Finite Group Databasebeta

← C109×#15133 #42133127

Subgroups — C109×#15133 #42133127

Order 27904.

1454 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C109C212yesmaximal
2C2×#389×C109C211yesmaximal, characteristic
3C2×#389×C109C211yesmaximal, characteristic
4C2×#384×C109C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C109C211yesmaximal, characteristic
6C109×#1441C212yesmaximal
7C109×#1441C212yesmaximal
8C109×#1441C212yesmaximal
9C109×C4⋊#95C211yesmaximal, characteristic
10C109×C4⋊#95C211yesmaximal, characteristic
11C109×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C109C2211yescharacteristic
13C22×C4⋊C4×C109C2211yescharacteristic
14C22×C4⋊C4×C109C2212yes—
15C22×C4⋊C4×C109C2212yes—
16C22×C4⋊C4×C109C2212yes—
17C22×C4⋊C4×C109C2212yes—
18C22×C4⋊C4×C109C2211yescharacteristic
19C22×C4⋊C4×C109C2211yescharacteristic
20C22×C4⋊C4×C109C2211yescharacteristic
21C22×C4⋊C4×C109C2211yescharacteristic
22C22×C42×C109C2211yescharacteristic
23C22×C42×C109C2211yescharacteristic
24C22×C42×C109C2211yescharacteristic
25#398×C109—28no—
26#389×C109—24no—
27#389×C109—24no—
28#384×C109—24no—
29C4×C4⋊C4×C109—24no—
30C2×#95×C109C2212yes—
31C2×#95×C109C2212yes—
32C2×#95×C109C2212yes—
33C2×#95×C109C2211yescharacteristic
34C2×#95×C109C2211yescharacteristic
35C2×#95×C109C2212yes—
36C2×#95×C109C2212yes—
37C2×#95×C109C2212yes—
38C2×#95×C109C2212yes—
39C2×#95×C109C2212yes—
40C23×C4×C109C2312yes—
41C23×C4×C109C2312yes—
42C23×C4×C109C2311yescharacteristic
43C23×C4×C109C2312yes—
44C23×C4×C109C2311yescharacteristic
45C23×C4×C109C2311yescharacteristic
46C23×C4×C109C2312yes—
47C23×C4×C109C2311yescharacteristic
48C23×C4×C109C2311yescharacteristic
49C23×C4×C109C2311yescharacteristic
50C23×C4×C109C2311yescharacteristic
51C2×C4⋊C4×C109—22no—
52C2×C4⋊C4×C109—22no—
53C2×C4⋊C4×C109—22no—
54C2×C4⋊C4×C109—22no—
55C2×C4⋊C4×C109—22no—
56C2×C4⋊C4×C109—22no—
57C2×C4⋊C4×C109—22no—
58C2×C4⋊C4×C109—22no—
59C2×C4⋊C4×C109—24no—
60C2×C4⋊C4×C109—24no—
61C2×C4⋊C4×C109—22no—
62C2×C4⋊C4×C109—24no—
63C2×C4⋊C4×C109—24no—
64C2×C4⋊C4×C109—22no—
65C2×C4⋊C4×C109—22no—
66C2×C4⋊C4×C109—24no—
67C2×C4⋊C4×C109—24no—
68C2×C4⋊C4×C109—24no—
69C2×C4⋊C4×C109—24no—
70C2×C4⋊C4×C109—24no—
71C2×C4⋊C4×C109—22no—
72C2×C4⋊C4×C109—22no—
73C2×C4⋊C4×C109—22no—
74C2×C4⋊C4×C109—42no—
75C2×C4⋊C4×C109—42no—
76C2×C4⋊C4×C109—42no—
77C2×C4⋊C4×C109D414yes—
78C2×C4⋊C4×C109D414yes—
79C2×C4⋊C4×C109Q814yes—
80C2×C4⋊C4×C109Q814yes—
81C2×C42×C109—22no—
82C2×C42×C109—22no—
83C2×C42×C109—22no—
84C2×C42×C109—22no—
85C2×C42×C109—22no—
86C2×C42×C109—22no—
87C2×C42×C109—22no—
88C2×C42×C109D414yes—
89C2×C42×C109Q814yes—
90#95×C109—22no—
91#95×C109—22no—
92#95×C109—24no—
93#95×C109—24no—
94#95×C109—24no—
95#95×C109—24no—
96#95×C109—24no—
97#95×C109—42no—
98#95×C109—42no—
99#95×C109—42no—
100C24×C109C2411yescharacteristic
101C22×C4×C109—21no—
102C22×C4×C109—21no—
103C22×C4×C109—21no—
104C22×C4×C109—21no—
105C22×C4×C109—21no—
106C22×C4×C109—21no—
107C22×C4×C109—21no—
108C22×C4×C109—21no—
