Finite Group Databasebeta

← C109×#14403 #42132397

Subgroups — C109×#14403 #42132397

Order 27904.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C109C211yesmaximal, characteristic
2C2×#388×C109C211yesmaximal, characteristic
3C2×#385×C109C211yesmaximal, characteristic
4C2×#385×C109C211yesmaximal, characteristic
5C2×#382×C109C211yesmaximal, characteristic, complemented
6C109×#1444C211yesmaximal, characteristic, complemented
7C109×#1444C211yesmaximal, characteristic, complemented
8C109×#1442C211yesmaximal, characteristic, complemented
9C109×#1441C211yesmaximal, characteristic, complemented
10C109×#1439C211yesmaximal, characteristic
11C109×#1439C211yesmaximal, characteristic
12C109×#1436C211yesmaximal, characteristic, complemented
13C109×C4⋊#95C211yesmaximal, characteristic, complemented
14C109×C4⋊#95C211yesmaximal, characteristic, complemented
15C109×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C109C2211yescharacteristic
17C22×C4⋊C4×C109C2211yescharacteristic
18C22×C4⋊C4×C109C2211yescharacteristic
19C22×C4⋊C4×C109C2211yescharacteristic
20C22×C4⋊C4×C109C2211yescharacteristic
21C22×C4⋊C4×C109C2211yescharacteristic
22C22×C4⋊C4×C109C2211yescharacteristic
23C22×C4⋊C4×C109C2211yescharacteristic
24C22×C4⋊C4×C109C2211yescharacteristic
25C22×C22⋊C4×C109C2211yescharacteristic
26C22×C22⋊C4×C109C2211yescharacteristic
27C22×C22⋊C4×C109C2211yescharacteristic
28C22×C22⋊C4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2211yescharacteristic
30C22×C22⋊C4×C109C2211yescharacteristic
31C22×C42×C109C2211yescharacteristic
32C22×C42×C109C2211yescharacteristic
33#388×C109—24no—
34#388×C109C418yescomplemented
35#385×C109—24no—
36#385×C109—24no—
37#382×C109—24no—
38C2×#95×C109C2211yescharacteristic
39C2×#95×C109C2211yescharacteristic
40C2×#95×C109C2211yescharacteristic
41C2×#95×C109C2211yescharacteristic
42C2×#95×C109C2211yescharacteristic
43C2×#95×C109C2211yescharacteristic
44C2×#95×C109C2211yescharacteristic
45C2×#95×C109C2211yescharacteristic
46C2×#95×C109C2211yescharacteristic
47C2×#95×C109C2211yescharacteristic
48C2×#95×C109C2211yescharacteristic
49C2×#95×C109C2211yescharacteristic
50C2×#95×C109C2211yescharacteristic
51C2×#95×C109C2211yescharacteristic
52C2×#95×C109C2211yescharacteristic
53C2×#95×C109C2211yescharacteristic
54C2×#95×C109C2211yescharacteristic
55C2×#95×C109C2211yescharacteristic
56C25×C109C2311yescharacteristic
57C23×C4×C109—22no—
58C23×C4×C109—22no—
59C23×C4×C109—22no—
60C23×C4×C109—41no—
61C23×C4×C109—41no—
62C23×C4×C109—41no—
63C23×C4×C109—41no—
64C23×C4×C109C2311yescharacteristic
65C23×C4×C109C2311yescharacteristic
66C23×C4×C109C2311yescharacteristic
67C23×C4×C109C2311yescharacteristic
68C23×C4×C109C2311yescharacteristic
69C23×C4×C109C2311yescharacteristic
70C23×C4×C109C2311yescharacteristic
71C23×C4×C109C2311yescharacteristic
72C23×C4×C109C2311yescharacteristic
73C23×C4×C109C2311yescharacteristic
74C23×C4×C109C2311yescharacteristic
