Finite Group Databasebeta

← C3×#62987 #10681594

Subgroups — C3×#62987 #10681594

Order 768.

11596 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#585C211yesmaximal, characteristic, complemented
2C22×C3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3C3×#3500C216yesmaximal, complemented
4C3×#3496C219yesmaximal, complemented
5C3×#3489C216yesmaximal, complemented
6C3×#3488C216yesmaximal, complemented
7C3×#3485C219yesmaximal, complemented
8C3×#3484C219yesmaximal, complemented
9C3×D4×#41C216yesmaximal, complemented
10C2×C3×#546C219yesmaximal, complemented
11C3×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
12#62987C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#585—216no—
14C2×C3×2−1+4C2216yescomplemented
15C2×C3×H(5,𝔽2)—216no—
16C2×C3×H(5,𝔽2)C2211yescharacteristic
17C2×C3×H(5,𝔽2)C2219yescomplemented
18C2×C3×H(5,𝔽2)C2216yescomplemented
19C2×C3×H(5,𝔽2)C2219yescomplemented
20C22×C3×#41C2216yescomplemented
21C22×C3×#41C2219yescomplemented
22C22×C3×#41C2216yescomplemented
23C23×C3×D4C2219yescomplemented
24C3×#550C2216yescomplemented
25C3×D4×Q8C2216yescomplemented
26C3×#548C2212yescomplemented
27C3×#548C2216yescomplemented
28C3×#548C22112yescomplemented
29C3×#547C22118yescomplemented
30C3×#547C22136yescomplemented
31C3×#546C22118yescomplemented
32C3×#546C22136yescomplemented
33C3×#546C22136yescomplemented
34C3×#546C22136yescomplemented
35C3×#546C22136yescomplemented
36C3×#546C22118yescomplemented
37C3×D42C22118yescomplemented
38C3×D42C22136yescomplemented
39C3×#537C22118yescomplemented
40C3×#536C22118yescomplemented
41C3×#535C22118yescomplemented
42C3×#534C22136yescomplemented
43C3×#532C22118yescomplemented
44C2×C3×#124C2219yescomplemented
45C3×#525C22118yescomplemented
46C3×#525C22118yescomplemented
47C2×C3×#123C22118yescomplemented
48C2×C3×C22⋊Q8C2219yescomplemented
49C2×C3×#121C2219yescomplemented
50C2×C3×#121C22118yescomplemented
51C2×C3×#120C22118yescomplemented
52C3×#520C2216yescomplemented
53C3×#518C2219yescomplemented
54C3×C4×#41C2216yescomplemented
55C2×C3×C4×D4C2219yescomplemented
56C2×C3×C4×D4C2219yescomplemented
57C22×C3×C22⋊C4C2216yescomplemented
58C2×#585C2×C311yescharacteristic, complemented
59C22×H(5,𝔽2)C2×C311yescharacteristic, complemented
60#3500C2×C316yescomplemented
61#3496C2×C319yescomplemented
62#3489C2×C316yescomplemented
63#3488C2×C316yescomplemented
64#3485C2×C319yescomplemented
65#3484C2×C319yescomplemented
66D4×#41C2×C316yescomplemented
67C2×#546C2×C319yescomplemented
68C4×H(5,𝔽2)C2×C311yescharacteristic, complemented
69C25×C3C2316yes—
70C3×2−1+4—248no—