109C22×C4×C109—21no—
110C22×C4×C109—21no—
111C22×C4×C109—21no—
112C22×C4×C109—21no—
113C22×C4×C109—21no—
114C22×C4×C109—21no—
115C22×C4×C109—22no—
116C22×C4×C109—21no—
117C22×C4×C109—21no—
118C22×C4×C109—22no—
119C22×C4×C109—22no—
120C22×C4×C109—21no—
121C22×C4×C109—21no—
122C22×C4×C109—21no—
123C22×C4×C109—21no—
124C22×C4×C109—21no—
125C22×C4×C109—21no—
126C22×C4×C109—22no—
127C22×C4×C109—22no—
128C22×C4×C109—22no—
129C22×C4×C109—22no—
130C22×C4×C109—22no—
131C22×C4×C109—21no—
132C22×C4×C109—21no—
133C22×C4×C109—21no—
134C22×C4×C109—22no—
135C22×C4×C109—22no—
136C22×C4×C109—21no—
137C22×C4×C109—22no—
138C22×C4×C109—21no—
139C22×C4×C109—21no—
140C22×C4×C109—21no—
141C22×C4×C109—21no—
142C22×C4×C109—22no—
143C22×C4×C109—22no—
144C22×C4×C109—22no—
145C22×C4×C109—22no—
146C22×C4×C109—22no—
147C22×C4×C109—22no—
148C22×C4×C109—22no—
149C22×C4×C109—22no—
150C22×C4×C109—22no—
151C22×C4×C109—22no—
152C22×C4×C109—22no—
153C22×C4×C109—22no—
154C22×C4×C109—22no—
155C22×C4×C109—22no—
156C22×C4×C109—22no—
157C22×C4×C109C2×D412yes—
158C22×C4×C109C2×D414yes—
159C22×C4×C109C2×D412yes—
160C22×C4×C109C2×D412yes—
161C22×C4×C109C2×D412yes—
162C22×C4×C109C2×D412yes—
163C22×C4×C109C2×D412yes—
164C22×C4×C109C2×D412yes—
165C22×C4×C109C2×Q812yes—
166C22×C4×C109C2×Q814yes—
167C22×C4×C109C2×Q812yes—
168C22×C4×C109C2×Q812yes—
169C22×C4×C109C2×Q812yes—
170C22×C4×C109C2×Q812yes—
171C22×C4×C109C2×Q812yes—
172C22×C4×C109C2×Q812yes—
173C22×C4×C109#4112yes—
174C22×C4×C109#4112yes—
175C22×C4×C109#4112yes—
176C22×C4×C109#4112yes—
177C22×C4×C109#4112yes—
178C4⋊C4×C109—28no—
179C4⋊C4×C109—28no—
180C4⋊C4×C109—28no—
181C4⋊C4×C109—28no—
182C4⋊C4×C109—48no—
183C4⋊C4×C109—48no—
184C4⋊C4×C109—48no—
185C4⋊C4×C109—48no—
186C4⋊C4×C109—44no—
187C4⋊C4×C109—44no—
188C42×C109—28no—
189C42×C109—28no—
190C42×C109—44no—
191C23×C109C22×D411yescharacteristic
192C23×C109C22×D411yescharacteristic
193C23×C109C22×D411yescharacteristic
194C23×C109C22×Q811yescharacteristic
195C23×C109C22×Q811yescharacteristic
196C23×C109C22×Q811yescharacteristic
197C23×C109C2×#4111yescharacteristic
198C23×C109C2×#4111yescharacteristic
199C23×C109C2×#4111yescharacteristic
200C23×C109C2×#4111yescharacteristic
201C23×C109C2×#4111yescharacteristic
202C23×C109H(5,𝔽2)11yescharacteristic
203C23×C109H(5,𝔽2)11yescharacteristic
204C23×C1092−1+411yescharacteristic
205C23×C1092−1+411yescharacteristic
206C2×C4×C109—22no—
207C2×C4×C109—22no—
208C2×C4×C109—22no—
209C2×C4×C109—22no—
210C2×C4×C109—22no—
211C2×C4×C109—22no—
212C2×C4×C109—22no—
213C2×C4×C109—22no—
214C2×C4×C109—22no—
215C2×C4×C109—22no—
216C2×C4×C109—22no—
217C2×C4×C109—22no—
218C2×C4×C109—22no—
219C2×C4×C109—22no—
220C2×C4×C109—22no—
221C2×C4×C109—22no—
222C2×C4×C109—22no—
223C2×C4×C109—22no—
224C2×C4×C109—22no—
225C2×C4×C109—22no—
226C2×C4×C109—22no—
227C2×C4×C109—24no—
228C2×C4×C109—24no—
229C2×C4×C109—22no—
230C2×C4×C109—22no—
231C2×C4×C109—22no—
232C2×C4×C109—24no—
233C2×C4×C109—24no—
234C2×C4×C109—22no—
235C2×C4×C109—22no—
