#3697—31no—
72C9×C22⋊Q8—31no—
73#63506—31no—
74C4×#611—31no—
75#63459—31no—
76#63456—31no—
77#63456—31no—
78#63455—31no—
79C4⋊C4×D9—31no—
80C4⋊C4×D9—31no—
81#63446—31no—
82#63446—31no—
83#63446—61no—
84#63445—31no—
85#63445D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92#6233—22no—
93#6233—22no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4⋊(C3⋊D9)—22no—
97C4×C3⋊D9—22no—
98C3×#611—22no—
99C2×C9×Dic3—22no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C3×C4×D9—22no—
108C9×Dic6—22no—
109#6192—22no—
110#6192D414yescomplemented
111(C3⋊D9)⋊C4—22no—
112(C3⋊D9)⋊C4—22no—
113(C3⋊D9)⋊C4—22no—
114Dic3×D9—22no—
115Dic3×D9—22no—
116#6189—22no—
117#5655—91no—
118#5631—91no—
119C2×#638—31no—
120C2×#638—31no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4×C3⋊D3—31no—
123C2×C3×#67—31no—
124C22×C3×Dic3C2×D311yescharacteristic
125C2×C3×C4×D3—31no—
126C2×C3×Dic6C2×D311yescharacteristic
127C2×#627—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#624—31no—
131C2×#624—31no—
132C2×#624—31no—
133#3804—64no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136#3799—64no—
137C32×C22⋊C4C2×D311yescharacteristic
138#3752—31no—
139#3750—31no—
140C3×#217—31no—
141C3×#217C2×D311yescharacteristic
142C3×(C2×D3)⋊C4—31no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3C2×D311yescharacteristic
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4C2×D311yescharacteristic
147C3×Dic3⋊C4C2×D311yescharacteristic
148#3724—31no—
149#3724—31no—
150Dic3⋊Dic3—31no—
151Dic3⋊Dic3—31no—
152#3722—31no—
153#3722—31no—
154#3722—31no—
155Dic32—31no—
156C2×Q8×C9—31no—
157C22×C4×C9—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—61no—
161C2×#611—61no—
162C2×#611C2×D311yescharacteristic
163#3701—64no—
164#3697—64no—
165C2×D36—31no—
166C2×D36—31no—
167C2×D36—31no—
168C2×D36—61no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—61no—
176C2×C4×D9C2×D311yescharacteristic
177C2×Dic18—31no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4—31no—
180C9×C4⋊C4—31no—
181C9×C22⋊C4—21no—
182C9×C22⋊C4—31no—
183C9×C22⋊C4C2×D311yescharacteristic
184#3676C2×D311yescharacteristic
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4C2×D311yescharacteristic
191C4⋊Dic9—31no—
192C4⋊Dic9C2×D311yescharacteristic
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—61no—
198Dic9⋊C4C2×D311yescharacteristic
199C4×Dic9—31no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9C2×D412yes—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9C2×D412yes—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9#4112yescomplemented
217C9×Dic3—21no—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3C2×D412yes—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C2×#239—91no—
225C2×#237—91no—
226C2×#235—91no—
227C2×#235—91no—
228C3×#123—91no—
229C3×C22⋊Q8—31no—
230#944—91no—
231#939—91no—
232C4×#67—91no—
233C2×Dic3⋊C4—91no—
234#897—91no—
235#896—91no—
236#894—91no—
237#894—91no—
238#894—91no—
239#893—91no—
240D3×C4⋊C4—91no—
241D3×C4⋊C4—91no—
242D3×C4⋊C4—91no—
243#888—91no—
244#886—91no—
245#884—91no—
246#884—91no—
247#884—91no—
248#884—181no—
249#883—31no—
250#883—91no—
251#883—91no—
252#67⋊C4—91no—
253#67⋊C4—91no—
254#878D911yescharacteristic, complemented
255C23×C32C22×D311yescharacteristic
256C22×C3⋊D3—31no—
257C22×C3⋊D3—31no—
258C22×C3×D3—31no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261#638—62no—
262#638—62no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C4⋊(C3⋊D3)—62no—
266C4×C3⋊D3—62no—
267C3×#67—62no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C3×C4×D3—62no—
277C3×Dic6—22no—
278#627—62no—
279#626—34no—
280#626—62no—
281#624—62no—
282#624—62no—
283#624—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—21no—
287C23×C9C22×D311yescharacteristic
288C22×D9—31no—
289C22×D9—31no—
290C22×D9—61no—
291C22×D9—61no—
292C22×D9C22×D311yescharacteristic
293Q8×C9—62no—
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—62no—
301C2×C4×C9C22×D311yescharacteristic
302C2×C4×C9C22×D311yescharacteristic
303#611—22no—
304#611—62no—
305#611—62no—
306#611—122no—
307#611—122no—
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9C22×D311yescharacteristic