75C23×C4×C109C2311yescharacteristic
76C23×C4×C109C2311yescharacteristic
77C23×C4×C109C2311yescharacteristic
78C2×C4⋊C4×C109—22no—
79C2×C4⋊C4×C109—22no—
80C2×C4⋊C4×C109—22no—
81C2×C4⋊C4×C109—22no—
82C2×C4⋊C4×C109—22no—
83C2×C4⋊C4×C109—22no—
84C2×C4⋊C4×C109—22no—
85C2×C4⋊C4×C109—22no—
86C2×C4⋊C4×C109—22no—
87C2×C4⋊C4×C109—22no—
88C2×C4⋊C4×C109—22no—
89C2×C4⋊C4×C109—41no—
90C2×C4⋊C4×C109—41no—
91C2×C4⋊C4×C109—41no—
92C2×C4⋊C4×C109—41no—
93C2×C4⋊C4×C109—41no—
94C2×C4⋊C4×C109—41no—
95C2×C4⋊C4×C109—41no—
96C2×C4⋊C4×C109—41no—
97C2×C4⋊C4×C109—41no—
98C2×C4⋊C4×C109—41no—
99C2×C4⋊C4×C109—41no—
100C2×C4⋊C4×C109—41no—
101C2×C4⋊C4×C109C2×C414yescomplemented
102C2×C22⋊C4×C109—22no—
103C2×C22⋊C4×C109—22no—
104C2×C22⋊C4×C109—22no—
105C2×C22⋊C4×C109—22no—
106C2×C22⋊C4×C109—22no—
107C2×C22⋊C4×C109—22no—
108C2×C22⋊C4×C109—22no—
109C2×C22⋊C4×C109—41no—
110C2×C22⋊C4×C109—41no—
111C2×C22⋊C4×C109—41no—
112C2×C22⋊C4×C109—41no—
113C2×C22⋊C4×C109—41no—
114C2×C22⋊C4×C109—41no—
115C2×C22⋊C4×C109C2×C414yes—
116C2×C22⋊C4×C109C2×C414yes—
117C2×C22⋊C4×C109C2×C414yes—
118C2×C22⋊C4×C109D414yes—
119C2×C22⋊C4×C109Q814yes—
120C2×C42×C109—22no—
121C2×C42×C109—22no—
122C2×C42×C109—22no—
123C2×C42×C109—22no—
124C2×C42×C109—41no—
125C2×C42×C109C2×C414yescomplemented
126#95×C109—22no—
127#95×C109—22no—
128#95×C109—22no—
129#95×C109—22no—
130#95×C109—22no—
131#95×C109—22no—
132#95×C109—22no—
133#95×C109—22no—
134#95×C109—41no—
135#95×C109—41no—
136#95×C109—41no—
137#95×C109—41no—
138#95×C109—41no—
139#95×C109—41no—
140#95×C109—41no—
141#95×C109C2×C414yescomplemented
142#95×C109C2×C414yescomplemented
143#95×C109D414yes—
144C24×C109—21no—
145C24×C109—21no—
146C24×C109—21no—
147C24×C109—21no—
148C24×C109—21no—
149C24×C109—21no—
150C24×C109—21no—
151C24×C109—21no—
152C24×C109—21no—
153C24×C109—21no—
154C24×C109—21no—
155C24×C109—21no—
156C24×C109C22×C412yes—
157C24×C109C2×D412yes—
158C24×C109C2×Q812yes—
159C24×C109C2411yescharacteristic
160C22×C4×C109—21no—
161C22×C4×C109—21no—
162C22×C4×C109—21no—
163C22×C4×C109—21no—
164C22×C4×C109—21no—
165C22×C4×C109—21no—
166C22×C4×C109—21no—
167C22×C4×C109—21no—
168C22×C4×C109—21no—
169C22×C4×C109—21no—
170C22×C4×C109—21no—
171C22×C4×C109—21no—
172C22×C4×C109—21no—
173C22×C4×C109—21no—
174C22×C4×C109—21no—
175C22×C4×C109—21no—
176C22×C4×C109—21no—
177C22×C4×C109—21no—
178C22×C4×C109—21no—
179C22×C4×C109—21no—
180C22×C4×C109—21no—
181C22×C4×C109—21no—
182C22×C4×C109—21no—
183C22×C4×C109—21no—
184C22×C4×C109—21no—
185C22×C4×C109—21no—
186C22×C4×C109—21no—
187C22×C4×C109—21no—
188C22×C4×C109—21no—
189C22×C4×C109—21no—
190C22×C4×C109—21no—
191C22×C4×C109—21no—
192C22×C4×C109—21no—
193C22×C4×C109—21no—
194C22×C4×C109—21no—
195C22×C4×C109—21no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—21no—
199C22×C4×C109—21no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—21no—
206C22×C4×C109—21no—
207C22×C4×C109—21no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—21no—