236C2×C4×C109—24no—
237C2×C4×C109—22no—
238C2×C4×C109—24no—
239C2×C4×C109—41no—
240C2×C4×C109—41no—
241C2×C4×C109—42no—
242C2×C4×C109—42no—
243C2×C4×C109—41no—
244C2×C4×C109—41no—
245C2×C4×C109—41no—
246C2×C4×C109—41no—
247C2×C4×C109—42no—
248C2×C4×C109—41no—
249C2×C4×C109—42no—
250C2×C4×C109—41no—
251C2×C4×C109—41no—
252C2×C4×C109—41no—
253C2×C4×C109—42no—
254C2×C4×C109—42no—
255C2×C4×C109—41no—
256C2×C4×C109—41no—
257C2×C4×C109—42no—
258C2×C4×C109—42no—
259C2×C4×C109—42no—
260C2×C4×C109—42no—
261C2×C4×C109—42no—
262C2×C4×C109—42no—
263C2×C4×C109—42no—
264C2×C4×C109—42no—
265C2×C4×C109—42no—
266C2×C4×C109—42no—
267C2×C4×C109—42no—
268C2×C4×C109—42no—
269C2×C4×C109—42no—
270C2×C4×C109—42no—
271C2×C4×C109—42no—
272C2×C4×C109—42no—
273C2×C4×C109#12114yes—
274C2×C4×C109#12114yes—
275C2×C4×C109C22⋊Q814yes—
276C2×C4×C109C22⋊Q814yes—
277C2×C4×C109C22⋊Q814yes—
278C2×C4×C109#12314yes—
279C2×C4×C109#12514yes—
280C2×C4×C109#12514yes—
281C2×C4×C109C4⋊Q814yes—
282C2×C4×C109C4⋊Q814yes—
283C22×C109C2×#12111yescharacteristic
284C22×C109C2×#12111yescharacteristic
285C22×C109C2×C22⋊Q811yescharacteristic
286C22×C109C2×C22⋊Q811yescharacteristic
287C22×C109C2×C22⋊Q811yescharacteristic
288C22×C109C2×#12311yescharacteristic
289C22×C109C2×#12511yescharacteristic
290C22×C109C2×#12511yescharacteristic
291C22×C109C2×C4⋊Q811yescharacteristic
292C22×C109C2×C4⋊Q811yescharacteristic
293C22×C109#53211yescharacteristic
294C22×C109#53311yescharacteristic
295C22×C109#53311yescharacteristic
296C22×C109#53711yescharacteristic
297C22×C109#53711yescharacteristic
298C22×C109#54011yescharacteristic
299C22×C109#54111yescharacteristic
300C22×C109#54411yescharacteristic
301C22×C109#54411yescharacteristic
302C22×C109D4211yescharacteristic
303C22×C109#54611yescharacteristic
304C22×C109#54711yescharacteristic
305C22×C109#54811yescharacteristic
306C22×C109D4×Q811yescharacteristic
307C22×C109D4×Q811yescharacteristic
308C22×C109#55011yescharacteristic
309C22×C109#55211yescharacteristic
310C22×C109#55311yescharacteristic
311C22×C109#55411yescharacteristic
312C22×C109#55411yescharacteristic
313C22×C109#55611yescharacteristic
314C22×C109#55711yescharacteristic
315C22×C109#55711yescharacteristic
316C22×C109Q8211yescharacteristic
317C22×C109#55911yescharacteristic
318C4×C109—24no—
319C4×C109—24no—
320C4×C109—24no—
321C4×C109—42no—
322C4×C109—42no—
323C4×C109—42no—
324C4×C109—44no—
325C4×C109—44no—
326C4×C109—82no—
327C4×C109—82no—
328C4×C109#39818yescomplemented
329#15133C10911yesmaximal, characteristic, direct product factor, Sylow
330C2×C109C2×#39811yescharacteristic
331C2×C109#241611yescharacteristic
332C2×C109#241711yescharacteristic
333C2×C109#244511yescharacteristic
334C2×C109#244611yescharacteristic
335C2×C109#250611yescharacteristic
336C2×C109#250711yescharacteristic
337C2×C109#253811yescharacteristic
338C2×C109#255011yescharacteristic
339C2×C109#255111yescharacteristic
340C2×C109#255211yescharacteristic
341C2×C109#257011yescharacteristic
