Finite Group Databasebeta

← C3×#15688 #10634295

Subgroups — C3×#15688 #10634295

Order 768.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#397C211yesmaximal, characteristic, complemented
2C2×C3×#386C211yesmaximal, characteristic
3C3×#1443C211yesmaximal, characteristic, complemented
4C3×#1443C211yesmaximal, characteristic, complemented
5C3×#1443C211yesmaximal, characteristic, complemented
6C3×#1440C211yesmaximal, characteristic, complemented
7C3×#1440C211yesmaximal, characteristic, complemented
8C3×#1439C211yesmaximal, characteristic, complemented
9C3×#1438C211yesmaximal, characteristic
10C3×#1438C211yesmaximal, characteristic
11C3×#1437C211yesmaximal, characteristic, complemented
12C3×#1437C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×C22⋊#95C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#15688C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊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
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C42C2211yescharacteristic
32C3×#397—24no—
33C3×#386—24no—
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
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×#397C2×C311yescharacteristic, complemented
55C2×#386C2×C311yescharacteristic
56#1443C2×C311yescharacteristic, complemented
57#1443C2×C311yescharacteristic, complemented
58#1443C2×C311yescharacteristic, complemented
59#1440C2×C311yescharacteristic, complemented
60#1440C2×C311yescharacteristic, complemented
61#1439C2×C311yescharacteristic, complemented
62#1438C2×C311yescharacteristic
63#1438C2×C311yescharacteristic
64#1437C2×C311yescharacteristic, complemented
65#1437C2×C311yescharacteristic, complemented
66#1436C2×C311yescharacteristic, complemented
67C22⋊#95C2×C311yescharacteristic, complemented
68C22⋊#95C2×C311yescharacteristic, complemented
69C25×C3C2311yescharacteristic
70C25×C3C2311yescharacteristic
71C22×C3×D4—22no—
72C22×C3×D4—22no—
73C22×C3×D4—22no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—41no—
77C22×C3×D4—41no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—41no—
82C23×C3×C4—41no—
83C23×C3×C4—41no—
84C23×C3×C4—41no—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
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—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—41no—
118C2×C3×C22⋊C4—41no—
119C2×C3×C22⋊C4—41no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4—41no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4—41no—
128C2×C3×C22⋊C4—41no—
129C2×C3×C22⋊C4—41no—
130C2×C3×C22⋊C4—41no—
131C2×C3×C22⋊C4—41no—
132C2×C3×C22⋊C4—41no—
133C2×C3×C22⋊C4D414yes—
134C2×C3×C42—41no—
135C2×C3×C42—41no—
136C2×C3×C42—41no—
137C3×#95—22no—
138C3×#95—22no—
139C3×#95—22no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—22no—
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—41no—
148C3×#95—41no—
149C3×#95—41no—
150C3×#95—41no—
151C3×#95—41no—
152C3×#95—41no—
153C3×#95—41no—
154C3×#95—41no—
155C3×#95—41no—
156C3×#95—41no—
157C23×D4C22×C311yescharacteristic
158C24×C4C22×C311yescharacteristic
159C22×C4⋊C4C22×C311yescharacteristic
160C22×C22⋊C4C22×C311yescharacteristic
161C22×C22⋊C4C22×C311yescharacteristic
162C22×C22⋊C4C22×C311yescharacteristic
163C22×C22⋊C4C22×C311yescharacteristic
164C22×C22⋊C4C22×C311yescharacteristic
165C22×C22⋊C4C22×C311yescharacteristic
166C22×C22⋊C4C22×C311yescharacteristic
167C22×C22⋊C4C22×C311yescharacteristic
168C22×C22⋊C4C22×C311yescharacteristic
169C22×C22⋊C4C22×C311yescharacteristic
170C22×C22⋊C4C22×C311yescharacteristic
171C22×C42C22×C311yescharacteristic
172#397—24no—
173#386—24no—
174C2×#95C22×C311yescharacteristic
175C2×#95C22×C311yescharacteristic
176C2×#95C22×C311yescharacteristic
177C2×#95C22×C311yescharacteristic
178C2×#95C22×C311yescharacteristic
179C2×#95C22×C311yescharacteristic
180C2×#95C22×C311yescharacteristic
181C2×#95C22×C311yescharacteristic
182C2×#95C22×C311yescharacteristic
183C2×#95C22×C311yescharacteristic
184C2×#95C22×C311yescharacteristic
185C2×#95C22×C311yescharacteristic
186C2×#95C22×C311yescharacteristic
187C2×#95C22×C311yescharacteristic
188C2×#95C22×C311yescharacteristic
189C2×#95C22×C311yescharacteristic
190C2×#95C22×C311yescharacteristic
191C2×#95C22×C311yescharacteristic
192C2×#95C22×C311yescharacteristic
193C2×#95C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3C2×D412yes—