71C3×H(5,𝔽2)—248no—
72C3×H(5,𝔽2)—272no—
73C3×H(5,𝔽2)—272no—
74C3×H(5,𝔽2)D4116yescomplemented
75C2×C3×#41—248no—
76C2×C3×#41—248no—
77C2×C3×#41—272no—
78C2×C3×#41C23118yes—
79C2×C3×#41C23118yes—
80C2×C3×#41C2316yes—
81C2×C3×#41C2316yes—
82C2×C3×#41C23118yescomplemented
83C2×C3×#41C2312yescomplemented
84C2×C3×#41C23118yescomplemented
85C2×C3×#41C23136yescomplemented
86C22×C3×Q8C2312yes—
87C22×C3×Q8C2319yescomplemented
88C22×C3×Q8C2316yescomplemented
89C22×C3×D4—272no—
90C22×C3×D4C23118yes—
91C22×C3×D4C23118yes—
92C22×C3×D4C2319yes—
93C22×C3×D4C23136yes—
94C22×C3×D4C2319yes—
95C22×C3×D4C2319yes—
96C22×C3×D4C23118yescomplemented
97C22×C3×D4C23118yescomplemented
98C22×C3×D4C23118yescomplemented
99C23×C3×C4C2319yes—
100C23×C3×C4C2316yescomplemented
101C23×C3×C4C2319yescomplemented
102C23×C3×C4C2316yescomplemented
103C3×C4⋊Q8C23118yescomplemented
104C3×#127C23118yescomplemented
105C3×#124C23118yescomplemented
106C3×#124C23136yescomplemented
107C3×#124C2316yescomplemented
108C3×#123C23136yescomplemented
109C3×#123C23172yescomplemented
110C3×#123C23136yescomplemented
111C3×C22⋊Q8C23118yes—
112C3×C22⋊Q8C23136yescomplemented
113C3×C22⋊Q8C2316yescomplemented
114C3×C22⋊Q8C23118yescomplemented
115C3×C22⋊Q8C23118yescomplemented
116C3×#121C2316yes—
117C3×#121C23118yescomplemented
118C3×#121C23136yescomplemented
119C3×#121C23172yescomplemented
120C3×#121C23136yescomplemented
121C3×#121C23118yescomplemented
122C3×#121C23118yescomplemented
123C3×#121C23136yescomplemented
124C3×#120C23136yes—
125C3×#120C23172yescomplemented
126C3×#120C23136yescomplemented
127C3×C4×Q8C2312yescomplemented
128C3×C4×Q8C2316yescomplemented
129C3×C4×D4C2316yes—
130C3×C4×D4C23118yes—
131C3×C4×D4C23118yescomplemented
132C3×C4×D4C23136yescomplemented
133C3×C4×D4C23118yescomplemented
134C3×C4×D4C23118yescomplemented
135C3×C4×D4C23118yescomplemented
136C3×C4×D4C23136yescomplemented
137C3×#117C23118yescomplemented
138C2×C3×C4⋊C4C2319yescomplemented
139C2×C3×C4⋊C4C2319yescomplemented
140C2×C3×C4⋊C4C23118yescomplemented
141C2×C3×C22⋊C4C2319yes—
142C2×C3×C22⋊C4C23118yes—
143C2×C3×C22⋊C4C23118yescomplemented
144C2×C3×C22⋊C4C23118yescomplemented
145C2×C3×C22⋊C4C23118yescomplemented
146C2×C3×C22⋊C4C2319yescomplemented
147C2×C3×C22⋊C4C23118yescomplemented
148C2×C3×C42C2319yescomplemented
149#585—216no—
150C2×2−1+4C22×C316yescomplemented
151C2×H(5,𝔽2)—216no—
152C2×H(5,𝔽2)C22×C311yescharacteristic
153C2×H(5,𝔽2)C22×C319yescomplemented
154C2×H(5,𝔽2)C22×C316yescomplemented
155C2×H(5,𝔽2)C22×C319yescomplemented
156C22×#41C22×C316yescomplemented
157C22×#41C22×C319yescomplemented
