Finite Group Databasebeta

← C2×C3×#2700 #10670728

Subgroups — C2×C3×#2700 #10670728

Order 768.

2850 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#124C211yesmaximal, characteristic
2C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C3×#2700C2116yesmaximal, direct product factor
4C2×C3×#397C211yesmaximal, characteristic, complemented
5C2×C3×#397C211yesmaximal, characteristic, complemented
6C2×C3×#396C211yesmaximal, characteristic, complemented
7C2×C3×#395C211yesmaximal, characteristic, complemented
8C2×C3×#394C211yesmaximal, characteristic
9C2×C3×#393C211yesmaximal, characteristic, complemented
10C2×C3×#391C211yesmaximal, characteristic, complemented
11C2×C3×#391C211yesmaximal, characteristic, complemented
12C2×C3×#388C211yesmaximal, characteristic, complemented
13C2×C3×#388C211yesmaximal, characteristic, complemented
14C2×C3×#387C211yesmaximal, characteristic, complemented
15C2×C3×#386C211yesmaximal, characteristic
16C2×C3×#381C211yesmaximal, characteristic, complemented
17C2×#2700C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C2×C3×#124—28no—
23C2×C3×#124C2218yes—
24C2×C3×C22⋊Q8—28no—
25C2×C3×C22⋊Q8C2218yescomplemented
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C42C2211yescharacteristic
44C22×C3×C42C2211yescharacteristic
45C3×#397C2218yescomplemented
46C3×#397C2218yescomplemented
47C3×#396C2218yescomplemented
48C3×#395C2218yescomplemented
49C3×#394C2218yes—
50C3×#393C2218yescomplemented
51C3×#391C2218yescomplemented
52C3×#391C2218yescomplemented
53C3×#388C2218yescomplemented
54C3×#388C2218yescomplemented
55C3×#387C2218yescomplemented
56C3×#386C2218yes—
57C3×#381C2218yescomplemented
58C2×C3×#95C2211yescharacteristic
59C2×C3×#95C2211yescharacteristic
60C2×C3×#95C2211yescharacteristic
61C2×C3×#95C2211yescharacteristic
62C2×C3×#95C2211yescharacteristic
63C2×C3×#95C2211yescharacteristic
64C2×C3×#95C2211yescharacteristic
65C2×C3×#95C2211yescharacteristic
66C2×C3×#95C2211yescharacteristic
67C2×C3×#95C2211yescharacteristic
68C2×C3×#95C2211yescharacteristic
69C2×C3×#95C2211yescharacteristic
70C22×#124C2×C311yescharacteristic
71C22×C22⋊Q8C2×C311yescharacteristic, complemented
72#2700C2×C3116yesdirect product factor
73C2×#397C2×C311yescharacteristic, complemented
74C2×#397C2×C311yescharacteristic, complemented
75C2×#396C2×C311yescharacteristic, complemented
76C2×#395C2×C311yescharacteristic, complemented
77C2×#394C2×C311yescharacteristic
78C2×#393C2×C311yescharacteristic, complemented
79C2×#391C2×C311yescharacteristic, complemented
80C2×#391C2×C311yescharacteristic, complemented
81C2×#388C2×C311yescharacteristic, complemented
82C2×#388C2×C311yescharacteristic, complemented
83C2×#387C2×C311yescharacteristic, complemented
84C2×#386C2×C311yescharacteristic
85C2×#381C2×C311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C22×C3×Q8—24no—
89C22×C3×Q8—24no—
90C22×C3×Q8—24no—
91C22×C3×Q8—24no—
92C22×C3×Q8—42no—