342C2×C109#258211yescharacteristic
343C2×C109#262911yescharacteristic
344C2×C109#285711yescharacteristic
345C2×#398C2×C10912yes—
346C2×#389C2×C10911yescharacteristic
347C2×#389C2×C10911yescharacteristic
348C2×#384C2×C10911yescharacteristic
349C2×C4×C4⋊C4C2×C10911yescharacteristic
350#1441C2×C10912yes—
351#1441C2×C10912yes—
352#1441C2×C10912yes—
353C4⋊#95C2×C10911yescharacteristic
354C4⋊#95C2×C10911yescharacteristic
355C4⋊#95C2×C10911yescharacteristic
356C109#1513311yescharacteristic, direct product factor, Sylow
357C22×C4⋊C4C22×C10912yes—
358C22×C4⋊C4C22×C10911yescharacteristic
359C22×C4⋊C4C22×C10911yescharacteristic
360C22×C4⋊C4C22×C10912yes—
361C22×C4⋊C4C22×C10912yes—
362C22×C4⋊C4C22×C10912yes—
363C22×C4⋊C4C22×C10911yescharacteristic
364C22×C4⋊C4C22×C10911yescharacteristic
365C22×C4⋊C4C22×C10911yescharacteristic
366C22×C4⋊C4C22×C10911yescharacteristic
367C22×C42C22×C10911yescharacteristic
368C22×C42C22×C10911yescharacteristic
369C22×C42C22×C10911yescharacteristic
370#398—28no—
371#389—24no—
372#389—24no—
373#384—24no—
374C4×C4⋊C4—24no—
375C2×#95C22×C10912yes—
376C2×#95C22×C10912yes—
377C2×#95C22×C10912yes—
378C2×#95C22×C10911yescharacteristic
379C2×#95C22×C10911yescharacteristic
380C2×#95C22×C10912yes—
381C2×#95C22×C10912yes—
382C2×#95C22×C10912yes—
383C2×#95C22×C10912yes—
384C2×#95C22×C10912yes—
385C23×C4C23×C10912yes—
386C23×C4C23×C10912yes—
387C23×C4C23×C10912yes—
388C23×C4C23×C10911yescharacteristic
389C23×C4C23×C10912yes—
390C23×C4C23×C10911yescharacteristic
391C23×C4C23×C10911yescharacteristic
392C23×C4C23×C10911yescharacteristic
393C23×C4C23×C10911yescharacteristic
394C23×C4C23×C10911yescharacteristic
395C23×C4C23×C10911yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4D4×C10914yes—
423C2×C4⋊C4D4×C10914yes—
424C2×C4⋊C4Q8×C10914yes—
425C2×C4⋊C4Q8×C10914yes—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42D4×C10914yes—
434C2×C42Q8×C10914yes—
435#95—22no—
436#95—22no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—42no—
443#95—42no—
444#95—42no—
445C24C24×C10911yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4C2×D4×C10912yes—
503C22×C4C2×D4×C10914yes—
504C22×C4C2×D4×C10912yes—
505C22×C4C2×D4×C10912yes—
506C22×C4C2×D4×C10912yes—
507C22×C4C2×D4×C10912yes—
508C22×C4C2×D4×C10912yes—
509C22×C4C2×D4×C10912yes—
510C22×C4C2×Q8×C10912yes—
511C22×C4C2×Q8×C10914yes—
512C22×C4C2×Q8×C10912yes—
513C22×C4C2×Q8×C10912yes—
514C22×C4C2×Q8×C10912yes—
515C22×C4C2×Q8×C10912yes—
516C22×C4C2×Q8×C10912yes—
517C22×C4C2×Q8×C10912yes—
518C22×C4#41×C10912yes—
519C22×C4#41×C10912yes—
520C22×C4#41×C10912yes—
521C22×C4#41×C10912yes—
522C22×C4#41×C10912yes—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—48no—
528C4⋊C4—48no—
529C4⋊C4—48no—
530C4⋊C4—48no—
531C4⋊C4—44no—
532C4⋊C4—44no—
533C42—28no—
534C42—28no—
535C42—44no—
536C23C22×D4×C10911yescharacteristic
537C23C22×D4×C10911yescharacteristic
538C23C22×D4×C10911yescharacteristic
539C23C22×Q8×C10911yescharacteristic
540C23C22×Q8×C10911yescharacteristic
