Finite Group Databasebeta

← C109×#15132 #42133126

Subgroups — C109×#15132 #42133126

Order 27904.

1626 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C109C212yesmaximal
2C2×#389×C109C211yesmaximal, characteristic, complemented
3C2×#380×C109C211yesmaximal, characteristic
4C2×#380×C109C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C109C211yesmaximal, characteristic
6C109×#1443C212yesmaximal, complemented
7C109×#1442C212yesmaximal, complemented
8C109×#1440C212yesmaximal
9C109×C4⋊#95C211yesmaximal, characteristic, complemented
10C109×C4⋊#95C211yesmaximal, characteristic, complemented
11C109×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C109C2211yescharacteristic
13C22×C4⋊C4×C109C2211yescharacteristic
14C22×C4⋊C4×C109C2211yescharacteristic
15C22×C4⋊C4×C109C2211yescharacteristic
16C22×C4⋊C4×C109C2212yes—
17C22×C4⋊C4×C109C2211yescharacteristic
18C22×C22⋊C4×C109C2211yescharacteristic
19C22×C22⋊C4×C109C2212yes—
20C22×C22⋊C4×C109C2212yes—
21C22×C22⋊C4×C109C2211yescharacteristic
22C22×C42×C109C2211yescharacteristic
23C22×C42×C109C2211yescharacteristic
24#397×C109—28no—
25#389×C109—24no—
26#380×C109—24no—
27#380×C109—24no—
28C4×C22⋊C4×C109—24no—
29C2×#95×C109C2212yes—
30C2×#95×C109C2212yes—
31C2×#95×C109C2212yes—
32C2×#95×C109C2212yes—
33C2×#95×C109C2212yes—
34C2×#95×C109C2212yes—
35C2×#95×C109C2211yescharacteristic
36C2×#95×C109C2212yes—
37C2×#95×C109C2212yes—
38C2×#95×C109C2211yescharacteristic
39C2×#95×C109C2212yes—
40C25×C109C2311yescharacteristic
41C23×C4×C109—22no—
42C23×C4×C109—22no—
43C23×C4×C109—22no—
44C23×C4×C109—22no—
45C23×C4×C109—22no—
46C23×C4×C109—22no—
47C23×C4×C109D414yes—
48C23×C4×C109C2312yes—
49C23×C4×C109C2312yes—
50C23×C4×C109C2312yes—
51C23×C4×C109C2311yescharacteristic
52C23×C4×C109C2311yescharacteristic
53C23×C4×C109C2312yes—
54C23×C4×C109C2311yescharacteristic
55C23×C4×C109C2311yescharacteristic
56C23×C4×C109C2311yescharacteristic
57C23×C4×C109C2311yescharacteristic
58C2×C4⋊C4×C109—22no—
59C2×C4⋊C4×C109—22no—
60C2×C4⋊C4×C109—22no—
61C2×C4⋊C4×C109—22no—
62C2×C4⋊C4×C109—22no—
63C2×C4⋊C4×C109—24no—
64C2×C4⋊C4×C109—22no—
65C2×C4⋊C4×C109—24no—
66C2×C4⋊C4×C109—22no—
67C2×C4⋊C4×C109—22no—
68C2×C4⋊C4×C109—22no—
69C2×C4⋊C4×C109—22no—
70C2×C4⋊C4×C109—22no—
71C2×C4⋊C4×C109—42no—
72C2×C4⋊C4×C109D414yes—
73C2×C22⋊C4×C109—22no—
74C2×C22⋊C4×C109—22no—
75C2×C22⋊C4×C109—22no—
76C2×C22⋊C4×C109—22no—
77C2×C22⋊C4×C109—22no—
78C2×C22⋊C4×C109—24no—
79C2×C22⋊C4×C109—24no—
80C2×C22⋊C4×C109—24no—
81C2×C22⋊C4×C109—24no—
82C2×C22⋊C4×C109—24no—
83C2×C22⋊C4×C109—42no—
84C2×C22⋊C4×C109D414yes—
85C2×C42×C109—22no—
86C2×C42×C109—22no—
87C2×C42×C109—22no—
88C2×C42×C109—22no—
89C2×C42×C109—22no—
90C2×C42×C109—22no—
91#95×C109—22no—
92#95×C109—22no—