93C22×C3×Q8—42no—
94C22×C3×Q8C2314yes—
95C22×C3×Q8C2314yes—
96C22×C3×D4—24no—
97C22×C3×D4—24no—
98C22×C3×D4—42no—
99C22×C3×D4C2314yes—
100C23×C3×C4—24no—
101C23×C3×C4—24no—
102C23×C3×C4—42no—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2314yes—
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C3×#124—232no—
118C3×C22⋊Q8—232no—
119C2×C3×C4⋊C4—24no—
120C2×C3×C4⋊C4—24no—
121C2×C3×C4⋊C4—24no—
122C2×C3×C4⋊C4—24no—
123C2×C3×C4⋊C4—42no—
124C2×C3×C4⋊C4—42no—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C4⋊C4C2314yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C22⋊C4—24no—
132C2×C3×C22⋊C4—24no—
133C2×C3×C22⋊C4—24no—
134C2×C3×C22⋊C4—24no—
135C2×C3×C22⋊C4—24no—
136C2×C3×C22⋊C4—42no—
137C2×C3×C22⋊C4—42no—
138C2×C3×C22⋊C4—42no—
139C2×C3×C22⋊C4—42no—
140C2×C3×C22⋊C4—42no—
141C2×C3×C22⋊C4D418yes—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C22⋊C4C2314yes—
144C2×C3×C22⋊C4C2314yes—
145C2×C3×C22⋊C4C2314yes—
146C2×C3×C22⋊C4C2314yes—
147C2×C3×C22⋊C4C2314yes—
148C2×C3×C22⋊C4C2314yes—
149C2×C3×C22⋊C4C2314yes—
150C2×C3×C22⋊C4C2314yes—
151C2×C3×C22⋊C4C2314yes—
152C2×C3×C22⋊C4C2314yes—
153C2×C3×C42—24no—
154C2×C3×C42—42no—
155C2×C3×C42C2314yes—
156C2×C3×C42C2314yes—
157C3×#95C2314yes—
158C3×#95C2314yes—
159C3×#95C2314yes—
160C3×#95C2314yes—
161C3×#95C2314yes—
162C3×#95C2314yes—
163C3×#95C2314yes—
164C3×#95C2314yes—
165C3×#95C2314yes—
166C3×#95C2314yes—
167C3×#95C2314yes—
168C3×#95C2314yes—
169C23×Q8C22×C311yescharacteristic
170C23×Q8C22×C311yescharacteristic
171C23×D4C22×C311yescharacteristic
172C24×C4C22×C311yescharacteristic
173C2×#124—28no—
174C2×#124C22×C318yes—
175C2×C22⋊Q8—28no—
176C2×C22⋊Q8C22×C318yescomplemented
177C22×C4⋊C4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C4⋊C4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C22⋊C4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C22×C22⋊C4C22×C311yescharacteristic
186C22×C22⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C22⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C42C22×C311yescharacteristic
195C22×C42C22×C311yescharacteristic
196#397C22×C318yescomplemented
197#397C22×C318yescomplemented
198#396C22×C318yescomplemented
199#395C22×C318yescomplemented
200#394C22×C318yes—
201#393C22×C318yescomplemented
202#391C22×C318yescomplemented
203#391C22×C318yescomplemented
204#388C22×C318yescomplemented
205#388C22×C318yescomplemented
206#387C22×C318yescomplemented
207#386C22×C318yes—
208#381C22×C318yescomplemented
209C2×#95C22×C311yescharacteristic
210C2×#95C22×C311yescharacteristic
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
216C2×#95C22×C311yescharacteristic
217C2×#95C22×C311yescharacteristic
218C2×#95C22×C311yescharacteristic
219C2×#95C22×C311yescharacteristic
220C2×#95C22×C311yescharacteristic
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3C2×D414yes—
235C24×C3C2412yes—
236C24×C3C2412yes—
237C24×C3C2411yescharacteristic