158C22×#41C22×C316yescomplemented
159C23×D4C22×C319yescomplemented
160#550C22×C316yescomplemented
161D4×Q8C22×C316yescomplemented
162#548C22×C312yescomplemented
163#548C22×C316yescomplemented
164#548C22×C3112yescomplemented
165#547C22×C3118yescomplemented
166#547C22×C3136yescomplemented
167#546C22×C3118yescomplemented
168#546C22×C3136yescomplemented
169#546C22×C3136yescomplemented
170#546C22×C3136yescomplemented
171#546C22×C3136yescomplemented
172#546C22×C3118yescomplemented
173D42C22×C3118yescomplemented
174D42C22×C3136yescomplemented
175#537C22×C3118yescomplemented
176#536C22×C3118yescomplemented
177#535C22×C3118yescomplemented
178#534C22×C3136yescomplemented
179#532C22×C3118yescomplemented
180C2×#124C22×C319yescomplemented
181#525C22×C3118yescomplemented
182#525C22×C3118yescomplemented
183C2×#123C22×C3118yescomplemented
184C2×C22⋊Q8C22×C319yescomplemented
185C2×#121C22×C319yescomplemented
186C2×#121C22×C3118yescomplemented
187C2×#120C22×C3118yescomplemented
188#520C22×C316yescomplemented
189#518C22×C319yescomplemented
190C4×#41C22×C316yescomplemented
191C2×C4×D4C22×C319yescomplemented
192C2×C4×D4C22×C319yescomplemented
193C22×C22⋊C4C22×C316yescomplemented
194C24×C3—224no—
195C24×C3—412no—
196C24×C3—86no—
197C24×C3C2419yes—
198C24×C3C24118yes—
199C24×C3C2419yes—
200C24×C3C2416yes—
201C3×#41—28no—
202C3×#41—224no—
203C3×#41—272no—
204C3×#41—272no—
205C3×#41—2144no—
206C3×#41—272no—
207C3×#41—272no—
208C3×#41C2×D4148yescomplemented
209C2×C3×Q8—28no—
210C2×C3×Q8—224no—
211C2×C3×Q8—236no—
212C2×C3×Q8C24118yes—
213C2×C3×Q8C2416yes—
214C2×C3×Q8C2412yes—
215C2×C3×D4—272no—
216C2×C3×D4—272no—
217C2×C3×D4—272no—
218C2×C3×D4—2144no—
219C2×C3×D4—272no—
220C2×C3×D4—236no—
221C2×C3×D4—418no—
222C2×C3×D4—818no—
223C2×C3×D4C2×D4172yescomplemented
224C2×C3×D4C2416yes—
225C2×C3×D4C24136yes—
226C2×C3×D4C24136yes—
227C2×C3×D4C2416yes—
228C2×C3×D4C24118yes—
229C2×C3×D4C24118yes—
230C2×C3×D4C24136yes—
231C2×C3×D4C24118yes—
232C22×C3×C4—224no—
233C22×C3×C4—236no—
234C22×C3×C4—236no—
235C22×C3×C4—86no—
236C22×C3×C4C2419yes—
237C22×C3×C4C24118yes—
238C22×C3×C4C2419yes—
239C22×C3×C4C2416yes—
240C22×C3×C4C2416yes—
241C22×C3×C4C24118yes—
242C22×C3×C4C24118yes—
243C22×C3×C4C2419yes—
244C22×C3×C4C2419yes—
245C22×C3×C4C24118yes—
246C22×C3×C4C2419yes—
247C3×C4⋊C4C2416yes—
248C3×C4⋊C4C24118yes—
249C3×C4⋊C4C24136yes—
250C3×C4⋊C4C24118yes—
251C3×C4⋊C4C2416yes—
252C3×C22⋊C4C2411yescharacteristic
253C3×C22⋊C4C2419yes—
254C3×C22⋊C4C2419yes—
255C3×C22⋊C4C2419yes—
256C3×C22⋊C4C24136yes—
257C3×C22⋊C4C2416yes—
258C3×C22⋊C4C24136yes—
259C3×C22⋊C4C24136yes—