313C2×Dic9C22×D311yescharacteristic
314C2×Dic9C22×D311yescharacteristic
315D36—34no—
316D36—62no—
317D36—62no—
318D36—122no—
319C4×D9—22no—
320C4×D9—62no—
321C4×D9—62no—
322C4×D9—62no—
323C4×D9—62no—
324C4×D9—62no—
325C4×D9—62no—
326C4×D9—122no—
327Dic18—62no—
328#547—271noSylow
329C2×C3×C9—41no—
330C2×C3×C9C22×D411yescharacteristic
331C2×C3×C9C2×#4111yescharacteristic
332C2×C3×C92−1+411yescharacteristic
333C3⋊D9—22no—
334C3⋊D9—41no—
335C3×D9—22no—
336C2×C3×Q8—31no—
337C2×C3×D4—91no—
338C22×C3×C4—31no—
339C22×C3×C4—91no—
340C2×#67—31no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—181no—
348C2×#67—181no—
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3C2×D911yescharacteristic
352#239—184no—
353#237—184no—
354#235—184no—
355#235—184no—
356C2×D12—91no—
357C2×D12—91no—
358C2×D12—91no—
359C2×D12—91no—
360C2×D12—181no—
361C2×C4×D3—31no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3—181no—
373C2×Dic6—91no—
374C2×Dic6—91no—
375C2×Dic6C2×D911yescharacteristic
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—91no—
380C3×C4⋊C4—91no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4C2×D911yescharacteristic
386C3×C22⋊C4D3211yescharacteristic
387#217—31no—
388#217C2×D911yescharacteristic
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—181no—
399C4⋊Dic3—31no—
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402C4⋊Dic3C2×D911yescharacteristic
403Dic3⋊C4—31no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—181no—
413Dic3⋊C4C2×D911yescharacteristic
414Dic3⋊C4C2×D911yescharacteristic
415C4×Dic3—91no—
416C4×Dic3—91no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32C23×D311yescharacteristic
421C2×C3⋊D3—32no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
424C2×C3⋊D3—61no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—61no—
427C2×C3×D3—32no—
428C2×C3×D3—61no—
429C2×C3×D3—61no—
430C32×C4—21no—
431C32×C4—21no—
432C3⋊Dic3—32no—
433C3⋊Dic3—61no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C3×Dic3—61no—
440C3×Dic3D3×D412yes—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—41no—
446C22×C9—41no—
447C22×C9—41no—
448C22×C9C23×D311yescharacteristic
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—32no—
452C2×D9—62no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9—61no—
457C2×D9—61no—
458C2×D9—121no—
459C2×D9—121no—
460C2×D9—121no—
461C2×D9—121no—
462C2×D9—121no—
463C2×D9D3×D412yes—
464C4×C9—21no—
465C4×C9—21no—
466C4×C9—32no—
467C4×C9—41no—
468C4×C9—41no—
469C4×C9—61no—
470C4×C9—61no—
471C4×C9—61no—
472Dic9—21no—
473Dic9—21no—
474Dic9—21no—
475Dic9—32no—
476Dic9—62no—
477Dic9—61no—
478Dic9—121no—
479C2×#41—271no—
480C2×#41—271no—
481C4⋊Q8—271no—
482#123—91no—
483#123—271no—
484#123—271no—
485#123—271no—
486C22⋊Q8—31no—
487C22⋊Q8—271no—
488#121—271no—
489#121—271no—
490C4×D4—271no—
491C4×D4—271no—
492C2×C4⋊C4—271no—
493C2×C4⋊C4—271no—
494C3×C9#54711yescharacteristic, complemented, Sylow
495C23×C3—21no—
496C23×C3—91no—
497C23×C3C22×D911yescharacteristic
498C23×C3C2×D3211yescharacteristic
499C22×D3—31no—
500C22×D3—91no—
501C22×D3—91no—
502C22×D3—91no—
503C22×D3—91no—
504C22×D3—181no—
505C22×D3—181no—
506C3×Q8—62no—
507C3×D4—182no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—62no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—182no—
519C2×C3×C4C22×D911yescharacteristic
520C2×C3×C4C22×D911yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523#67—62no—
524#67—94no—
525#67—182no—
526#67—182no—
527#67—182no—
528#67—182no—
529#67—182no—
530#67—362no—
531#67—362no—
532C2×Dic3—22no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—181no—
541C2×Dic3—181no—
542C2×Dic3—182no—
543C2×Dic3—182no—
544C2×Dic3C22×D911yescharacteristic
545C2×Dic3C22×D911yescharacteristic
546C2×Dic3C22×D911yescharacteristic
547C2×Dic3C22×D911yescharacteristic
548D12—94no—
549D12—182no—
550D12—182no—
551D12—182no—
552D12—362no—
553C4×D3—62no—
554C4×D3—182no—
555C4×D3—182no—
556C4×D3—182no—
557C4×D3—182no—
558C4×D3—182no—
559C4×D3—182no—
560C4×D3—182no—
561C4×D3—182no—
562C4×D3—182no—
563C4×D3—182no—
564C4×D3—362no—
565Dic6—22no—
566Dic6—182no—