238C2×C3×Q8—28no—
239C2×C3×Q8—28no—
240C2×C3×Q8—28no—
241C2×C3×Q8—28no—
242C2×C3×Q8—44no—
243C2×C3×Q8—44no—
244C2×C3×Q8—416no—
245C2×C3×Q8—416no—
246C2×C3×D4—28no—
247C2×C3×D4—28no—
248C2×C3×D4—44no—
249C2×C3×D4—416no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—28no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—28no—
287C22×C3×C4—44no—
288C22×C3×C4—416no—
289C22×C3×C4C2×D414yes—
290C22×C3×C4C2×D414yes—
291C22×C3×C4#4114yes—
292C22×C3×C4#4114yes—
293C22×C3×C4C2412yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2412yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C22×C3×C4C2412yes—
305C22×C3×C4C2412yes—
306C3×C4⋊C4—28no—
307C3×C4⋊C4—28no—
308C3×C4⋊C4—28no—
309C3×C4⋊C4—28no—
310C3×C4⋊C4—44no—
311C3×C4⋊C4—44no—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—28no—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—28no—
316C3×C22⋊C4—28no—
317C3×C22⋊C4—44no—
318C3×C22⋊C4—44no—
319C3×C22⋊C4—44no—
320C3×C22⋊C4—44no—
321C3×C22⋊C4—44no—
322C3×C22⋊C4C2×D4116yes—
323C3×C42—28no—
324C3×C42—44no—
325C25C23×C311yescharacteristic
326C25C23×C311yescharacteristic
327C22×Q8—24no—
328C22×Q8—24no—
329C22×Q8—24no—
330C22×Q8—24no—
331C22×Q8—42no—
332C22×Q8—42no—
333C22×Q8C23×C314yes—
334C22×Q8C23×C314yes—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—42no—
338C22×D4C23×C314yes—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4—42no—
342C23×C4C23×C311yescharacteristic
343C23×C4C23×C311yescharacteristic
344C23×C4C23×C311yescharacteristic
345C23×C4C23×C311yescharacteristic
346C23×C4C23×C311yescharacteristic
347C23×C4C23×C311yescharacteristic
348C23×C4C23×C311yescharacteristic
349C23×C4C23×C311yescharacteristic
350C23×C4C23×C311yescharacteristic
351C23×C4C23×C314yes—
352C23×C4C23×C311yescharacteristic
353C23×C4C23×C311yescharacteristic
354C23×C4C23×C311yescharacteristic
355C23×C4C23×C311yescharacteristic
356#124—232no—
357C22⋊Q8—232no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4C23×C314yes—
365C2×C4⋊C4C23×C314yes—
366C2×C4⋊C4C23×C314yes—
367C2×C4⋊C4C23×C314yes—
368C2×C4⋊C4C23×C314yes—
369C2×C4⋊C4C23×C314yes—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4C3×D418yes—
381C2×C22⋊C4C23×C314yes—
382C2×C22⋊C4C23×C314yes—
383C2×C22⋊C4C23×C314yes—
384C2×C22⋊C4C23×C314yes—
385C2×C22⋊C4C23×C314yes—
386C2×C22⋊C4C23×C314yes—
387C2×C22⋊C4C23×C314yes—
388C2×C22⋊C4C23×C314yes—
389C2×C22⋊C4C23×C314yes—
390C2×C22⋊C4C23×C314yes—
391C2×C22⋊C4C23×C314yes—
392C2×C42—24no—
393C2×C42—42no—
394C2×C42C23×C314yes—
395C2×C42C23×C314yes—
396#95C23×C314yes—
397#95C23×C314yes—
398#95C23×C314yes—
399#95C23×C314yes—
400#95C23×C314yes—
401#95C23×C314yes—
402#95C23×C314yes—
403#95C23×C314yes—
404#95C23×C314yes—
405#95C23×C314yes—
406#95C23×C314yes—
407#95C23×C314yes—
408C23×C3—28no—
409C23×C3—28no—
410C23×C3—28no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3—44no—
435C23×C3C22×D414yes—
436C23×C3C22×D412yes—
