Finite Group Databasebeta

← #11808949

Subgroups — #11808949

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592356C211yesmaximal, characteristic
2C3×#4660C211yesmaximal, characteristic
3C3×#4648C211yesmaximal, characteristic
4#10591356C211yesmaximal, characteristic
5#10591345C211yesmaximal, characteristic
6Dic3×C4⋊Dic3C211yesmaximal, characteristic
7#10591243C211yesmaximal, characteristic
8#10591243C211yesmaximal, characteristic
9#10591243C211yesmaximal, characteristic
10#10591242C211yesmaximal, characteristic
11Dic3×Dic3⋊C4C211yesmaximal, characteristic
12#10591218C211yesmaximal, characteristic
13#10591211C211yesmaximal, characteristic
14#10591210C211yesmaximal, characteristic
15#10591198C211yesmaximal, characteristic
16#78133—31nomaximal
17#73398—31nomaximal
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic32C2211yescharacteristic
34C2×Dic32C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C32×#95C2211yescharacteristic
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×#400—31no—
54C3×#376—31no—
55#4983—31no—
56#4982—31no—
57Dic3×C4⋊C4—31no—
58Dic3×C4⋊C4—31no—
59C4×C4⋊Dic3—31no—
60C4×C4⋊Dic3—31no—
61C4×Dic3⋊C4—31no—
62C4×Dic3⋊C4—31no—
63C4×Dic3⋊C4—31no—
64C4×Dic3⋊C4—31no—
65#4660—31no—
66#4660—31no—
67#4660—31no—
68#4660—31no—
69#4660D311yescharacteristic
70#4658—31no—
71#4658—31no—
72#4657—31no—
73#4657—31no—
74#4657—31no—
75#4657—31no—
76#4657—31no—
77#4657—31no—
78#4657—61no—
79#4649—31no—
80#4649—31no—
81#4649—31no—
82#4649—31no—
83#4648D311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C4⋊(C3⋊Dic3)—22no—
100#3750—22no—
101#3750—22no—
102#3750—22no—
103C3×C4⋊Dic3—22no—
104C3×Dic3⋊C4—22no—
105C3×C4×Dic3—22no—
106C3×C4×Dic3—22no—
107C3×C4×Dic3Q814yes—
108#3724—22no—
109#3724—22no—
110#3724—22no—
111Dic3⋊Dic3—22no—
112Dic3⋊Dic3—22no—
113Dic3⋊Dic3—22no—
114Dic32—22no—
115Dic32—22no—
116Dic32—22no—
117Dic32—22no—
118#2402—91noSylow
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C42—31no—
122C2×C3×C42—31no—
123C2×C3×C42—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—61no—
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—31no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—61no—
147C2×Dic3⋊C4—61no—
148C2×Dic3⋊C4—61no—
149C2×Dic3⋊C4C2×D311yescharacteristic
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3C2×D311yescharacteristic
159C2×C4×Dic3C2×D311yescharacteristic
160C2×C4×Dic3C2×D311yescharacteristic
161C3×#95—21no—
162C3×#95—31no—
163C3×#95—31no—
164C3×#95—31no—
165C3×#95—31no—
166C3×#95—31no—
167C3×#95—31no—
168C3×#95—31no—
169C3×#95C2×D311yescharacteristic
170C3×#95C2×D311yescharacteristic
171C3⋊#95—31no—
172C3⋊#95—31no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—61no—
188C3⋊#95—61no—
189C3⋊#95C2×D311yescharacteristic
190C3⋊#95C2×D311yescharacteristic
191C3⋊#95C2×D311yescharacteristic
192C3⋊#95C2×D311yescharacteristic
193C3⋊#95C2×D311yescharacteristic
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C23×C32C2411yescharacteristic
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4C2×Q812yes—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3#4112yes—
216C2×C3⋊Dic3#4112yes—
217C2×C3⋊Dic3#4112yes—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3C2×Q812yes—
238C2×C3×Dic3C2×Q812yes—
239C2×C3×Dic3#4112yes—
240C2×C3×Dic3#4112yes—
241C2×C3×Dic3#4112yes—
242#400—31no—
243#400—91no—
244#400—91no—
245#400—91no—
246#398—91no—
247#398—91no—
248#398—91no—
249#398—91no—
250C4×C4⋊C4—91no—