93#95×C109—24no—
94#95×C109—24no—
95#95×C109—24no—
96#95×C109—24no—
97#95×C109—24no—
98#95×C109—24no—
99#95×C109—24no—
100#95×C109—24no—
101#95×C109—42no—
102C24×C109—21no—
103C24×C109—21no—
104C24×C109—21no—
105C24×C109—21no—
106C24×C109—21no—
107C24×C109—21no—
108C24×C109—21no—
109C24×C109—21no—
110C24×C109—21no—
111C24×C109—21no—
112C24×C109—21no—
113C24×C109—21no—
114C24×C109C2×D412yes—
115C24×C109C2×D412yes—
116C24×C109#4112yes—
117C24×C109C2411yescharacteristic
118C22×C4×C109—21no—
119C22×C4×C109—21no—
120C22×C4×C109—21no—
121C22×C4×C109—21no—
122C22×C4×C109—21no—
123C22×C4×C109—21no—
124C22×C4×C109—22no—
125C22×C4×C109—21no—
126C22×C4×C109—22no—
127C22×C4×C109—21no—
128C22×C4×C109—21no—
129C22×C4×C109—21no—
130C22×C4×C109—21no—
131C22×C4×C109—21no—
132C22×C4×C109—21no—
133C22×C4×C109—21no—
134C22×C4×C109—21no—
135C22×C4×C109—21no—
136C22×C4×C109—21no—
137C22×C4×C109—22no—
138C22×C4×C109—22no—
139C22×C4×C109—21no—
140C22×C4×C109—21no—
141C22×C4×C109—21no—
142C22×C4×C109—21no—
143C22×C4×C109—21no—
144C22×C4×C109—21no—
145C22×C4×C109—22no—
146C22×C4×C109—21no—
147C22×C4×C109—21no—
148C22×C4×C109—21no—
149C22×C4×C109—21no—
150C22×C4×C109—22no—
151C22×C4×C109—21no—
152C22×C4×C109—21no—
153C22×C4×C109—21no—
154C22×C4×C109—28no—
155C22×C4×C109—28no—
156C22×C4×C109—28no—
157C22×C4×C109—22no—
158C22×C4×C109—22no—
159C22×C4×C109—22no—
160C22×C4×C109—22no—
161C22×C4×C109—22no—
162C22×C4×C109—22no—
163C22×C4×C109—22no—
164C22×C4×C109—22no—
165C22×C4×C109—22no—
166C22×C4×C109—22no—
167C22×C4×C109—22no—
168C22×C4×C109—22no—
169C22×C4×C109—22no—
170C22×C4×C109—22no—
171C22×C4×C109—22no—
172C22×C4×C109—22no—
173C22×C4×C109—22no—
174C22×C4×C109—22no—
175C22×C4×C109—22no—
176C22×C4×C109—22no—
177C22×C4×C109—22no—
178C22×C4×C109—44no—
179C22×C4×C109—44no—
180C22×C4×C109—44no—
181C22×C4×C109—44no—
182C22×C4×C109C2×D412yes—
183C22×C4×C109C2×D412yes—
184C22×C4×C109C2×D414yes—
185C22×C4×C109C2×D412yes—
186C22×C4×C109C2×D412yes—
187C22×C4×C109C2×D412yes—
188C22×C4×C109#4112yes—
189C22×C4×C109#4112yes—
190C22×C4×C109#4112yes—
191C22×C4×C109#4112yes—
192C22×C4×C109#4112yes—
193C22×C4×C109#4112yes—
194C22×C4×C109#4112yes—
195C4⋊C4×C109—28no—
196C4⋊C4×C109—48no—
197C4⋊C4×C109—44no—
198C4⋊C4×C109—44no—
199C4⋊C4×C109—44no—
200C22⋊C4×C109—28no—
201C22⋊C4×C109—28no—
202C22⋊C4×C109—48no—
203C22⋊C4×C109—48no—
204C42×C109—44no—
205C42×C109—44no—
206C23×C109—22no—
207C23×C109—22no—
208C23×C109—22no—
209C23×C109—22no—
210C23×C109—22no—
211C23×C109—22no—
212C23×C109—22no—
213C23×C109—22no—
214C23×C109—22no—
215C23×C109—22no—
216C23×C109—22no—
217C23×C109—22no—
218C23×C109—22no—
219C23×C109—22no—
220C23×C109—22no—
221C23×C109—22no—
222C23×C109—22no—
223C23×C109—22no—
224C23×C109—41no—
225C23×C109—41no—