211C22×C4×C109—21no—
212C22×C4×C109—21no—
213C22×C4×C109—21no—
214C22×C4×C109—21no—
215C22×C4×C109—21no—
216C22×C4×C109—21no—
217C22×C4×C109—21no—
218C22×C4×C109—21no—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—21no—
227C22×C4×C109—21no—
228C22×C4×C109—21no—
229C22×C4×C109—21no—
230C22×C4×C109—21no—
231C22×C4×C109—21no—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—21no—
237C22×C4×C109—21no—
238C22×C4×C109—21no—
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—44no—
243C22×C4×C109—44no—
244C22×C4×C109—44no—
245C22×C4×C109—44no—
246C22×C4×C109—44no—
247C22×C4×C109—44no—
248C22×C4×C109—44no—
249C22×C4×C109C22×C412yes—
250C22×C4×C109C22×C412yes—
251C22×C4×C109C22×C412yes—
252C22×C4×C109C22×C412yes—
253C22×C4×C109C22×C412yes—
254C22×C4×C109C22×C412yes—
255C22×C4×C109C2×D412yes—
256C22×C4×C109C2×D412yes—
257C22×C4×C109C2×D412yes—
258C22×C4×C109C2×D412yes—
259C22×C4×C109C2×D412yes—
260C22×C4×C109C2×Q812yes—
261C22×C4×C109C2×Q812yes—
262C22×C4×C109#4112yes—
263C22×C4×C109#4112yes—
264C22×C4×C109#4112yes—
265C4⋊C4×C109—44no—
266C4⋊C4×C109—44no—
267C4⋊C4×C109—44no—
268C4⋊C4×C109—44no—
269C4⋊C4×C109—44no—
270C4⋊C4×C109—44no—
271C4⋊C4×C109—44no—
272C4⋊C4×C109—44no—
273C22⋊C4×C109—28no—
274C22⋊C4×C109—44no—
275C22⋊C4×C109—44no—
276C22⋊C4×C109—44no—
277C22⋊C4×C109—44no—
278C22⋊C4×C109C4⋊C4116yescomplemented
279C42×C109—28no—
280C42×C109—44no—
281C23×C109—22no—
282C23×C109—22no—
283C23×C109—22no—
284C23×C109—22no—
285C23×C109—22no—
286C23×C109—22no—
287C23×C109—22no—
288C23×C109—22no—
289C23×C109—22no—
290C23×C109—22no—
291C23×C109—22no—
292C23×C109—22no—
293C23×C109—22no—
294C23×C109—22no—
295C23×C109—22no—
296C23×C109—22no—
297C23×C109—22no—
298C23×C109—22no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109—41no—
302C23×C109—41no—
303C23×C109—41no—
304C23×C109—41no—
305C23×C109—41no—
306C23×C109—41no—
307C23×C109—41no—
308C23×C109—41no—
309C23×C109—41no—
310C23×C109—41no—
311C23×C109—41no—
312C23×C109—41no—
313C23×C109—41no—
314C23×C109—41no—
315C23×C109C2×C4⋊C414yes—
316C23×C109C23×C411yescharacteristic
317C23×C109C22×D411yescharacteristic
318C23×C109C22×D411yescharacteristic
319C23×C109C22×Q811yescharacteristic
320C23×C109C2×#4111yescharacteristic
321C23×C109C2×#4111yescharacteristic
322C23×C109C2×#4111yescharacteristic
323C23×C109H(5,𝔽2)11yescharacteristic
324C23×C109H(5,𝔽2)11yescharacteristic
325C23×C109H(5,𝔽2)11yescharacteristic
326C23×C109H(5,𝔽2)11yescharacteristic
327C23×C109H(5,𝔽2)11yescharacteristic
328C23×C1092−1+411yescharacteristic
329C23×C1092−1+411yescharacteristic
330C23×C1092−1+411yescharacteristic
331C2×C4×C109—22no—
332C2×C4×C109—22no—
333C2×C4×C109—22no—
334C2×C4×C109—22no—
335C2×C4×C109—22no—
336C2×C4×C109—22no—
337C2×C4×C109—22no—
338C2×C4×C109—22no—
339C2×C4×C109—22no—
340C2×C4×C109—22no—
341C2×C4×C109—22no—
342C2×C4×C109—22no—
343C2×C4×C109—22no—
344C2×C4×C109—22no—
345C2×C4×C109—22no—
