Finite Group Databasebeta

← C3×#16708 #10635315

Subgroups — C3×#16708 #10635315

Order 768.

1306 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#1444C211yesmaximal, characteristic, complemented
2C3×#1443C211yesmaximal, characteristic, complemented
3C3×#1443C211yesmaximal, characteristic, complemented
4C3×#1443C211yesmaximal, characteristic, complemented
5C3×#1442C211yesmaximal, characteristic, complemented
6C3×#1442C211yesmaximal, characteristic, complemented
7C3×#1442C211yesmaximal, characteristic, complemented
8C3×#1441C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic
10C3×#1439C211yesmaximal, characteristic
11C3×#1439C211yesmaximal, characteristic
12C3×#1439C211yesmaximal, characteristic
13C3×C22⋊#95C211yesmaximal, characteristic
14C3×C22⋊#95C211yesmaximal, characteristic
15C3×C22⋊#95C211yesmaximal, characteristic
16#16708C311yesmaximal, characteristic, direct product factor, Sylow
17C24×C3×C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52#1444C2×C311yescharacteristic, complemented
53#1443C2×C311yescharacteristic, complemented
54#1443C2×C311yescharacteristic, complemented
55#1443C2×C311yescharacteristic, complemented
56#1442C2×C311yescharacteristic, complemented
57#1442C2×C311yescharacteristic, complemented
58#1442C2×C311yescharacteristic, complemented
59#1441C2×C311yescharacteristic, complemented
60#1439C2×C311yescharacteristic
61#1439C2×C311yescharacteristic
62#1439C2×C311yescharacteristic
63#1439C2×C311yescharacteristic
64C22⋊#95C2×C311yescharacteristic
65C22⋊#95C2×C311yescharacteristic
66C22⋊#95C2×C311yescharacteristic
67C25×C3C2311yescharacteristic
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4—41no—
72C23×C3×C4—41no—
73C23×C3×C4—41no—
74C23×C3×C4—41no—
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—41no—
91C2×C3×C4⋊C4—41no—
92C2×C3×C4⋊C4—41no—
93C2×C3×C4⋊C4—41no—
94C2×C3×C4⋊C4—41no—
95C2×C3×C4⋊C4—41no—
96C2×C3×C4⋊C4—41no—
97C2×C3×C4⋊C4—41no—
98C2×C3×C4⋊C4—41no—
99C2×C3×C4⋊C4—41no—
100C2×C3×C4⋊C4—41no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—41no—
109C2×C3×C22⋊C4—41no—
110C2×C3×C22⋊C4—41no—
111C2×C3×C22⋊C4—41no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C22⋊C4—41no—
116C2×C3×C22⋊C4—41no—
117C2×C3×C22⋊C4—41no—
118C2×C3×C22⋊C4Q814yes—
119C3×#95—22no—
120C3×#95—22no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—22no—
124C3×#95—22no—
125C3×#95—22no—
126C3×#95—41no—
127C3×#95—41no—
128C3×#95—41no—
129C3×#95—41no—
130C3×#95—41no—
131C3×#95—41no—
132C3×#95—41no—
133C3×#95—41no—
134C3×#95—41no—
135C3×#95—41no—
136C3×#95—41no—
137C3×#95—41no—
138C3×#95—41no—
139C3×#95—41no—
140C3×#95—41no—
141C3×#95—41no—
142C3×#95—41no—
143C24×C4C22×C311yescharacteristic
144C22×C4⋊C4C22×C311yescharacteristic
145C22×C4⋊C4C22×C311yescharacteristic
146C22×C4⋊C4C22×C311yescharacteristic
147C22×C4⋊C4C22×C311yescharacteristic
148C22×C22⋊C4C22×C311yescharacteristic
149C22×C22⋊C4C22×C311yescharacteristic
150C22×C22⋊C4C22×C311yescharacteristic
151C22×C22⋊C4C22×C311yescharacteristic
152C22×C22⋊C4C22×C311yescharacteristic
153C22×C22⋊C4C22×C311yescharacteristic
154C2×#95C22×C311yescharacteristic
155C2×#95C22×C311yescharacteristic
156C2×#95C22×C311yescharacteristic
157C2×#95C22×C311yescharacteristic
158C2×#95C22×C311yescharacteristic
159C2×#95C22×C311yescharacteristic
160C2×#95C22×C311yescharacteristic
161C2×#95C22×C311yescharacteristic
162C2×#95C22×C311yescharacteristic
163C2×#95C22×C311yescharacteristic
164C2×#95C22×C311yescharacteristic
165C2×#95C22×C311yescharacteristic
166C2×#95C22×C311yescharacteristic
167C2×#95C22×C311yescharacteristic
168C2×#95C22×C311yescharacteristic
169C2×#95C22×C311yescharacteristic
170C2×#95C22×C311yescharacteristic
171C2×#95C22×C311yescharacteristic
172C2×#95C22×C311yescharacteristic
173C2×#95C22×C311yescharacteristic
174C2×#95C22×C311yescharacteristic
175C2×#95C22×C311yescharacteristic
176C2×#95C22×C311yescharacteristic
177C2×#95C22×C311yescharacteristic