251C4×C4⋊C4—91no—
252C4×C4⋊C4—91no—
253C4×C4⋊C4—91no—
254C4×C4⋊C4—91no—
255C4×C4⋊C4—91no—
256#376—31no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—31no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C22×D311yescharacteristic
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D311yescharacteristic
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—61no—
283C22×Dic3—61no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286C22×Dic3C22×D311yescharacteristic
287C22×Dic3C22×D311yescharacteristic
288C22×Dic3C22×D311yescharacteristic
289C22×Dic3C22×D311yescharacteristic
290C22×Dic3C22×D311yescharacteristic
291C22×Dic3C22×D311yescharacteristic
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D311yescharacteristic
294C3×C4⋊C4—62no—
295C3×C4⋊C4—62no—
296C3×C42—34no—
297C3×C42—62no—
298C3×C42—62no—
299C4⋊Dic3—22no—
300C4⋊Dic3—62no—
301C4⋊Dic3—62no—
302C4⋊Dic3—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3—62no—
305C4⋊Dic3—122no—
306Dic3⋊C4—22no—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309Dic3⋊C4—62no—
310Dic3⋊C4—62no—
311Dic3⋊C4—62no—
312Dic3⋊C4—62no—
313Dic3⋊C4—62no—
314Dic3⋊C4—62no—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317Dic3⋊C4—62no—
318Dic3⋊C4—62no—
319Dic3⋊C4—62no—
320Dic3⋊C4—62no—
321Dic3⋊C4—62no—
322Dic3⋊C4—122no—
323Dic3⋊C4—122no—
324Dic3⋊C4—122no—
325C4×Dic3—22no—
326C4×Dic3—22no—
327C4×Dic3—62no—
328C4×Dic3—62no—
329C4×Dic3—62no—
330C4×Dic3—62no—
331C4×Dic3—62no—
332C4×Dic3—62no—
333C4×Dic3—62no—
334C4×Dic3—62no—
335C4×Dic3Dic614yes—
336C22×C32C22×Q811yescharacteristic
337C22×C32C2×#4111yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C22×C32C2×#4111yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C22×C32C2×#4111yescharacteristic
343C32×C4—22no—
344C32×C4—41no—
345C32×C4—41no—
346C3⋊Dic3—22no—
347C3⋊Dic3—22no—
348C3⋊Dic3—22no—
349C3⋊Dic3—41no—
350C3×Dic3—22no—
351C3×Dic3—22no—
352C3×Dic3—41no—
353C3×Dic3—41no—
354C3×Dic3—41no—
355C3×Dic3—41no—
356C3×Dic3—41no—
357C3×Dic3#12514yes—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4—91no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C42—31no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42—91no—
374C2×C42—91no—
375C2×C42—91no—
376C2×C42—91no—
377#95—31no—
378#95—31no—
379#95—31no—
380#95—31no—
381#95—31no—
382#95—31no—
383#95—31no—
384#95—91no—
385#95—91no—
386#95—91no—
387#95—91no—
388#95—91no—
389#95—91no—
390#95—91no—
391#95—91no—
392#95D3211yescharacteristic
393C23×C3—21no—
394C23×C3C23×D311yescharacteristic
395C23×C3C23×D311yescharacteristic
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4C2×Dic612yes—
446C2×C3×C4D3×Q812yes—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—32no—
467C2×Dic3—32no—
468C2×Dic3—32no—
469C2×Dic3—32no—
470C2×Dic3—32no—
471C2×Dic3—32no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—121no—
494C2×Dic3—121no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3C2×Dic612yes—
503C2×Dic3C2×Dic612yes—
504C2×Dic3#23512yes—
505C2×Dic3#23512yes—
506C2×Dic3#23712yes—
507C2×C32C2×#12511yescharacteristic
508C2×C32#52911yescharacteristic
509C2×C32#52911yescharacteristic
510C2×C32#52911yescharacteristic
511C2×C32#52911yescharacteristic
512C2×C32#53311yescharacteristic
513C2×C32#53311yescharacteristic
514C22×C4—31no—
515C22×C4—31no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4C2×D3211yescharacteristic
527C22×C4C2×D3211yescharacteristic
528C22×C4C2×D3211yescharacteristic
529C4⋊C4—62no—
530C4⋊C4—62no—