437C23×C3C2×#4112yes—
438C23×C3C2×#4112yes—
439C23×C3H(5,𝔽2)12yes—
440C23×C3H(5,𝔽2)12yes—
441C23×C32−1+412yes—
442C23×C32−1+412yes—
443C23×C3C2511yescharacteristic
444C3×Q8—416no—
445C3×Q8—416no—
446C3×D4—416no—
447C2×C3×C4—28no—
448C2×C3×C4—28no—
449C2×C3×C4—28no—
450C2×C3×C4—28no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—416no—
487C2×C3×C4—44no—
488C2×C3×C4—44no—
489C2×C3×C4—44no—
490C2×C3×C4—44no—
491C2×C3×C4—44no—
492C2×C3×C4—44no—
493C2×C3×C4—44no—
494C2×C3×C4—44no—
495C2×C3×C4—44no—
496C2×C3×C4C22×D414yes—
497C2×C3×C4C22×D414yes—
498C2×C3×C4C2×#4114yes—
499C2×C3×C4C2×#4114yes—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24C2×C3×D414yes—
514C24C24×C312yes—
515C24C24×C312yes—
516C24C24×C311yescharacteristic
517C2×Q8—28no—
518C2×Q8—28no—
519C2×Q8—28no—
520C2×Q8—28no—
521C2×Q8—44no—
522C2×Q8—44no—
523C2×Q8—416no—
524C2×Q8—416no—
525C2×D4—28no—
526C2×D4—28no—
527C2×D4—44no—
528C2×D4—416no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—28no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—44no—
567C22×C4—416no—
568C22×C4C2×C3×D414yes—
569C22×C4C2×C3×D414yes—
570C22×C4C3×#4114yes—
571C22×C4C3×#4114yes—
572C22×C4C24×C312yes—
573C22×C4C24×C312yes—
574C22×C4C24×C312yes—
575C22×C4C24×C312yes—
576C22×C4C24×C312yes—
577C22×C4C24×C312yes—
578C22×C4C24×C312yes—
579C22×C4C24×C312yes—
580C22×C4C24×C312yes—
581C22×C4C24×C312yes—
582C22×C4C24×C312yes—
583C22×C4C24×C312yes—
584C22×C4C24×C312yes—
585C4⋊C4—28no—
586C4⋊C4—28no—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C22⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4C2×C3×D4116yes—
602C42—28no—
603C42—44no—
604C22×C3—24no—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—416no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—88no—
620C22×C3#53614yes—
621C22×C3#54214yes—
622C22×C3#54214yes—
623C22×C3#54614yes—
624C22×C3#54614yes—
625C22×C3#55614yes—
626C22×C3#56214yes—
627C22×C3C23×D411yescharacteristic
628C22×C3C22×#4111yescharacteristic
629C22×C3C22×#4111yescharacteristic
630C22×C3C2×H(5,𝔽2)11yescharacteristic
631C22×C3C2×H(5,𝔽2)11yescharacteristic
632C22×C3C2×2−1+411yescharacteristic
633C22×C3C2×2−1+411yescharacteristic
634C3×C4—24no—
635C3×C4—24no—
636C3×C4—24no—
637C3×C4—24no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—42no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23C22×C3×D414yes—
675C23C22×C3×D412yes—
676C23C2×C3×#4112yes—
677C23C2×C3×#4112yes—
678C23C3×H(5,𝔽2)12yes—
679C23C3×H(5,𝔽2)12yes—
680C23C3×2−1+412yes—
681C23C3×2−1+412yes—
682C23C25×C311yescharacteristic
683Q8—416no—
684Q8—416no—
685D4—416no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—416no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4C22×C3×D414yes—
736C2×C4C22×C3×D414yes—
737C2×C4C2×C3×#4114yes—
738C2×C4C2×C3×#4114yes—
739C2×C3—44no—
740C2×C3—82no—
741C2×C3#270018yesdirect product factor
742C2×C3C2×#53611yescharacteristic