260C3×C22⋊C4C24118yes—
261C3×C22⋊C4C24112yes—
262C3×C42C2416yes—
263C3×C42C24118yes—
264C25C23×C316yes—
2652−1+4—248no—
266H(5,𝔽2)—248no—
267H(5,𝔽2)—272no—
268H(5,𝔽2)—272no—
269H(5,𝔽2)C3×D4116yescomplemented
270C2×#41—248no—
271C2×#41—248no—
272C2×#41—272no—
273C2×#41C23×C3118yes—
274C2×#41C23×C3118yes—
275C2×#41C23×C316yes—
276C2×#41C23×C316yes—
277C2×#41C23×C3118yescomplemented
278C2×#41C23×C3118yescomplemented
279C2×#41C23×C3136yescomplemented
280C2×#41C23×C312yescomplemented
281C22×Q8C23×C312yes—
282C22×Q8C23×C319yescomplemented
283C22×Q8C23×C316yescomplemented
284C22×D4—272no—
285C22×D4C23×C3118yes—
286C22×D4C23×C319yes—
287C22×D4C23×C3118yes—
288C22×D4C23×C3136yes—
289C22×D4C23×C319yes—
290C22×D4C23×C319yes—
291C22×D4C23×C3118yescomplemented
292C22×D4C23×C3118yescomplemented
293C22×D4C23×C3118yescomplemented
294C23×C4C23×C319yes—
295C23×C4C23×C316yescomplemented
296C23×C4C23×C319yescomplemented
297C23×C4C23×C316yescomplemented
298C4⋊Q8C23×C3118yescomplemented
299#127C23×C3118yescomplemented
300#124C23×C3118yescomplemented
301#124C23×C3136yescomplemented
302#124C23×C316yescomplemented
303#123C23×C3136yescomplemented
304#123C23×C3172yescomplemented
305#123C23×C3136yescomplemented
306C22⋊Q8C23×C3118yes—
307C22⋊Q8C23×C3136yescomplemented
308C22⋊Q8C23×C316yescomplemented
309C22⋊Q8C23×C3118yescomplemented
310C22⋊Q8C23×C3118yescomplemented
311#121C23×C316yes—
312#121C23×C3118yescomplemented
313#121C23×C3136yescomplemented
314#121C23×C3172yescomplemented
315#121C23×C3136yescomplemented
316#121C23×C3118yescomplemented
317#121C23×C3118yescomplemented
318#121C23×C3136yescomplemented
319#120C23×C3136yes—
320#120C23×C3172yescomplemented
321#120C23×C3136yescomplemented
322C4×Q8C23×C312yescomplemented
323C4×Q8C23×C316yescomplemented
324C4×D4C23×C316yes—
325C4×D4C23×C3118yes—
326C4×D4C23×C3118yescomplemented
327C4×D4C23×C3136yescomplemented
328C4×D4C23×C3118yescomplemented
329C4×D4C23×C3118yescomplemented
330C4×D4C23×C3118yescomplemented
331C4×D4C23×C3136yescomplemented
332#117C23×C3118yescomplemented
333C2×C4⋊C4C23×C319yescomplemented
334C2×C4⋊C4C23×C319yescomplemented
335C2×C4⋊C4C23×C3118yescomplemented
336C2×C22⋊C4C23×C319yes—
337C2×C22⋊C4C23×C3118yes—
338C2×C22⋊C4C23×C3118yescomplemented
339C2×C22⋊C4C23×C3118yescomplemented
340C2×C22⋊C4C23×C3118yescomplemented
341C2×C22⋊C4C23×C319yescomplemented
342C2×C22⋊C4C23×C3118yescomplemented
343C2×C42C23×C319yescomplemented
344C23×C3—218no—
345C23×C3—218no—
346C23×C3—218no—
347C23×C3—236no—
348C23×C3—46no—
349C23×C3—46no—
350C23×C3—49no—
351C23×C3—49no—
352C23×C3—49no—