346C2×C4×C109—22no—
347C2×C4×C109—22no—
348C2×C4×C109—22no—
349C2×C4×C109—22no—
350C2×C4×C109—22no—
351C2×C4×C109—22no—
352C2×C4×C109—22no—
353C2×C4×C109—22no—
354C2×C4×C109—22no—
355C2×C4×C109—22no—
356C2×C4×C109—22no—
357C2×C4×C109—22no—
358C2×C4×C109—22no—
359C2×C4×C109—22no—
360C2×C4×C109—22no—
361C2×C4×C109—22no—
362C2×C4×C109—22no—
363C2×C4×C109—22no—
364C2×C4×C109—22no—
365C2×C4×C109—22no—
366C2×C4×C109—22no—
367C2×C4×C109—22no—
368C2×C4×C109—22no—
369C2×C4×C109—22no—
370C2×C4×C109—416no—
371C2×C4×C109—41no—
372C2×C4×C109—41no—
373C2×C4×C109—41no—
374C2×C4×C109—41no—
375C2×C4×C109—41no—
376C2×C4×C109—41no—
377C2×C4×C109—41no—
378C2×C4×C109—41no—
379C2×C4×C109—41no—
380C2×C4×C109—41no—
381C2×C4×C109—41no—
382C2×C4×C109—41no—
383C2×C4×C109—41no—
384C2×C4×C109—41no—
385C2×C4×C109—41no—
386C2×C4×C109—41no—
387C2×C4×C109—41no—
388C2×C4×C109—41no—
389C2×C4×C109—41no—
390C2×C4×C109—41no—
391C2×C4×C109—41no—
392C2×C4×C109—41no—
393C2×C4×C109—41no—
394C2×C4×C109—41no—
395C2×C4×C109—41no—
396C2×C4×C109—41no—
397C2×C4×C109—41no—
398C2×C4×C109—41no—
399C2×C4×C109—41no—
400C2×C4×C109—41no—
401C2×C4×C109—41no—
402C2×C4×C109—41no—
403C2×C4×C109—41no—
404C2×C4×C109—41no—
405C2×C4×C109—41no—
406C2×C4×C109—41no—
407C2×C4×C109—41no—
408C2×C4×C109—41no—
409C2×C4×C109—41no—
410C2×C4×C109—41no—
411C2×C4×C109—41no—
412C2×C4×C109—41no—
413C2×C4×C109—41no—
414C2×C4×C109—41no—
415C2×C4×C109—41no—
416C2×C4×C109—41no—
417C2×C4×C109—41no—
418C2×C4×C109—41no—
419C2×C4×C109—41no—
420C2×C4×C109—41no—
421C2×C4×C109—41no—
422C2×C4×C109—41no—
423C2×C4×C109—41no—
424C2×C4×C109—41no—
425C2×C4×C109—41no—
426C2×C4×C109—41no—
427C2×C4×C109C2×C4⋊C414yes—
428C2×C4×C109C2×C4⋊C414yes—
429C2×C4×C109C4×D414yes—
430C22×C109—24no—
431C22×C109—24no—
432C22×C109—24no—
433C22×C109—42no—
434C22×C109—42no—
435C22×C109—42no—
436C22×C109—42no—
437C22×C109—42no—
438C22×C109—42no—
439C22×C109—42no—
440C22×C109—42no—
441C22×C109—42no—
442C22×C109—42no—
443C22×C109—42no—
444C22×C109—42no—
445C22×C109C22×C4⋊C411yescharacteristic
446C22×C109C2×C4×D411yescharacteristic
447C22×C109C4×#4111yescharacteristic
448C22×C109#51811yescharacteristic
449C22×C109#52011yescharacteristic
450C22×C109#52011yescharacteristic
451C22×C109#52011yescharacteristic
452C22×C109#53511yescharacteristic
453C22×C109#53511yescharacteristic
454C22×C109#53611yescharacteristic
455C22×C109#53711yescharacteristic
456C22×C109#53811yescharacteristic
457C22×C109#53911yescharacteristic
458C22×C109#54011yescharacteristic
459C22×C109#54111yescharacteristic
460C22×C109#54211yescharacteristic
461C22×C109#54211yescharacteristic
462C22×C109#54411yescharacteristic
463C22×C109#54411yescharacteristic
464C22×C109D4211yescharacteristic
465C22×C109#54611yescharacteristic
466C22×C109#54611yescharacteristic
467C22×C109#54611yescharacteristic
468C22×C109#54711yescharacteristic
469C22×C109#54711yescharacteristic
470C22×C109D4×Q811yescharacteristic