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3C2×Q812yes—
191C24×C3#4112yes—
192C24×C3#4112yes—
193C24×C3C2411yescharacteristic
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—44no—
287C22×C3×C4—44no—
288C22×C3×C4—44no—
289C22×C3×C4—44no—
290C22×C3×C4—44no—
291C22×C3×C4—44no—
292C22×C3×C4—44no—
293C22×C3×C4C2×Q812yes—
294C22×C3×C4C2×Q812yes—
295C22×C3×C4#4112yes—
296C22×C3×C4#4112yes—
297C22×C3×C4#4112yes—
298C22×C3×C4#4112yes—
299C3×C4⋊C4—44no—
300C3×C4⋊C4—44no—
301C3×C4⋊C4—44no—
302C3×C4⋊C4—44no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4—44no—
305C3×C22⋊C4—44no—
306C3×C22⋊C4—44no—
307C3×C22⋊C4—44no—
308C3×C22⋊C4—44no—
309C25C23×C311yescharacteristic
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—41no—
314C23×C4—41no—
315C23×C4—41no—
316C23×C4—41no—
317C23×C4C23×C311yescharacteristic
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320C23×C4C23×C311yescharacteristic
321C23×C4C23×C311yescharacteristic
322C23×C4C23×C311yescharacteristic
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C311yescharacteristic
326C23×C4C23×C311yescharacteristic
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C311yescharacteristic
330C23×C4C23×C311yescharacteristic
331C2×C4⋊C4—22no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4C3×Q814yes—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—41no—
369#95—41no—
370#95—41no—
371#95—41no—
372#95—41no—
373#95—41no—
374#95—41no—
375#95—41no—
376#95—41no—
377#95—41no—
378#95—41no—
379#95—41no—
380#95—41no—
381#95—41no—
382#95—41no—
383#95—41no—
384#95—41no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3#12514yes—
420C23×C3C22×Q811yescharacteristic
421C23×C3C2×#4111yescharacteristic
422C23×C3C2×#4111yescharacteristic
423C23×C3C2×#4111yescharacteristic
424C23×C3C2×#4111yescharacteristic
425C23×C3C2×#4111yescharacteristic
426C23×C3C2×#4111yescharacteristic
427C23×C3H(5,𝔽2)11yescharacteristic
428C23×C3H(5,𝔽2)11yescharacteristic
429C23×C3H(5,𝔽2)11yescharacteristic
430C23×C3H(5,𝔽2)11yescharacteristic
431C23×C3H(5,𝔽2)11yescharacteristic
432C23×C3H(5,𝔽2)11yescharacteristic
433C23×C3H(5,𝔽2)11yescharacteristic
434C23×C32−1+411yescharacteristic
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—416no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24C2×C3×Q812yes—
547C24C3×#4112yes—
548C24C3×#4112yes—
549C24C24×C311yescharacteristic
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4C2×C3×Q812yes—
650C22×C4C2×C3×Q812yes—
651C22×C4C3×#4112yes—
652C22×C4C3×#4112yes—
653C22×C4C3×#4112yes—
654C22×C4C3×#4112yes—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22×C3—24no—
666C22×C3—24no—
667C22×C3—24no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3C2×#12511yescharacteristic
681C22×C3#52911yescharacteristic
682C22×C3#52911yescharacteristic
683C22×C3#53811yescharacteristic
684C22×C3#53811yescharacteristic
685C22×C3#53811yescharacteristic
686C22×C3#53811yescharacteristic
687C22×C3#53811yescharacteristic
688C22×C3#53811yescharacteristic
689C22×C3#53811yescharacteristic
690C22×C3#53911yescharacteristic
691C22×C3#53911yescharacteristic
692C22×C3#53911yescharacteristic
693C22×C3#54011yescharacteristic
694C22×C3#54211yescharacteristic
695C22×C3#54211yescharacteristic
696C22×C3#54211yescharacteristic
697C22×C3#54311yescharacteristic
698C22×C3#54411yescharacteristic
699C22×C3#55111yescharacteristic
700C22×C3#55111yescharacteristic
701C22×C3#55111yescharacteristic
702C22×C3#55111yescharacteristic
703C22×C3#55111yescharacteristic
704C22×C3#55311yescharacteristic
705C22×C3#55311yescharacteristic
706C22×C3#55411yescharacteristic
707C22×C3#55411yescharacteristic
708C22×C3#55411yescharacteristic
709C22×C3#55411yescharacteristic
710C22×C3#55511yescharacteristic
711C22×C3#56011yescharacteristic
712C22×C3#56011yescharacteristic
713C22×C3#56011yescharacteristic
714C22×C3#56011yescharacteristic
715C3×C4—42no—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—81no—