226C23×C109—41no—
227C23×C109—41no—
228C23×C109—41no—
229C23×C109—41no—
230C23×C109—41no—
231C23×C109—41no—
232C23×C109—41no—
233C23×C109—41no—
234C23×C109—41no—
235C23×C109—41no—
236C23×C109—41no—
237C23×C109—41no—
238C23×C109—41no—
239C23×C109—41no—
240C23×C109#12114yes—
241C23×C109C22×D411yescharacteristic
242C23×C109C22×D411yescharacteristic
243C23×C109C22×D411yescharacteristic
244C23×C109C2×#4111yescharacteristic
245C23×C109C2×#4111yescharacteristic
246C23×C109C2×#4111yescharacteristic
247C23×C109C2×#4111yescharacteristic
248C23×C109C2×#4111yescharacteristic
249C23×C109C2×#4111yescharacteristic
250C23×C109C2×#4111yescharacteristic
251C23×C109C2×#4111yescharacteristic
252C23×C109H(5,𝔽2)11yescharacteristic
253C23×C1092−1+411yescharacteristic
254C23×C1092−1+411yescharacteristic
255C23×C1092−1+411yescharacteristic
256C2×C4×C109—22no—
257C2×C4×C109—22no—
258C2×C4×C109—22no—
259C2×C4×C109—24no—
260C2×C4×C109—22no—
261C2×C4×C109—22no—
262C2×C4×C109—22no—
263C2×C4×C109—22no—
264C2×C4×C109—24no—
265C2×C4×C109—22no—
266C2×C4×C109—22no—
267C2×C4×C109—24no—
268C2×C4×C109—22no—
269C2×C4×C109—22no—
270C2×C4×C109—22no—
271C2×C4×C109—22no—
272C2×C4×C109—22no—
273C2×C4×C109—22no—
274C2×C4×C109—41no—
275C2×C4×C109—41no—
276C2×C4×C109—41no—
277C2×C4×C109—41no—
278C2×C4×C109—41no—
279C2×C4×C109—41no—
280C2×C4×C109—41no—
281C2×C4×C109—41no—
282C2×C4×C109—42no—
283C2×C4×C109—41no—
284C2×C4×C109—41no—
285C2×C4×C109—41no—
286C2×C4×C109—41no—
287C2×C4×C109—42no—
288C2×C4×C109—41no—
289C2×C4×C109—42no—
290C2×C4×C109—41no—
291C2×C4×C109—41no—
292C2×C4×C109—41no—
293C2×C4×C109—41no—
294C2×C4×C109—42no—
295C2×C4×C109—41no—
296C2×C4×C109—41no—
297C2×C4×C109—41no—
298C2×C4×C109—416no—
299C2×C4×C109—42no—
300C2×C4×C109—42no—
301C2×C4×C109—42no—
302C2×C4×C109—42no—
303C2×C4×C109—42no—
304C2×C4×C109—42no—
305C2×C4×C109—42no—
306C2×C4×C109—42no—
307C2×C4×C109—42no—
308C2×C4×C109—42no—
309C2×C4×C109—42no—
310C2×C4×C109—42no—
311C2×C4×C109—42no—
312C2×C4×C109—42no—
313C2×C4×C109—42no—
314C2×C4×C109—42no—
315C2×C4×C109—42no—
316C2×C4×C109—42no—
317C2×C4×C109—42no—
318C2×C4×C109—42no—
319C2×C4×C109—42no—
320C2×C4×C109#12114yes—
321C2×C4×C109#12314yes—
322C2×C4×C109#12314yes—
323C2×C4×C109#12314yes—
324C2×C4×C109#12414yes—
325C2×C4×C109#12614yes—
326C2×C4×C109#12614yes—
327C22×C109—24no—
328C22×C109—24no—
329C22×C109—24no—
330C22×C109—42no—
331C22×C109—42no—
332C22×C109—42no—
333C22×C109—42no—
334C22×C109—42no—
335C22×C109—42no—
336C22×C109—42no—
337C22×C109—42no—
338C22×C109—42no—
339C22×C109—42no—
340C22×C109—42no—
341C22×C109—42no—
342C22×C109C2×#12111yescharacteristic
343C22×C109C2×#12111yescharacteristic
344C22×C109C2×#12311yescharacteristic
345C22×C109C2×#12311yescharacteristic