221C24×C3#4112yes—
222C24×C3#4112yes—
223C24×C3#4112yes—
224C24×C3C2411yescharacteristic
225C2×C3×D4—28no—
226C2×C3×D4—44no—
227C2×C3×D4—44no—
228C2×C3×D4—44no—
229C2×C3×D4—44no—
230C2×C3×D4—44no—
231C2×C3×D4—44no—
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—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—44no—
317C22×C3×C4—44no—
318C22×C3×C4—44no—
319C22×C3×C4—44no—
320C22×C3×C4—44no—
321C22×C3×C4—44no—
322C22×C3×C4—44no—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4#4112yes—
326C22×C3×C4#4112yes—
327C22×C3×C4#4112yes—
328C22×C3×C4#4112yes—
329C22×C3×C4#4112yes—
330C3×C4⋊C4—44no—
331C3×C22⋊C4—44no—
332C3×C22⋊C4—44no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—44no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4—44no—
342C3×C42—44no—
343C25C23×C311yescharacteristic
344C25C23×C311yescharacteristic
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—41no—
351C22×D4—41no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—41no—
356C23×C4—41no—
357C23×C4—41no—
358C23×C4—41no—
359C23×C4C23×C311yescharacteristic
360C23×C4C23×C311yescharacteristic
361C23×C4C23×C311yescharacteristic
362C23×C4C23×C311yescharacteristic
363C23×C4C23×C311yescharacteristic
364C23×C4C23×C311yescharacteristic
365C23×C4C23×C311yescharacteristic
366C23×C4C23×C311yescharacteristic
367C23×C4C23×C311yescharacteristic
368C23×C4C23×C311yescharacteristic
369C23×C4C23×C311yescharacteristic
370C23×C4C23×C311yescharacteristic
371C23×C4C23×C311yescharacteristic
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—41no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—41no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4C3×D414yes—
408C2×C42—41no—
409C2×C42—41no—
410C2×C42—41no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—41no—
422#95—41no—
423#95—41no—
424#95—41no—
425#95—41no—
426#95—41no—
427#95—41no—
428#95—41no—
429#95—41no—
430#95—41no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3#12614yes—
501C23×C3C22×D411yescharacteristic
502C23×C3C2×#4111yescharacteristic
503C23×C3C2×#4111yescharacteristic
504C23×C3C2×#4111yescharacteristic
505C23×C3C2×#4111yescharacteristic
506C23×C3C2×#4111yescharacteristic
507C23×C3C2×#4111yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3H(5,𝔽2)11yescharacteristic
511C23×C3H(5,𝔽2)11yescharacteristic
512C23×C3H(5,𝔽2)11yescharacteristic
513C23×C3H(5,𝔽2)11yescharacteristic
514C23×C3H(5,𝔽2)11yescharacteristic
515C23×C3H(5,𝔽2)11yescharacteristic
516C3×D4—416no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—416no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24C2×C3×D412yes—
636C24C3×#4112yes—
637C24C3×#4112yes—
638C24C3×#4112yes—
639C24C24×C311yescharacteristic
640C2×D4—28no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—44no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4C2×C3×D412yes—
739C22×C4C2×C3×D412yes—
740C22×C4C3×#4112yes—
741C22×C4C3×#4112yes—
742C22×C4C3×#4112yes—
743C22×C4C3×#4112yes—
744C22×C4C3×#4112yes—
745C4⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C42—44no—
758C22×C3—24no—
759C22×C3—24no—
760C22×C3—24no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—81no—
781C22×C3—81no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3#52511yescharacteristic
789C22×C3C2×#12611yescharacteristic
790C22×C3#52911yescharacteristic
791C22×C3#52911yescharacteristic
792C22×C3#52911yescharacteristic
793C22×C3#53211yescharacteristic
794C22×C3#53411yescharacteristic
795C22×C3#53811yescharacteristic
796C22×C3#53811yescharacteristic
797C22×C3#53811yescharacteristic
798C22×C3#53811yescharacteristic
799C22×C3#53811yescharacteristic
800C22×C3#53811yescharacteristic
801C22×C3#54011yescharacteristic
802C22×C3#54011yescharacteristic
803C22×C3#54611yescharacteristic
804C22×C3#54611yescharacteristic
805C22×C3#54611yescharacteristic
806C22×C3#54611yescharacteristic
807C22×C3#55111yescharacteristic
808C22×C3#55111yescharacteristic
809C22×C3#55111yescharacteristic
810C22×C3#55111yescharacteristic
811C22×C3#55111yescharacteristic
812C22×C3#55111yescharacteristic
813C22×C3#55311yescharacteristic
814C22×C3#55311yescharacteristic
815C22×C3#55311yescharacteristic
816C22×C3#55311yescharacteristic
817C22×C3#55311yescharacteristic
818C22×C3#55311yescharacteristic
819C22×C3#55911yescharacteristic
820C22×C3#55911yescharacteristic
821C22×C3#56011yescharacteristic