353C23×C3—418no—
354C23×C3—418no—
355C23×C3—848no—
356C23×C3C22×D4124yes—
357C23×C3C2519yes—
358C23×C3C2516yes—
359C23×C3C2519yes—
360C23×C3C2511yescharacteristic
361C3×Q8—236no—
362C3×Q8—212no—
363C3×Q8C22×D418yes—
364C3×D4—272no—
365C3×D4—272no—
366C3×D4—212no—
367C3×D4—236no—
368C3×D4—212no—
369C3×D4—418no—
370C3×D4—436no—
371C3×D4C22×D4172yes—
372C2×C3×C4—218no—
373C2×C3×C4—218no—
374C2×C3×C4—236no—
375C2×C3×C4—212no—
376C2×C3×C4—212no—
377C2×C3×C4—236no—
378C2×C3×C4—236no—
379C2×C3×C4—49no—
380C2×C3×C4—418no—
381C2×C3×C4—49no—
382C2×C3×C4C22×D4136yes—
383C2×C3×C4C2511yescharacteristic
384C2×C3×C4C2516yes—
385C2×C3×C4C2519yes—
386C2×C3×C4C2511yescharacteristic
387C2×C3×C4C2519yes—
388C2×C3×C4C2516yes—
389C2×C3×C4C2516yes—
390C24—224no—
391C24—412no—
392C24—86no—
393C24C24×C319yes—
394C24C24×C3118yes—
395C24C24×C319yes—
396C24C24×C316yes—
397#41—28no—
398#41—224no—
399#41—272no—
400#41—272no—
401#41—2144no—
402#41—272no—
403#41—272no—
404#41C2×C3×D4148yescomplemented
405C2×Q8—28no—
406C2×Q8—224no—
407C2×Q8—236no—
408C2×Q8C24×C3118yes—
409C2×Q8C24×C316yes—
410C2×Q8C24×C312yes—
411C2×D4—272no—
412C2×D4—272no—
413C2×D4—272no—
414C2×D4—2144no—
415C2×D4—272no—
416C2×D4—236no—
417C2×D4—418no—
418C2×D4—818no—
419C2×D4C2×C3×D4172yescomplemented
420C2×D4C24×C316yes—
421C2×D4C24×C3136yes—
422C2×D4C24×C3136yes—
423C2×D4C24×C316yes—
424C2×D4C24×C3118yes—
425C2×D4C24×C3118yes—
426C2×D4C24×C3136yes—
427C2×D4C24×C3118yes—
428C22×C4—224no—
429C22×C4—236no—
430C22×C4—236no—
431C22×C4—86no—
432C22×C4C24×C319yes—
433C22×C4C24×C3118yes—
434C22×C4C24×C319yes—
435C22×C4C24×C316yes—
436C22×C4C24×C316yes—
437C22×C4C24×C3118yes—
438C22×C4C24×C3118yes—
439C22×C4C24×C319yes—
440C22×C4C24×C319yes—
441C22×C4C24×C3118yes—
442C22×C4C24×C319yes—
443C4⋊C4C24×C316yes—
444C4⋊C4C24×C3118yes—
445C4⋊C4C24×C3136yes—
446C4⋊C4C24×C3118yes—
447C4⋊C4C24×C316yes—
448C22⋊C4C24×C311yescharacteristic
449C22⋊C4C24×C319yes—
450C22⋊C4C24×C319yes—
451C22⋊C4C24×C319yes—
452C22⋊C4C24×C3136yes—
453C22⋊C4C24×C316yes—
454C22⋊C4C24×C3136yes—
455C22⋊C4C24×C3136yes—
456C22⋊C4C24×C3118yes—
457C22⋊C4C24×C3112yes—
458C42C24×C316yes—
459C42C24×C3118yes—
460C22×C3—21no—
461C22×C3—29no—
462C22×C3—29no—
463C22×C3—21no—
464C22×C3—26no—
465C22×C3—29no—
466C22×C3—26no—
467C22×C3—29no—
468C22×C3—26no—
469C22×C3—29no—
470C22×C3—424no—
471C22×C3—436no—
472C22×C3—818no—
473C22×C3—836no—
474C22×C3C23×D4118yes—
475C22×C3#58512yescomplemented
476C22×C3C2611yescharacteristic
477C3×C4—21no—
478C3×C4—26no—
479C3×C4—29no—
480C3×C4—26no—
481C3×C4—21no—
482C3×C4—29no—
483C3×C4C23×D4112yes—