471C22×C109#55111yescharacteristic
472C22×C109#55211yescharacteristic
473C22×C109#55411yescharacteristic
474C22×C109#55411yescharacteristic
475C22×C109#55411yescharacteristic
476C22×C109H(3,𝔽4)11yescharacteristic
477C22×C109#56211yescharacteristic
478C22×C109#56211yescharacteristic
479C22×C109#56311yescharacteristic
480C4×C109—24no—
481C4×C109—24no—
482C4×C109—24no—
483C4×C109—42no—
484C4×C109—42no—
485C4×C109—42no—
486C4×C109—42no—
487C4×C109—42no—
488C4×C109—42no—
489C4×C109—42no—
490C4×C109—81no—
491C4×C109—81no—
492C4×C109—81no—
493C4×C109—81no—
494#14403C10911yesmaximal, characteristic, direct product factor, Sylow
495C2×C109—44no—
496C2×C109#231711yescharacteristic
497C2×C109#232411yescharacteristic
498C2×C109#233411yescharacteristic
499C2×C109D4×C4⋊C411yescharacteristic
500C2×C109#234911yescharacteristic
501C2×C109#235911yescharacteristic
502C2×C109#237911yescharacteristic
503C2×C109#267011yescharacteristic
504C2×C109#267211yescharacteristic
505C2×C109#269811yescharacteristic
506C2×C109#270411yescharacteristic
507C2×C109#270611yescharacteristic
508C2×C109#272011yescharacteristic
509C2×C109#276311yescharacteristic
510C2×C109#276811yescharacteristic
511C2×#388C2×C10911yescharacteristic
512C2×#388C2×C10911yescharacteristic
513C2×#385C2×C10911yescharacteristic
514C2×#385C2×C10911yescharacteristic
515C2×#382C2×C10911yescharacteristic, complemented
516#1444C2×C10911yescharacteristic, complemented
517#1444C2×C10911yescharacteristic, complemented
518#1442C2×C10911yescharacteristic, complemented
519#1441C2×C10911yescharacteristic, complemented
520#1439C2×C10911yescharacteristic
521#1439C2×C10911yescharacteristic
522#1436C2×C10911yescharacteristic, complemented
523C4⋊#95C2×C10911yescharacteristic, complemented
524C4⋊#95C2×C10911yescharacteristic, complemented
525C22⋊#95C2×C10911yescharacteristic
526C109#1440311yescharacteristic, direct product factor, Sylow
527C24×C4C22×C10911yescharacteristic
528C22×C4⋊C4C22×C10911yescharacteristic
529C22×C4⋊C4C22×C10911yescharacteristic
530C22×C4⋊C4C22×C10911yescharacteristic
531C22×C4⋊C4C22×C10911yescharacteristic
532C22×C4⋊C4C22×C10911yescharacteristic
533C22×C4⋊C4C22×C10911yescharacteristic
534C22×C4⋊C4C22×C10911yescharacteristic
535C22×C4⋊C4C22×C10911yescharacteristic
536C22×C22⋊C4C22×C10911yescharacteristic
537C22×C22⋊C4C22×C10911yescharacteristic
538C22×C22⋊C4C22×C10911yescharacteristic
539C22×C22⋊C4C22×C10911yescharacteristic
540C22×C22⋊C4C22×C10911yescharacteristic
541C22×C22⋊C4C22×C10911yescharacteristic
542C22×C42C22×C10911yescharacteristic
543C22×C42C22×C10911yescharacteristic
544#388—24no—
545#388C4×C10918yescomplemented
546#385—24no—
547#385—24no—
548#382—24no—
549C2×#95C22×C10911yescharacteristic
550C2×#95C22×C10911yescharacteristic
551C2×#95C22×C10911yescharacteristic
552C2×#95C22×C10911yescharacteristic
553C2×#95C22×C10911yescharacteristic
554C2×#95C22×C10911yescharacteristic
555C2×#95C22×C10911yescharacteristic
