Finite Group Databasebeta

← C3×#15041 #10633648

Subgroups — C3×#15041 #10633648

Order 768.

1218 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#1443C211yesmaximal, characteristic, complemented
2C3×#1443C211yesmaximal, characteristic, complemented
3C3×#1443C211yesmaximal, characteristic, complemented
4C3×#1442C211yesmaximal, characteristic, complemented
5C3×#1440C211yesmaximal, characteristic
6C3×#1440C211yesmaximal, characteristic
7C3×#1440C211yesmaximal, characteristic
8C3×#1439C211yesmaximal, characteristic
9C3×#1437C211yesmaximal, characteristic
10C3×#1437C211yesmaximal, characteristic
11C3×#1437C211yesmaximal, characteristic
12C3×#1436C211yesmaximal, characteristic, complemented
13C3×#1434C211yesmaximal, characteristic, complemented
14C3×#1434C211yesmaximal, characteristic, complemented
15C3×C4×#95C211yesmaximal, characteristic, complemented
16#15041C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C22×C3×C42C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
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#1443C2×C311yescharacteristic, complemented
53#1443C2×C311yescharacteristic, complemented
54#1443C2×C311yescharacteristic, complemented
55#1442C2×C311yescharacteristic, complemented
56#1440C2×C311yescharacteristic
57#1440C2×C311yescharacteristic
58#1440C2×C311yescharacteristic
59#1439C2×C311yescharacteristic
60#1437C2×C311yescharacteristic
61#1437C2×C311yescharacteristic
62#1437C2×C311yescharacteristic
63#1436C2×C311yescharacteristic, complemented
64#1434C2×C311yescharacteristic, complemented
65#1434C2×C311yescharacteristic, complemented
66C4×#95C2×C311yescharacteristic, complemented
67C25×C3C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—41no—
84C2×C3×C4⋊C4—41no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—41no—
99C2×C3×C22⋊C4—41no—
100C2×C3×C22⋊C4—41no—
101C2×C3×C22⋊C4—41no—
102C2×C3×C22⋊C4—41no—
103C2×C3×C22⋊C4—41no—
104C2×C3×C22⋊C4—41no—
105C2×C3×C22⋊C4—41no—
106C2×C3×C42—22no—
107C2×C3×C42—22no—
108C2×C3×C42—22no—
109C2×C3×C42—22no—
110C2×C3×C42—22no—
111C2×C3×C42—41no—
112C2×C3×C42—41no—
113C2×C3×C42—41no—
114C2×C3×C42—41no—
115C3×#95—22no—
116C3×#95—22no—
117C3×#95—22no—
118C3×#95—22no—
119C3×#95—22no—
120C3×#95—22no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—22no—
124C3×#95—22no—
125C3×#95—22no—
126C3×#95—22no—
127C3×#95—22no—
128C3×#95—22no—
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—
139C22×C4⋊C4C22×C311yescharacteristic
140C22×C22⋊C4C22×C311yescharacteristic
141C22×C22⋊C4C22×C311yescharacteristic
142C22×C22⋊C4C22×C311yescharacteristic
143C22×C22⋊C4C22×C311yescharacteristic
144C22×C22⋊C4C22×C311yescharacteristic
145C22×C22⋊C4C22×C311yescharacteristic
146C22×C22⋊C4C22×C311yescharacteristic
147C22×C42C22×C311yescharacteristic
148C22×C42C22×C311yescharacteristic
149C22×C42C22×C311yescharacteristic
150C2×#95C22×C311yescharacteristic
151C2×#95C22×C311yescharacteristic
152C2×#95C22×C311yescharacteristic
153C2×#95C22×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
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—21no—
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#4112yes—
189C24×C3C2411yescharacteristic
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
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#4112yes—
279C22×C3×C4#4112yes—
280C22×C3×C4#4112yes—
281C22×C3×C4#4112yes—
282C22×C3×C4#4112yes—
283C22×C3×C4#4112yes—
284C22×C3×C4#4112yes—
285C22×C3×C4#4112yes—
286C22×C3×C4#4112yes—
287C22×C3×C4#4112yes—
288C3×C4⋊C4—44no—
289C3×C22⋊C4—44no—
290C3×C22⋊C4—44no—
291C3×C22⋊C4—44no—
292C3×C22⋊C4—44no—
293C3×C22⋊C4—44no—
294C3×C22⋊C4—44no—
295C3×C22⋊C4—44no—
296C3×C42—44no—
297C3×C42—44no—
298C3×C42—44no—
299C25C23×C311yescharacteristic