743C2×C3C2×#54211yescharacteristic
744C2×C3C2×#54211yescharacteristic
745C2×C3C2×#54611yescharacteristic
746C2×C3C2×#54611yescharacteristic
747C2×C3C2×#55611yescharacteristic
748C2×C3C2×#56211yescharacteristic
749C22—24no—
750C22—24no—
751C22—24no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—416no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—88no—
765C22C3×#53614yes—
766C22C3×#54214yes—
767C22C3×#54214yes—
768C22C3×#54614yes—
769C22C3×#54614yes—
770C22C3×#55614yes—
771C22C3×#56214yes—
772C22C23×C3×D411yescharacteristic
773C22C22×C3×#4111yescharacteristic
774C22C22×C3×#4111yescharacteristic
775C22C2×C3×H(5,𝔽2)11yescharacteristic
776C22C2×C3×H(5,𝔽2)11yescharacteristic
777C22C2×C3×2−1+411yescharacteristic
778C22C2×C3×2−1+411yescharacteristic
779C4—24no—
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—42no—
792C3C2×#270011yescharacteristic, direct product factor, Sylow
793C2—44no—
794C2—82no—
795C2C3×#270018yesdirect product factor
796C2C2×C3×#53611yescharacteristic
797C2C2×C3×#54211yescharacteristic
798C2C2×C3×#54211yescharacteristic
799C2C2×C3×#54611yescharacteristic
800C2C2×C3×#54611yescharacteristic
801C2C2×C3×#55611yescharacteristic
802C2C2×C3×#56211yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊Q8C2semidirect
3. C3×#2700C2direct (N × H)
4. C2×C3×#397C2semidirect
5. C2×C3×#397C2semidirect
6. C2×C3×#396C2semidirect
7. C2×C3×#395C2semidirect
9. C2×C3×#393C2semidirect
10. C2×C3×#391C2semidirect
11. C2×C3×#391C2semidirect
12. C2×C3×#388C2semidirect
13. C2×C3×#388C2semidirect
14. C2×C3×#387C2semidirect
16. C2×C3×#381C2semidirect
17. C2×#2700C3direct (N × H)
25. C2×C3×C22⋊Q8C22semidirect
45. C3×#397C22semidirect
46. C3×#397C22semidirect
47. C3×#396C22semidirect
48. C3×#395C22semidirect
50. C3×#393C22semidirect
51. C3×#391C22semidirect
52. C3×#391C22semidirect
53. C3×#388C22semidirect
54. C3×#388C22semidirect
55. C3×#387C22semidirect
57. C3×#381C22semidirect
71. C22×C22⋊Q8C2×C3semidirect
72. #2700C2×C3direct (N × H)
73. C2×#397C2×C3semidirect
74. C2×#397C2×C3semidirect
75. C2×#396C2×C3semidirect
76. C2×#395C2×C3semidirect
78. C2×#393C2×C3semidirect
79. C2×#391C2×C3semidirect
80. C2×#391C2×C3semidirect
81. C2×#388C2×C3semidirect
82. C2×#388C2×C3semidirect
83. C2×#387C2×C3semidirect
85. C2×#381C2×C3semidirect
176. C2×C22⋊Q8C22×C3semidirect
196. #397C22×C3semidirect
197. #397C22×C3semidirect
198. #396C22×C3semidirect
199. #395C22×C3semidirect
201. #393C22×C3semidirect
202. #391C22×C3semidirect
203. #391C22×C3semidirect
204. #388C22×C3semidirect
205. #388C22×C3semidirect
206. #387C22×C3semidirect
208. #381C22×C3semidirect
741. C2×C3#2700direct (N × H)
792. C3C2×#2700direct (N × H)
795. C2C3×#2700direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1242
C22×C3×C22⋊Q82
C3×#27002
C2×C3×#3972
C2×C3×#3962
C2×C3×#3952
C2×C3×#3942
C2×C3×#3932
C2×C3×#3912
C2×C3×#3882
C2×C3×#3872
C2×C3×#3862
C2×C3×#3812
C2×#27003