556C2×#95C22×C10911yescharacteristic
557C2×#95C22×C10911yescharacteristic
558C2×#95C22×C10911yescharacteristic
559C2×#95C22×C10911yescharacteristic
560C2×#95C22×C10911yescharacteristic
561C2×#95C22×C10911yescharacteristic
562C2×#95C22×C10911yescharacteristic
563C2×#95C22×C10911yescharacteristic
564C2×#95C22×C10911yescharacteristic
565C2×#95C22×C10911yescharacteristic
566C2×#95C22×C10911yescharacteristic
567C25C23×C10911yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C10911yescharacteristic
576C23×C4C23×C10911yescharacteristic
577C23×C4C23×C10911yescharacteristic
578C23×C4C23×C10911yescharacteristic
579C23×C4C23×C10911yescharacteristic
580C23×C4C23×C10911yescharacteristic
581C23×C4C23×C10911yescharacteristic
582C23×C4C23×C10911yescharacteristic
583C23×C4C23×C10911yescharacteristic
584C23×C4C23×C10911yescharacteristic
585C23×C4C23×C10911yescharacteristic
586C23×C4C23×C10911yescharacteristic
587C23×C4C23×C10911yescharacteristic
588C23×C4C23×C10911yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4C2×C4×C10914yescomplemented
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4C2×C4×C10914yes—
627C2×C22⋊C4C2×C4×C10914yes—
628C2×C22⋊C4C2×C4×C10914yes—
629C2×C22⋊C4D4×C10914yes—
630C2×C22⋊C4Q8×C10914yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—41no—
636C2×C42C2×C4×C10914yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95C2×C4×C10914yescomplemented
653#95C2×C4×C10914yescomplemented
654#95D4×C10914yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C10912yes—
668C24C2×D4×C10912yes—
669C24C2×Q8×C10912yes—
670C24C24×C10911yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C10912yes—
761C22×C4C22×C4×C10912yes—
762C22×C4C22×C4×C10912yes—
763C22×C4C22×C4×C10912yes—
764C22×C4C22×C4×C10912yes—
765C22×C4C22×C4×C10912yes—
766C22×C4C2×D4×C10912yes—
767C22×C4C2×D4×C10912yes—
768C22×C4C2×D4×C10912yes—
769C22×C4C2×D4×C10912yes—
770C22×C4C2×D4×C10912yes—
771C22×C4C2×Q8×C10912yes—
772C22×C4C2×Q8×C10912yes—
773C22×C4#41×C10912yes—
774C22×C4#41×C10912yes—
775C22×C4#41×C10912yes—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C109116yescomplemented
790C42—28no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C10914yes—
827C23C23×C4×C10911yescharacteristic
828C23C22×D4×C10911yescharacteristic
829C23C22×D4×C10911yescharacteristic
830C23C22×Q8×C10911yescharacteristic
831C23C2×#41×C10911yescharacteristic
832C23C2×#41×C10911yescharacteristic
833C23C2×#41×C10911yescharacteristic
834C23H(5,𝔽2)×C10911yescharacteristic
835C23H(5,𝔽2)×C10911yescharacteristic
836C23H(5,𝔽2)×C10911yescharacteristic
837C23H(5,𝔽2)×C10911yescharacteristic
838C23H(5,𝔽2)×C10911yescharacteristic
839C232−1+4×C10911yescharacteristic
840C232−1+4×C10911yescharacteristic
841C232−1+4×C10911yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4C2×C4⋊C4×C10914yes—
939C2×C4C2×C4⋊C4×C10914yes—
940C2×C4C4×D4×C10914yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C10911yescharacteristic