346C22×C109C2×#12311yescharacteristic
347C22×C109#52511yescharacteristic
348C22×C109C2×#12411yescharacteristic
349C22×C109C2×#12611yescharacteristic
350C22×C109C2×#12611yescharacteristic
351C22×C109#52911yescharacteristic
352C22×C109#52911yescharacteristic
353C22×C109#53211yescharacteristic
354C22×C109#53211yescharacteristic
355C22×C109#53611yescharacteristic
356C22×C109#53711yescharacteristic
357C22×C109#54111yescharacteristic
358C22×C109#54111yescharacteristic
359C22×C109#54211yescharacteristic
360C22×C109#54211yescharacteristic
361C22×C109D4211yescharacteristic
362C22×C109#54711yescharacteristic
363C22×C109#54711yescharacteristic
364C22×C109#54711yescharacteristic
365C22×C109#54711yescharacteristic
366C22×C109#54811yescharacteristic
367C22×C109#54811yescharacteristic
368C22×C109#55211yescharacteristic
369C22×C109#55211yescharacteristic
370C22×C109#55211yescharacteristic
371C22×C109#55211yescharacteristic
372C22×C109#55311yescharacteristic
373C22×C109#55311yescharacteristic
374C22×C109#55511yescharacteristic
375C22×C109#55611yescharacteristic
376C22×C109#55611yescharacteristic
377C4×C109—42no—
378C4×C109—42no—
379C4×C109—42no—
380C4×C109—44no—
381C4×C109—42no—
382C4×C109—42no—
383C4×C109—82no—
384C4×C109—82no—
385C4×C109—82no—
386C4×C109#39718yescomplemented
387#15132C10911yesmaximal, characteristic, direct product factor, Sylow
388C2×C109—44no—
389C2×C109C2×#39711yescharacteristic
390C2×C109#241511yescharacteristic
391C2×C109#241611yescharacteristic
392C2×C109#242111yescharacteristic
393C2×C109#242211yescharacteristic
394C2×C109#248511yescharacteristic
395C2×C109#248611yescharacteristic
396C2×C109#248911yescharacteristic
397C2×C109#249111yescharacteristic
398C2×C109#249411yescharacteristic
399C2×C109#249511yescharacteristic
400C2×C109#249611yescharacteristic
401C2×C109#249611yescharacteristic
402C2×C109#262511yescharacteristic
403C2×C109#285411yescharacteristic
404C2×#397C2×C10912yes—
405C2×#389C2×C10911yescharacteristic, complemented
406C2×#380C2×C10911yescharacteristic
407C2×#380C2×C10911yescharacteristic
408C2×C4×C22⋊C4C2×C10911yescharacteristic
409#1443C2×C10912yescomplemented
410#1442C2×C10912yescomplemented
411#1440C2×C10912yes—
412C4⋊#95C2×C10911yescharacteristic, complemented
413C4⋊#95C2×C10911yescharacteristic, complemented
414C4⋊#95C2×C10911yescharacteristic, complemented
415C109#1513211yescharacteristic, direct product factor, Sylow
416C24×C4C22×C10911yescharacteristic
417C22×C4⋊C4C22×C10911yescharacteristic
418C22×C4⋊C4C22×C10911yescharacteristic
419C22×C4⋊C4C22×C10911yescharacteristic
420C22×C4⋊C4C22×C10912yes—
421C22×C4⋊C4C22×C10911yescharacteristic
422C22×C22⋊C4C22×C10912yes—
423C22×C22⋊C4C22×C10911yescharacteristic
424C22×C22⋊C4C22×C10912yes—