484C23—218no—
485C23—218no—
486C23—218no—
487C23—236no—
488C23—46no—
489C23—46no—
490C23—49no—
491C23—49no—
492C23—49no—
493C23—418no—
494C23—418no—
495C23—848no—
496C23C22×C3×D4124yes—
497C23C25×C319yes—
498C23C25×C316yes—
499C23C25×C319yes—
500C23C25×C311yescharacteristic
501Q8—236no—
502Q8—212no—
503Q8C22×C3×D418yes—
504D4—272no—
505D4—272no—
506D4—212no—
507D4—236no—
508D4—212no—
509D4—418no—
510D4—436no—
511D4C22×C3×D4172yes—
512C2×C4—218no—
513C2×C4—218no—
514C2×C4—236no—
515C2×C4—212no—
516C2×C4—212no—
517C2×C4—236no—
518C2×C4—236no—
519C2×C4—49no—
520C2×C4—418no—
521C2×C4—49no—
522C2×C4C22×C3×D4136yes—
523C2×C4C25×C311yescharacteristic
524C2×C4C25×C316yes—
525C2×C4C25×C319yes—
526C2×C4C25×C311yescharacteristic
527C2×C4C25×C319yes—
528C2×C4C25×C316yes—
529C2×C4C25×C316yes—
530C2×C3—22no—
531C2×C3—218no—
532C2×C3—49no—
533C2×C3—46no—
534C2×C3C24×D411yescharacteristic
535C2×C3C2×#58511yescharacteristic
536C2×C3H(7,𝔽2)11yescharacteristic
537C22—21no—
538C22—29no—
539C22—29no—
540C22—21no—
541C22—26no—
542C22—29no—
543C22—26no—
544C22—29no—
545C22—26no—
546C22—29no—
547C22—424no—
548C22—436no—
549C22—836no—
550C22—818no—
551C22C23×C3×D4118yes—
552C22C3×#58512yescomplemented
553C22C26×C311yescharacteristic
554C4—21no—
555C4—26no—
556C4—29no—
557C4—26no—
558C4—21no—
559C4—29no—
560C4C23×C3×D4112yes—
561C3#6298711yescharacteristic, direct product factor, Sylow
562C2—22no—
563C2—218no—
564C2—49no—
565C2—46no—
566C2C24×C3×D411yescharacteristic
567C2C2×C3×#58511yescharacteristic
568C2C3×H(7,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#585C2semidirect
2. C22×C3×H(5,𝔽2)C2semidirect
3. C3×#3500C2semidirect
4. C3×#3496C2semidirect
5. C3×#3489C2semidirect
6. C3×#3488C2semidirect
7. C3×#3485C2semidirect
8. C3×#3484C2semidirect
9. C3×D4×#41C2semidirect
10. C2×C3×#546C2semidirect
11. C3×C4×H(5,𝔽2)C2semidirect
12. #62987C3direct (N × H)
14. C2×C3×2−1+4C22semidirect
17. C2×C3×H(5,𝔽2)C22semidirect
18. C2×C3×H(5,𝔽2)C22semidirect
19. C2×C3×H(5,𝔽2)C22semidirect
20. C22×C3×#41C22semidirect
21. C22×C3×#41C22semidirect
22. C22×C3×#41C22semidirect
23. C23×C3×D4C22semidirect
24. C3×#550C22semidirect
25. C3×D4×Q8C22semidirect
26. C3×#548C22semidirect
27. C3×#548C22semidirect
28. C3×#548C22semidirect
29. C3×#547C22semidirect
30. C3×#547C22semidirect
31. C3×#546C22semidirect
32. C3×#546C22semidirect
33. C3×#546C22semidirect
34. C3×#546C22semidirect
35. C3×#546C22semidirect
36. C3×#546C22semidirect
37. C3×D42C22semidirect
38. C3×D42C22semidirect
39. C3×#537C22semidirect
40. C3×#536C22semidirect
41. C3×#535C22semidirect