722C3×C4—81no—
723C3×C4—81no—
724C3×C4—81no—
725C3×C4—81no—
726C3×C4—81no—
727C3×C4—81no—
728C3×C4—81no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23C3×#12514yes—
764C23C22×C3×Q811yescharacteristic
765C23C2×C3×#4111yescharacteristic
766C23C2×C3×#4111yescharacteristic
767C23C2×C3×#4111yescharacteristic
768C23C2×C3×#4111yescharacteristic
769C23C2×C3×#4111yescharacteristic
770C23C2×C3×#4111yescharacteristic
771C23C3×H(5,𝔽2)11yescharacteristic
772C23C3×H(5,𝔽2)11yescharacteristic
773C23C3×H(5,𝔽2)11yescharacteristic
774C23C3×H(5,𝔽2)11yescharacteristic
775C23C3×H(5,𝔽2)11yescharacteristic
776C23C3×H(5,𝔽2)11yescharacteristic
777C23C3×H(5,𝔽2)11yescharacteristic
778C23C3×2−1+411yescharacteristic
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—416no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C3—44no—
879C2×C3#250511yescharacteristic
880C2×C3#250511yescharacteristic
881C2×C3#251811yescharacteristic
882C2×C3#264611yescharacteristic
883C2×C3#264911yescharacteristic
884C2×C3#265311yescharacteristic
885C2×C3#273511yescharacteristic
886C2×C3#273711yescharacteristic
887C2×C3#274211yescharacteristic
888C2×C3#274611yescharacteristic
889C2×C3#274911yescharacteristic
890C2×C3#278011yescharacteristic
891C2×C3#278411yescharacteristic
892C2×C3#279011yescharacteristic
893C2×C3#282511yescharacteristic
894C22—24no—
895C22—24no—
896C22—24no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22C2×C3×#12511yescharacteristic
910C22C3×#52911yescharacteristic
911C22C3×#52911yescharacteristic
912C22C3×#53811yescharacteristic
913C22C3×#53811yescharacteristic
914C22C3×#53811yescharacteristic
915C22C3×#53811yescharacteristic
916C22C3×#53811yescharacteristic
917C22C3×#53811yescharacteristic
918C22C3×#53811yescharacteristic
919C22C3×#53911yescharacteristic
920C22C3×#53911yescharacteristic
921C22C3×#53911yescharacteristic
922C22C3×#54011yescharacteristic
923C22C3×#54211yescharacteristic
924C22C3×#54211yescharacteristic
925C22C3×#54211yescharacteristic
926C22C3×#54311yescharacteristic
927C22C3×#54411yescharacteristic
928C22C3×#55111yescharacteristic
929C22C3×#55111yescharacteristic
930C22C3×#55111yescharacteristic
931C22C3×#55111yescharacteristic
932C22C3×#55111yescharacteristic
933C22C3×#55311yescharacteristic
934C22C3×#55311yescharacteristic
935C22C3×#55411yescharacteristic
936C22C3×#55411yescharacteristic
937C22C3×#55411yescharacteristic
938C22C3×#55411yescharacteristic
939C22C3×#55511yescharacteristic
940C22C3×#56011yescharacteristic
941C22C3×#56011yescharacteristic
942C22C3×#56011yescharacteristic
943C22C3×#56011yescharacteristic
944C4—42no—
945C4—42no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—81no—
951C4—81no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C3#1670811yescharacteristic, direct product factor, Sylow
959C2—44no—
960C2C3×#250511yescharacteristic
961C2C3×#250511yescharacteristic
962C2C3×#251811yescharacteristic
963C2C3×#264611yescharacteristic
964C2C3×#264911yescharacteristic
965C2C3×#265311yescharacteristic
966C2C3×#273511yescharacteristic
967C2C3×#273711yescharacteristic
968C2C3×#274211yescharacteristic
969C2C3×#274611yescharacteristic
970C2C3×#274911yescharacteristic
971C2C3×#278011yescharacteristic
972C2C3×#278411yescharacteristic
973C2C3×#279011yescharacteristic
974C2C3×#282511yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#1444C2semidirect
2. C3×#1443C2semidirect
3. C3×#1443C2semidirect
4. C3×#1443C2semidirect
5. C3×#1442C2semidirect
6. C3×#1442C2semidirect
7. C3×#1442C2semidirect
8. C3×#1441C2semidirect
16. #16708C3direct (N × H)
52. #1444C2×C3semidirect
53. #1443C2×C3semidirect
54. #1443C2×C3semidirect
55. #1443C2×C3semidirect
56. #1442C2×C3semidirect
57. #1442C2×C3semidirect
58. #1442C2×C3semidirect
59. #1441C2×C3semidirect
958. C3#16708direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#14442
C3×#14432
C3×#14422
C3×#14412
C3×#14392
C3×C22⋊#952
#167083