567Dic6—182no—
568C2×C32—41no—
569C2×C32C2×D3×D411yescharacteristic
570C2×C32#100711yescharacteristic
571C2×C32D3×#4111yescharacteristic
572C3⋊D3—62no—
573C3⋊D3—121no—
574C3×D3—62no—
575C2×C9—21no—
576C2×C9—21no—
577C2×C9—21no—
578C2×C9—41no—
579C2×C9—81no—
580C2×C9C2×D3×D411yescharacteristic
581C2×C9D3×#4111yescharacteristic
582C2×C9#101011yescharacteristic
583D9—22no—
584D9—62no—
585D9—122no—
586D9—121no—
587D9—241no—
588#41—544no—
589#41—544no—
590C2×Q8—31no—
591C2×Q8—271no—
592C2×D4—91no—
593C2×D4—271no—
594C2×D4—271no—
595C2×D4—271no—
596C2×D4—271no—
597C2×D4—271no—
598C22×C4—31no—
599C22×C4—91no—
600C22×C4—271no—
601C22×C4—271no—
602C22×C4—271no—
603C22×C4—271no—
604C22×C4—271no—
605C22×C4—271no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—271no—
612C4⋊C4—271no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C22⋊C4—31no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4D3×D911yescharacteristic
624C42—271no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—92no—
636C22×C3—181no—
637C22×C3—181no—
638C22×C3C23×D911yescharacteristic
639C22×C3C22×D3211yescharacteristic
640C2×D3—32no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—92no—
644C2×D3—92no—
645C2×D3—182no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—361no—
657C2×D3—361no—
658C2×D3—361no—
659C2×D3—361no—
660C2×D3—361no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—32no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—181no—
672C3×C4—181no—
673C3×C4—181no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—92no—
681Dic3—92no—
682Dic3—182no—
683Dic3—181no—
684Dic3—181no—
685Dic3—361no—
686Dic3D4×D912yes—
687C32#563111yescharacteristic
688C9—21no—
689C9#565511yescharacteristic, complemented
690C23—91no—
691C23—271no—
692C23—271no—
693C23C2×D3×D911yescharacteristic
694Q8—62no—
695Q8—542no—
696D4—182no—
697D4—274no—
698D4—542no—
699D4—542no—
700D4—542no—
701D4—542no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—62no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—182no—
711C2×C4—271no—
712C2×C4—271no—
713C2×C4—542no—
714C2×C4—542no—
715C2×C4—542no—
716C2×C4—542no—
717C2×C4—542no—
718C2×C4—542no—
719C2×C4C2×D3×D911yescharacteristic
720C2×C4C2×D3×D911yescharacteristic
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—81no—
727C2×C3—182no—
728C2×C3C2×D4×D911yescharacteristic
729C2×C3#6371311yescharacteristic
730C2×C3#41×D911yescharacteristic
731C2×C3#6429711yescharacteristic
732C2×C3D32×D411yescharacteristic
733C2×C3#6431211yescharacteristic
734D3—62no—
735D3—182no—
736D3—182no—
737D3—362no—
738D3—361no—
739D3—361no—
740D3—721no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—92no—
745C22—181no—
746C22—181no—
747C22—272no—
748C22—541no—
749C22—541no—
750C22—541no—
751C22—541no—
752C22—541no—
753C22C22×D3×D911yescharacteristic
754C4—21no—
755C4—21no—
756C4—32no—
757C4—61no—
758C4—61no—
759C4—61no—
760C4—181no—
761C4—181no—
762C4—181no—
763C4—272no—
764C4—541no—
765C3—21no—
766C3#1058973311yescharacteristic, complemented
767C3#1059406411yescharacteristic
768C2—41no—
769C2—182no—
770C2—542no—
771C2—1081no—
772C2#1172245811yescharacteristic
773C2D3×D4×D911yescharacteristic
774C2#1172249811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#547
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. C2×#88658C2semidirect
2. C2×#88635C2semidirect
3. #11721730C2semidirect
4. C3×#63445C2semidirect
5. C9×#878C2semidirect
6. #11721275C2semidirect
7. #11721271C2semidirect
8. #11721240C2semidirect
9. #11721000C2semidirect
10. #11720997C2semidirect
11. #11720995C2semidirect
12. #11720988C2semidirect
13. #11720978C2semidirect
14. D9×Dic3⋊C4C2semidirect
15. #11720903C2semidirect
85. #63445D3semidirect
110. #6192D4semidirect
216. C3⋊Dic9#41semidirect
254. #878D9semidirect
494. C3×C9#547semidirect
689. C9#5655semidirect
766. C3#10589733semidirect

Maximal subgroups

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

subgroupindex
C2×#886582
C2×#886352
#117217302
C3×#634452
C9×#8782
#117212752
#117212712
#117212402
#117210002
#117209972
#117209952
#117209882
#117209782
D9×Dic3⋊C42
#117209032
#105940643
#105897333