42. C3×#534C22semidirect
43. C3×#532C22semidirect
44. C2×C3×#124C22semidirect
45. C3×#525C22semidirect
46. C3×#525C22semidirect
47. C2×C3×#123C22semidirect
48. C2×C3×C22⋊Q8C22semidirect
49. C2×C3×#121C22semidirect
50. C2×C3×#121C22semidirect
51. C2×C3×#120C22semidirect
52. C3×#520C22semidirect
53. C3×#518C22semidirect
54. C3×C4×#41C22semidirect
55. C2×C3×C4×D4C22semidirect
56. C2×C3×C4×D4C22semidirect
57. C22×C3×C22⋊C4C22semidirect
58. C2×#585C2×C3semidirect
59. C22×H(5,𝔽2)C2×C3semidirect
60. #3500C2×C3semidirect
61. #3496C2×C3semidirect
62. #3489C2×C3semidirect
63. #3488C2×C3semidirect
64. #3485C2×C3semidirect
65. #3484C2×C3semidirect
66. D4×#41C2×C3semidirect
67. C2×#546C2×C3semidirect
68. C4×H(5,𝔽2)C2×C3semidirect
74. C3×H(5,𝔽2)D4semidirect
82. C2×C3×#41C23semidirect
83. C2×C3×#41C23semidirect
84. C2×C3×#41C23semidirect
85. C2×C3×#41C23semidirect
87. C22×C3×Q8C23semidirect
88. C22×C3×Q8C23semidirect
96. C22×C3×D4C23semidirect
97. C22×C3×D4C23semidirect
98. C22×C3×D4C23semidirect
100. C23×C3×C4C23semidirect
101. C23×C3×C4C23semidirect
102. C23×C3×C4C23semidirect
103. C3×C4⋊Q8C23semidirect
104. C3×#127C23semidirect
105. C3×#124C23semidirect
106. C3×#124C23semidirect
107. C3×#124C23semidirect
108. C3×#123C23semidirect
109. C3×#123C23semidirect
110. C3×#123C23semidirect
112. C3×C22⋊Q8C23semidirect
113. C3×C22⋊Q8C23semidirect
114. C3×C22⋊Q8C23semidirect
115. C3×C22⋊Q8C23semidirect
117. C3×#121C23semidirect
118. C3×#121C23semidirect
119. C3×#121C23semidirect
120. C3×#121C23semidirect
121. C3×#121C23semidirect
122. C3×#121C23semidirect
123. C3×#121C23semidirect
125. C3×#120C23semidirect
126. C3×#120C23semidirect
127. C3×C4×Q8C23semidirect
128. C3×C4×Q8C23semidirect
131. C3×C4×D4C23semidirect
132. C3×C4×D4C23semidirect
133. C3×C4×D4C23semidirect
134. C3×C4×D4C23semidirect
135. C3×C4×D4C23semidirect
136. C3×C4×D4C23semidirect
137. C3×#117C23semidirect
138. C2×C3×C4⋊C4C23semidirect
139. C2×C3×C4⋊C4C23semidirect
140. C2×C3×C4⋊C4C23semidirect
143. C2×C3×C22⋊C4C23semidirect
144. C2×C3×C22⋊C4C23semidirect
145. C2×C3×C22⋊C4C23semidirect
146. C2×C3×C22⋊C4C23semidirect
147. C2×C3×C22⋊C4C23semidirect
148. C2×C3×C42C23semidirect
150. C2×2−1+4C22×C3semidirect
153. C2×H(5,𝔽2)C22×C3semidirect
154. C2×H(5,𝔽2)C22×C3semidirect
155. C2×H(5,𝔽2)C22×C3semidirect
156. C22×#41C22×C3semidirect
157. C22×#41C22×C3semidirect
158. C22×#41C22×C3semidirect
159. C23×D4C22×C3semidirect
160. #550C22×C3semidirect
161. D4×Q8C22×C3semidirect
162. #548C22×C3semidirect
163. #548C22×C3semidirect
164. #548C22×C3semidirect
165. #547C22×C3semidirect