300C23×C4C23×C311yescharacteristic
301C23×C4C23×C311yescharacteristic
302C23×C4C23×C311yescharacteristic
303C23×C4C23×C311yescharacteristic
304C23×C4C23×C311yescharacteristic
305C23×C4C23×C311yescharacteristic
306C23×C4C23×C311yescharacteristic
307C23×C4C23×C311yescharacteristic
308C23×C4C23×C311yescharacteristic
309C23×C4C23×C311yescharacteristic
310C23×C4C23×C311yescharacteristic
311C23×C4C23×C311yescharacteristic
312C23×C4C23×C311yescharacteristic
313C23×C4C23×C311yescharacteristic
314C2×C4⋊C4—22no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—41no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—41no—
344C2×C42—41no—
345C2×C42—41no—
346C2×C42—41no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—22no—
351#95—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—22no—
357#95—22no—
358#95—22no—
359#95—22no—
360#95—22no—
361#95—41no—
362#95—41no—
363#95—41no—
364#95—41no—
365#95—41no—
366#95—41no—
367#95—41no—
368#95—41no—
369#95—41no—
370#95—41no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3C2×#4111yescharacteristic
407C23×C3C2×#4111yescharacteristic
408C23×C3C2×#4111yescharacteristic
409C23×C3C2×#4111yescharacteristic
410C23×C3C2×#4111yescharacteristic
411C23×C3C2×#4111yescharacteristic
412C23×C3C2×#4111yescharacteristic
413C23×C3C2×#4111yescharacteristic
414C23×C3C2×#4111yescharacteristic
415C23×C3C2×#4111yescharacteristic
416C23×C3C2×#4111yescharacteristic
417C23×C3H(5,𝔽2)11yescharacteristic
418C23×C3H(5,𝔽2)11yescharacteristic
419C23×C3H(5,𝔽2)11yescharacteristic
420C23×C3H(5,𝔽2)11yescharacteristic
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
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—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
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#12614yes—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C3×#4112yes—
534C24C24×C311yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
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×C4C3×#4112yes—
624C22×C4C3×#4112yes—
625C22×C4C3×#4112yes—
626C22×C4C3×#4112yes—
627C22×C4C3×#4112yes—
628C22×C4C3×#4112yes—
629C22×C4C3×#4112yes—
630C22×C4C3×#4112yes—
631C22×C4C3×#4112yes—
632C22×C4C3×#4112yes—
633C4⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C42—44no—
642C42—44no—
643C42—44no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3C2×#12611yescharacteristic
660C22×C3#52911yescharacteristic
661C22×C3#52911yescharacteristic
662C22×C3#52911yescharacteristic
663C22×C3#52911yescharacteristic
664C22×C3#52911yescharacteristic
665C22×C3#52911yescharacteristic
666C22×C3#52911yescharacteristic
667C22×C3#52911yescharacteristic
668C22×C3#52911yescharacteristic
669C22×C3#52911yescharacteristic
670C22×C3#52911yescharacteristic
671C22×C3#52911yescharacteristic
672C22×C3#53811yescharacteristic
673C22×C3#53811yescharacteristic
674C22×C3#53811yescharacteristic
675C22×C3#53811yescharacteristic
676C22×C3#54011yescharacteristic
677C22×C3#54011yescharacteristic
678C22×C3#55111yescharacteristic
679C22×C3#55111yescharacteristic
680C22×C3#55111yescharacteristic
681C22×C3#55111yescharacteristic
682C22×C3#55111yescharacteristic
683C22×C3#55111yescharacteristic
684C22×C3#55311yescharacteristic
685C22×C3#55311yescharacteristic
686C22×C3#55311yescharacteristic
687C22×C3#55311yescharacteristic
688C22×C3#55311yescharacteristic
689C22×C3#55311yescharacteristic
690C22×C3#55511yescharacteristic
691C22×C3#55511yescharacteristic
692C22×C3#55911yescharacteristic
693C22×C3#55911yescharacteristic
694C3×C4—24no—
695C3×C4—42no—
696C3×C4—42no—
697C3×C4—42no—
698C3×C4—42no—
699C3×C4—42no—
700C3×C4—42no—
701C3×C4—42no—
702C3×C4—81no—
703C3×C4—81no—
704C3×C4—81no—
705C3×C4—81no—
706C3×C4—81no—