425C22×C22⋊C4C22×C10911yescharacteristic
426C22×C42C22×C10911yescharacteristic
427C22×C42C22×C10911yescharacteristic
428#397—28no—
429#389—24no—
430#380—24no—
431#380—24no—
432C4×C22⋊C4—24no—
433C2×#95C22×C10912yes—
434C2×#95C22×C10912yes—
435C2×#95C22×C10912yes—
436C2×#95C22×C10912yes—
437C2×#95C22×C10912yes—
438C2×#95C22×C10912yes—
439C2×#95C22×C10911yescharacteristic
440C2×#95C22×C10912yes—
441C2×#95C22×C10912yes—
442C2×#95C22×C10911yescharacteristic
443C2×#95C22×C10912yes—
444C25C23×C10911yescharacteristic
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4D4×C10914yes—
452C23×C4C23×C10912yes—
453C23×C4C23×C10912yes—
454C23×C4C23×C10912yes—
455C23×C4C23×C10912yes—
456C23×C4C23×C10911yescharacteristic
457C23×C4C23×C10911yescharacteristic
458C23×C4C23×C10911yescharacteristic
459C23×C4C23×C10911yescharacteristic
460C23×C4C23×C10911yescharacteristic
461C23×C4C23×C10911yescharacteristic
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4D4×C10914yes—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4D4×C10914yes—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495#95—22no—
496#95—22no—
497#95—24no—
498#95—24no—
499#95—24no—
500#95—24no—
501#95—24no—
502#95—24no—
503#95—24no—
504#95—24no—
505#95—42no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24C2×D4×C10912yes—
519C24C2×D4×C10912yes—
520C24#41×C10912yes—
521C24C24×C10911yescharacteristic
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4C2×D4×C10912yes—
587C22×C4C2×D4×C10912yes—
588C22×C4C2×D4×C10914yes—
589C22×C4C2×D4×C10912yes—
590C22×C4C2×D4×C10912yes—
591C22×C4C2×D4×C10912yes—
592C22×C4#41×C10912yes—
593C22×C4#41×C10912yes—
594C22×C4#41×C10912yes—
595C22×C4#41×C10912yes—
596C22×C4#41×C10912yes—
597C22×C4#41×C10912yes—
598C22×C4#41×C10912yes—
599C4⋊C4—28no—
600C4⋊C4—48no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C42—44no—
609C42—44no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#121×C10914yes—
645C23C22×D4×C10911yescharacteristic
646C23C22×D4×C10911yescharacteristic
647C23C22×D4×C10911yescharacteristic
648C23C2×#41×C10911yescharacteristic
649C23C2×#41×C10911yescharacteristic
650C23C2×#41×C10911yescharacteristic
651C23C2×#41×C10911yescharacteristic
652C23C2×#41×C10911yescharacteristic
653C23C2×#41×C10911yescharacteristic
654C23C2×#41×C10911yescharacteristic
655C23C2×#41×C10911yescharacteristic
656C23H(5,𝔽2)×C10911yescharacteristic
657C232−1+4×C10911yescharacteristic
658C232−1+4×C10911yescharacteristic
659C232−1+4×C10911yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—416no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4#121×C10914yes—
725C2×C4#123×C10914yes—
726C2×C4#123×C10914yes—
727C2×C4#123×C10914yes—
728C2×C4#124×C10914yes—
729C2×C4#126×C10914yes—