166. #547C22×C3semidirect
167. #546C22×C3semidirect
168. #546C22×C3semidirect
169. #546C22×C3semidirect
170. #546C22×C3semidirect
171. #546C22×C3semidirect
172. #546C22×C3semidirect
173. D42C22×C3semidirect
174. D42C22×C3semidirect
175. #537C22×C3semidirect
176. #536C22×C3semidirect
177. #535C22×C3semidirect
178. #534C22×C3semidirect
179. #532C22×C3semidirect
180. C2×#124C22×C3semidirect
181. #525C22×C3semidirect
182. #525C22×C3semidirect
183. C2×#123C22×C3semidirect
184. C2×C22⋊Q8C22×C3semidirect
185. C2×#121C22×C3semidirect
186. C2×#121C22×C3semidirect
187. C2×#120C22×C3semidirect
188. #520C22×C3semidirect
189. #518C22×C3semidirect
190. C4×#41C22×C3semidirect
191. C2×C4×D4C22×C3semidirect
192. C2×C4×D4C22×C3semidirect
193. C22×C22⋊C4C22×C3semidirect
208. C3×#41C2×D4semidirect
223. C2×C3×D4C2×D4semidirect
269. H(5,𝔽2)C3×D4semidirect
277. C2×#41C23×C3semidirect
278. C2×#41C23×C3semidirect
279. C2×#41C23×C3semidirect
280. C2×#41C23×C3semidirect
282. C22×Q8C23×C3semidirect
283. C22×Q8C23×C3semidirect
291. C22×D4C23×C3semidirect
292. C22×D4C23×C3semidirect
293. C22×D4C23×C3semidirect
295. C23×C4C23×C3semidirect
296. C23×C4C23×C3semidirect
297. C23×C4C23×C3semidirect
298. C4⋊Q8C23×C3semidirect
299. #127C23×C3semidirect
300. #124C23×C3semidirect
301. #124C23×C3semidirect
302. #124C23×C3semidirect
303. #123C23×C3semidirect
304. #123C23×C3semidirect
305. #123C23×C3semidirect
307. C22⋊Q8C23×C3semidirect
308. C22⋊Q8C23×C3semidirect
309. C22⋊Q8C23×C3semidirect
310. C22⋊Q8C23×C3semidirect
312. #121C23×C3semidirect
313. #121C23×C3semidirect
314. #121C23×C3semidirect
315. #121C23×C3semidirect
316. #121C23×C3semidirect
317. #121C23×C3semidirect
318. #121C23×C3semidirect
320. #120C23×C3semidirect
321. #120C23×C3semidirect
322. C4×Q8C23×C3semidirect
323. C4×Q8C23×C3semidirect
326. C4×D4C23×C3semidirect
327. C4×D4C23×C3semidirect
328. C4×D4C23×C3semidirect
329. C4×D4C23×C3semidirect
330. C4×D4C23×C3semidirect
331. C4×D4C23×C3semidirect
332. #117C23×C3semidirect
333. C2×C4⋊C4C23×C3semidirect
334. C2×C4⋊C4C23×C3semidirect
335. C2×C4⋊C4C23×C3semidirect
338. C2×C22⋊C4C23×C3semidirect
339. C2×C22⋊C4C23×C3semidirect
340. C2×C22⋊C4C23×C3semidirect
341. C2×C22⋊C4C23×C3semidirect
342. C2×C22⋊C4C23×C3semidirect
343. C2×C42C23×C3semidirect
404. #41C2×C3×D4semidirect
419. C2×D4C2×C3×D4semidirect
475. C22×C3#585semidirect
552. C22C3×#585semidirect
561. C3#62987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5852
C22×C3×H(5,𝔽2)2
C3×#35002
C3×#34962
C3×#34892
C3×#34882
C3×#34852
C3×#34842
C3×D4×#412
C2×C3×#5462
C3×C4×H(5,𝔽2)2
#629873