822C22×C3#56011yescharacteristic
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—42no—
826C3×C4—42no—
827C3×C4—42no—
828C3×C4—42no—
829C3×C4—42no—
830C3×C4—81no—
831C3×C4—81no—
832C3×C4—81no—
833C3×C4—81no—
834C3×C4—81no—
835C3×C4—81no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23C3×#12614yes—
906C23C22×C3×D411yescharacteristic
907C23C2×C3×#4111yescharacteristic
908C23C2×C3×#4111yescharacteristic
909C23C2×C3×#4111yescharacteristic
910C23C2×C3×#4111yescharacteristic
911C23C2×C3×#4111yescharacteristic
912C23C2×C3×#4111yescharacteristic
913C23C2×C3×#4111yescharacteristic
914C23C2×C3×#4111yescharacteristic
915C23C3×H(5,𝔽2)11yescharacteristic
916C23C3×H(5,𝔽2)11yescharacteristic
917C23C3×H(5,𝔽2)11yescharacteristic
918C23C3×H(5,𝔽2)11yescharacteristic
919C23C3×H(5,𝔽2)11yescharacteristic
920C23C3×H(5,𝔽2)11yescharacteristic
921D4—416no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—416no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C3—44no—
1015C2×C3—82no—
1016C2×C3#245711yescharacteristic
1017C2×C3#248011yescharacteristic
1018C2×C3#251011yescharacteristic
1019C2×C3#251011yescharacteristic
1020C2×C3#251611yescharacteristic
1021C2×C3#255711yescharacteristic
1022C2×C3#255911yescharacteristic
1023C2×C3#259711yescharacteristic
1024C2×C3#260211yescharacteristic
1025C2×C3#268811yescharacteristic
1026C2×C3#269711yescharacteristic
1027C2×C3#274911yescharacteristic
1028C2×C3#277811yescharacteristic
1029C2×C3#279711yescharacteristic
1030C2×C3#279711yescharacteristic
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22C3×#52511yescharacteristic
1062C22C2×C3×#12611yescharacteristic
1063C22C3×#52911yescharacteristic
1064C22C3×#52911yescharacteristic
1065C22C3×#52911yescharacteristic
1066C22C3×#53211yescharacteristic
1067C22C3×#53411yescharacteristic
1068C22C3×#53811yescharacteristic
1069C22C3×#53811yescharacteristic
1070C22C3×#53811yescharacteristic
1071C22C3×#53811yescharacteristic
1072C22C3×#53811yescharacteristic
1073C22C3×#53811yescharacteristic
1074C22C3×#54011yescharacteristic
1075C22C3×#54011yescharacteristic
1076C22C3×#54611yescharacteristic
1077C22C3×#54611yescharacteristic
1078C22C3×#54611yescharacteristic
1079C22C3×#54611yescharacteristic
1080C22C3×#55111yescharacteristic
1081C22C3×#55111yescharacteristic
1082C22C3×#55111yescharacteristic
1083C22C3×#55111yescharacteristic
1084C22C3×#55111yescharacteristic
1085C22C3×#55111yescharacteristic
1086C22C3×#55311yescharacteristic
1087C22C3×#55311yescharacteristic
1088C22C3×#55311yescharacteristic
1089C22C3×#55311yescharacteristic
1090C22C3×#55311yescharacteristic
1091C22C3×#55311yescharacteristic
1092C22C3×#55911yescharacteristic
1093C22C3×#55911yescharacteristic
1094C22C3×#56011yescharacteristic
1095C22C3×#56011yescharacteristic
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—42no—
1101C4—42no—
1102C4—42no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C3#1568811yescharacteristic, direct product factor, Sylow
1110C2—44no—
1111C2—82no—
1112C2C3×#245711yescharacteristic
1113C2C3×#248011yescharacteristic
1114C2C3×#251011yescharacteristic
1115C2C3×#251011yescharacteristic
1116C2C3×#251611yescharacteristic
1117C2C3×#255711yescharacteristic
1118C2C3×#255911yescharacteristic
1119C2C3×#259711yescharacteristic
1120C2C3×#260211yescharacteristic
1121C2C3×#268811yescharacteristic
1122C2C3×#269711yescharacteristic
1123C2C3×#274911yescharacteristic
1124C2C3×#277811yescharacteristic
1125C2C3×#279711yescharacteristic
1126C2C3×#279711yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#397C2semidirect
3. C3×#1443C2semidirect
4. C3×#1443C2semidirect
5. C3×#1443C2semidirect
6. C3×#1440C2semidirect
7. C3×#1440C2semidirect
8. C3×#1439C2semidirect
11. C3×#1437C2semidirect
12. C3×#1437C2semidirect
13. C3×#1436C2semidirect
14. C3×C22⋊#95C2semidirect
15. C3×C22⋊#95C2semidirect
16. #15688C3direct (N × H)
54. C2×#397C2×C3semidirect
56. #1443C2×C3semidirect
57. #1443C2×C3semidirect
58. #1443C2×C3semidirect
59. #1440C2×C3semidirect
60. #1440C2×C3semidirect
61. #1439C2×C3semidirect
64. #1437C2×C3semidirect
65. #1437C2×C3semidirect
66. #1436C2×C3semidirect
67. C22⋊#95C2×C3semidirect
68. C22⋊#95C2×C3semidirect
1109. C3#15688direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×C3×#3862
C3×#14432
C3×#14402
C3×#14392
C3×#14382
C3×#14372
C3×#14362
C3×C22⋊#952
#156883