707C3×C4—81no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23C2×C3×#4111yescharacteristic
744C23C2×C3×#4111yescharacteristic
745C23C2×C3×#4111yescharacteristic
746C23C2×C3×#4111yescharacteristic
747C23C2×C3×#4111yescharacteristic
748C23C2×C3×#4111yescharacteristic
749C23C2×C3×#4111yescharacteristic
750C23C2×C3×#4111yescharacteristic
751C23C2×C3×#4111yescharacteristic
752C23C2×C3×#4111yescharacteristic
753C23C2×C3×#4111yescharacteristic
754C23C3×H(5,𝔽2)11yescharacteristic
755C23C3×H(5,𝔽2)11yescharacteristic
756C23C3×H(5,𝔽2)11yescharacteristic
757C23C3×H(5,𝔽2)11yescharacteristic
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
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×C4C3×#12614yes—
856C2×C3—82no—
857C2×C3#240111yescharacteristic
858C2×C3#251011yescharacteristic
859C2×C3#251311yescharacteristic
860C2×C3#251611yescharacteristic
861C2×C3#251811yescharacteristic
862C2×C3#252611yescharacteristic
863C2×C3#253111yescharacteristic
864C2×C3#257211yescharacteristic
865C2×C3#257611yescharacteristic
866C2×C3#257811yescharacteristic
867C2×C3#259311yescharacteristic
868C2×C3#259511yescharacteristic
869C2×C3#259711yescharacteristic
870C2×C3#264811yescharacteristic
871C2×C3#286611yescharacteristic
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×C3×#12611yescharacteristic
888C22C3×#52911yescharacteristic
889C22C3×#52911yescharacteristic
890C22C3×#52911yescharacteristic
891C22C3×#52911yescharacteristic
892C22C3×#52911yescharacteristic
893C22C3×#52911yescharacteristic
894C22C3×#52911yescharacteristic
895C22C3×#52911yescharacteristic
896C22C3×#52911yescharacteristic
897C22C3×#52911yescharacteristic
898C22C3×#52911yescharacteristic
899C22C3×#52911yescharacteristic
900C22C3×#53811yescharacteristic
901C22C3×#53811yescharacteristic
902C22C3×#53811yescharacteristic
903C22C3×#53811yescharacteristic
904C22C3×#54011yescharacteristic
905C22C3×#54011yescharacteristic
906C22C3×#55111yescharacteristic
907C22C3×#55111yescharacteristic
908C22C3×#55111yescharacteristic
909C22C3×#55111yescharacteristic
910C22C3×#55111yescharacteristic
911C22C3×#55111yescharacteristic
912C22C3×#55311yescharacteristic
913C22C3×#55311yescharacteristic
914C22C3×#55311yescharacteristic
915C22C3×#55311yescharacteristic
916C22C3×#55311yescharacteristic
917C22C3×#55311yescharacteristic
918C22C3×#55511yescharacteristic
919C22C3×#55511yescharacteristic
920C22C3×#55911yescharacteristic
921C22C3×#55911yescharacteristic
922C4—24no—
923C4—42no—
924C4—42no—
925C4—42no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—81no—
935C4—81no—
936C3#1504111yescharacteristic, direct product factor, Sylow
937C2—82no—
938C2C3×#240111yescharacteristic
939C2C3×#251011yescharacteristic
940C2C3×#251311yescharacteristic
941C2C3×#251611yescharacteristic
942C2C3×#251811yescharacteristic
943C2C3×#252611yescharacteristic
944C2C3×#253111yescharacteristic
945C2C3×#257211yescharacteristic
946C2C3×#257611yescharacteristic
947C2C3×#257811yescharacteristic
948C2C3×#259311yescharacteristic
949C2C3×#259511yescharacteristic
950C2C3×#259711yescharacteristic
951C2C3×#264811yescharacteristic
952C2C3×#286611yescharacteristic
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×#1443C2semidirect
2. C3×#1443C2semidirect
3. C3×#1443C2semidirect
4. C3×#1442C2semidirect
12. C3×#1436C2semidirect
13. C3×#1434C2semidirect
14. C3×#1434C2semidirect
15. C3×C4×#95C2semidirect
16. #15041C3direct (N × H)
52. #1443C2×C3semidirect
53. #1443C2×C3semidirect
54. #1443C2×C3semidirect
55. #1442C2×C3semidirect
63. #1436C2×C3semidirect
64. #1434C2×C3semidirect
65. #1434C2×C3semidirect
66. C4×#95C2×C3semidirect
936. C3#15041direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#14432
C3×#14422
C3×#14402
C3×#14392
C3×#14372
C3×#14362
C3×#14342
C3×C4×#952
#150413