541C23C22×Q8×C10911yescharacteristic
542C23C2×#41×C10911yescharacteristic
543C23C2×#41×C10911yescharacteristic
544C23C2×#41×C10911yescharacteristic
545C23C2×#41×C10911yescharacteristic
546C23C2×#41×C10911yescharacteristic
547C23H(5,𝔽2)×C10911yescharacteristic
548C23H(5,𝔽2)×C10911yescharacteristic
549C232−1+4×C10911yescharacteristic
550C232−1+4×C10911yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4#121×C10914yes—
619C2×C4#121×C10914yes—
620C2×C4C22⋊Q8×C10914yes—
621C2×C4C22⋊Q8×C10914yes—
622C2×C4C22⋊Q8×C10914yes—
623C2×C4#123×C10914yes—
624C2×C4#125×C10914yes—
625C2×C4#125×C10914yes—
626C2×C4C4⋊Q8×C10914yes—
627C2×C4C4⋊Q8×C10914yes—
628C22C2×#121×C10911yescharacteristic
629C22C2×#121×C10911yescharacteristic
630C22C2×C22⋊Q8×C10911yescharacteristic
631C22C2×C22⋊Q8×C10911yescharacteristic
632C22C2×C22⋊Q8×C10911yescharacteristic
633C22C2×#123×C10911yescharacteristic
634C22C2×#125×C10911yescharacteristic
635C22C2×#125×C10911yescharacteristic
636C22C2×C4⋊Q8×C10911yescharacteristic
637C22C2×C4⋊Q8×C10911yescharacteristic
638C22#532×C10911yescharacteristic
639C22#533×C10911yescharacteristic
640C22#533×C10911yescharacteristic
641C22#537×C10911yescharacteristic
642C22#537×C10911yescharacteristic
643C22#540×C10911yescharacteristic
644C22#541×C10911yescharacteristic
645C22#544×C10911yescharacteristic
646C22#544×C10911yescharacteristic
647C22D42×C10911yescharacteristic
648C22#546×C10911yescharacteristic
649C22#547×C10911yescharacteristic
650C22#548×C10911yescharacteristic
651C22D4×Q8×C10911yescharacteristic
652C22D4×Q8×C10911yescharacteristic
653C22#550×C10911yescharacteristic
654C22#552×C10911yescharacteristic
655C22#553×C10911yescharacteristic
656C22#554×C10911yescharacteristic
657C22#554×C10911yescharacteristic
658C22#556×C10911yescharacteristic
659C22#557×C10911yescharacteristic
660C22#557×C10911yescharacteristic
661C22Q82×C10911yescharacteristic
662C22#559×C10911yescharacteristic
663C4—24no—
664C4—24no—
665C4—24no—
666C4—44no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—82no—
672C4—82no—
673C4#398×C10918yescomplemented
674C2C2×#398×C10911yescharacteristic
675C2C109×#241611yescharacteristic
676C2C109×#241711yescharacteristic
677C2C109×#244511yescharacteristic
678C2C109×#244611yescharacteristic
679C2C109×#250611yescharacteristic
680C2C109×#250711yescharacteristic
681C2C109×#253811yescharacteristic
682C2C109×#255011yescharacteristic
683C2C109×#255111yescharacteristic
684C2C109×#255211yescharacteristic
685C2C109×#257011yescharacteristic
686C2C109×#258211yescharacteristic
687C2C109×#262911yescharacteristic
688C2C109×#285711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C109C24
commutator, Frattini, cosocleC24C24×C109
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
328. C4×C109#398semidirect
329. #15133C109direct (N × H)
356. C109#15133direct (N × H)
673. C4#398×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1092
C2×#389×C1092
C2×#384×C1092
C2×C4×C4⋊C4×C1092
C109×#14412
C109×C4⋊#952
#15133109