730C2×C4#126×C10914yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#121×C10911yescharacteristic
747C22C2×#121×C10911yescharacteristic
748C22C2×#123×C10911yescharacteristic
749C22C2×#123×C10911yescharacteristic
750C22C2×#123×C10911yescharacteristic
751C22#525×C10911yescharacteristic
752C22C2×#124×C10911yescharacteristic
753C22C2×#126×C10911yescharacteristic
754C22C2×#126×C10911yescharacteristic
755C22#529×C10911yescharacteristic
756C22#529×C10911yescharacteristic
757C22#532×C10911yescharacteristic
758C22#532×C10911yescharacteristic
759C22#536×C10911yescharacteristic
760C22#537×C10911yescharacteristic
761C22#541×C10911yescharacteristic
762C22#541×C10911yescharacteristic
763C22#542×C10911yescharacteristic
764C22#542×C10911yescharacteristic
765C22D42×C10911yescharacteristic
766C22#547×C10911yescharacteristic
767C22#547×C10911yescharacteristic
768C22#547×C10911yescharacteristic
769C22#547×C10911yescharacteristic
770C22#548×C10911yescharacteristic
771C22#548×C10911yescharacteristic
772C22#552×C10911yescharacteristic
773C22#552×C10911yescharacteristic
774C22#552×C10911yescharacteristic
775C22#552×C10911yescharacteristic
776C22#553×C10911yescharacteristic
777C22#553×C10911yescharacteristic
778C22#555×C10911yescharacteristic
779C22#556×C10911yescharacteristic
780C22#556×C10911yescharacteristic
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—44no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4#397×C10918yescomplemented
791C2—44no—
792C2C2×#397×C10911yescharacteristic
793C2C109×#241511yescharacteristic
794C2C109×#241611yescharacteristic
795C2C109×#242111yescharacteristic
796C2C109×#242211yescharacteristic
797C2C109×#248511yescharacteristic
798C2C109×#248611yescharacteristic
799C2C109×#248911yescharacteristic
800C2C109×#249111yescharacteristic
801C2C109×#249411yescharacteristic
802C2C109×#249511yescharacteristic
803C2C109×#249611yescharacteristic
804C2C109×#249611yescharacteristic
805C2C109×#262511yescharacteristic
806C2C109×#285411yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC24C24×C109
prime radicalC25×C109C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#389×C109C2semidirect
6. C109×#1443C2semidirect
7. C109×#1442C2semidirect
9. C109×C4⋊#95C2semidirect
10. C109×C4⋊#95C2semidirect
11. C109×C4⋊#95C2semidirect
386. C4×C109#397semidirect
387. #15132C109direct (N × H)
405. C2×#389C2×C109semidirect
409. #1443C2×C109semidirect
410. #1442C2×C109semidirect
412. C4⋊#95C2×C109semidirect
413. C4⋊#95C2×C109semidirect
414. C4⋊#95C2×C109semidirect
415. C109#15132direct (N × H)
790. C4#397×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1092
C2×#389×C1092
C2×#380×C1092
C2×C4×C22⋊C4×C1092
C109×#14432
C109×#14422
C109×#14402
C109×C4⋊#952
#15132109