531C4⋊C4—182no—
532C4⋊C4—182no—
533C4⋊C4—182no—
534C4⋊C4—182no—
535C4⋊C4—182no—
536C4⋊C4—182no—
537C4⋊C4—182no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—182no—
541C42—34no—
542C42—62no—
543C42—62no—
544C42—182no—
545C42—182no—
546C42—182no—
547C42—182no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3C22×Dic611yescharacteristic
556C22×C3C2×#23511yescharacteristic
557C22×C3C2×#23511yescharacteristic
558C22×C3C2×#23711yescharacteristic
559C22×C3C2×D3×Q811yescharacteristic
560C22×C3D3×#4111yescharacteristic
561C22×C3D3×#4111yescharacteristic
562C22×C3D3×#4111yescharacteristic
563C22×C3D3×#4111yescharacteristic
564C22×C3D3×#4111yescharacteristic
565C22×C3D3×#4111yescharacteristic
566C22×C3D3×#4111yescharacteristic
567C22×C3D3×#4111yescharacteristic
568C22×C3D3×#4111yescharacteristic
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—34no—
572C3×C4—42no—
573C3×C4—41no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—62no—
578C3×C4—62no—
579C3×C4—81no—
580C3×C4—81no—
581C3×C4—121no—
582C3×C4—121no—
583C3×C4—121no—
584C3×C4—121no—
585C3×C4—121no—
586Dic3—22no—
587Dic3—22no—
588Dic3—41no—
589Dic3—41no—
590Dic3—41no—
591Dic3—41no—
592Dic3—41no—
593Dic3—62no—
594Dic3—62no—
595Dic3—62no—
596Dic3—62no—
597Dic3—62no—
598Dic3—62no—
599Dic3—122no—
600Dic3—122no—
601Dic3—122no—
602Dic3—121no—
603Dic3—121no—
604Dic3—241no—
605Dic3#87014yes—
606C32#240211yescharacteristic, complemented, Sylow
607C23C22×D3211yescharacteristic
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—32no—
617C2×C4—32no—
618C2×C4—32no—
619C2×C4—32no—
620C2×C4—32no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—92no—
641C2×C4—92no—
642C2×C4—92no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4D3×Dic612yes—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3C2×#87011yescharacteristic
661C2×C3#551711yescharacteristic
662C2×C3#551711yescharacteristic
663C2×C3#552811yescharacteristic
664C2×C3#552811yescharacteristic
665C2×C3#552811yescharacteristic
666C2×C3#552811yescharacteristic
667C2×C3#562211yescharacteristic
668C2×C3#564911yescharacteristic
669C2×C3#568011yescharacteristic
670C2×C3D3×#12511yescharacteristic
671C2×C3#568811yescharacteristic
672C2×C3#570611yescharacteristic
673C2×C3#570611yescharacteristic
674C22C2×D3×Dic611yescharacteristic
675C22D3×#23511yescharacteristic
676C22D3×#23511yescharacteristic
677C22D3×#23711yescharacteristic
678C22#6431211yescharacteristic
679C22#6431211yescharacteristic
680C22#6431911yescharacteristic
681C4—22no—
682C4—34no—
683C4—41no—
684C4—41no—
685C4—62no—
686C4—62no—
687C4—121no—
688C4—121no—
689C4—121no—
690C4—121no—
691C4—121no—
692C4—182no—
693C4—182no—
694C4—182no—
695C4—361no—
696C3—21no—
697C3#7339811yescharacteristic, complemented
698C3#7813311yescharacteristic, complemented
699C2D3×#87011yescharacteristic
700C2#1059402911yescharacteristic
701C2#1059409911yescharacteristic
702C2#1059410611yescharacteristic
703C2#1059440411yescharacteristic
704C2#1059441711yescharacteristic
705C2#1059447711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2402
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
606. C32#2402semidirect
697. C3#73398semidirect
698. C3#78133semidirect

Maximal subgroups

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

subgroupindex
#105923562
C3×#46602
C3×#46482
#105913562
#105913452
Dic3×C4⋊Dic32
#105912432
#105912422
Dic3×Dic3⋊C42
#105912182
#105912112
#105912102
#105911982
#781333
#733983