957C22C2×C4×D4×C10911yescharacteristic
958C22C4×#41×C10911yescharacteristic
959C22#518×C10911yescharacteristic
960C22#520×C10911yescharacteristic
961C22#520×C10911yescharacteristic
962C22#520×C10911yescharacteristic
963C22#535×C10911yescharacteristic
964C22#535×C10911yescharacteristic
965C22#536×C10911yescharacteristic
966C22#537×C10911yescharacteristic
967C22#538×C10911yescharacteristic
968C22#539×C10911yescharacteristic
969C22#540×C10911yescharacteristic
970C22#541×C10911yescharacteristic
971C22#542×C10911yescharacteristic
972C22#542×C10911yescharacteristic
973C22#544×C10911yescharacteristic
974C22#544×C10911yescharacteristic
975C22D42×C10911yescharacteristic
976C22#546×C10911yescharacteristic
977C22#546×C10911yescharacteristic
978C22#546×C10911yescharacteristic
979C22#547×C10911yescharacteristic
980C22#547×C10911yescharacteristic
981C22D4×Q8×C10911yescharacteristic
982C22#551×C10911yescharacteristic
983C22#552×C10911yescharacteristic
984C22#554×C10911yescharacteristic
985C22#554×C10911yescharacteristic
986C22#554×C10911yescharacteristic
987C22H(3,𝔽4)×C10911yescharacteristic
988C22#562×C10911yescharacteristic
989C22#562×C10911yescharacteristic
990C22#563×C10911yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C109×#231711yescharacteristic
1007C2C109×#232411yescharacteristic
1008C2C109×#233411yescharacteristic
1009C2D4×C4⋊C4×C10911yescharacteristic
1010C2C109×#234911yescharacteristic
1011C2C109×#235911yescharacteristic
1012C2C109×#237911yescharacteristic
1013C2C109×#267011yescharacteristic
1014C2C109×#267211yescharacteristic
1015C2C109×#269811yescharacteristic
1016C2C109×#270411yescharacteristic
1017C2C109×#270611yescharacteristic
1018C2C109×#272011yescharacteristic
1019C2C109×#276311yescharacteristic
1020C2C109×#276811yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutatorC23C23×C4×C109
Frattini, cosocleC24C24×C109
prime radicalC25×C109C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×#382×C109C2semidirect
6. C109×#1444C2semidirect
7. C109×#1444C2semidirect
8. C109×#1442C2semidirect
9. C109×#1441C2semidirect
12. C109×#1436C2semidirect
13. C109×C4⋊#95C2semidirect
14. C109×C4⋊#95C2semidirect
34. #388×C109C4semidirect
101. C2×C4⋊C4×C109C2×C4semidirect
125. C2×C42×C109C2×C4semidirect
141. #95×C109C2×C4semidirect
142. #95×C109C2×C4semidirect
278. C22⋊C4×C109C4⋊C4semidirect
494. #14403C109direct (N × H)
515. C2×#382C2×C109semidirect
516. #1444C2×C109semidirect
517. #1444C2×C109semidirect
518. #1442C2×C109semidirect
519. #1441C2×C109semidirect
522. #1436C2×C109semidirect
523. C4⋊#95C2×C109semidirect
524. C4⋊#95C2×C109semidirect
526. C109#14403direct (N × H)
545. #388C4×C109semidirect
612. C2×C4⋊C4C2×C4×C109semidirect
636. C2×C42C2×C4×C109semidirect
652. #95C2×C4×C109semidirect
653. #95C2×C4×C109semidirect
789. C22⋊C4C4⋊C4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1092
C2×#385×C1092
C2×#382×C1092
C109×#14442
C109×#14422
C109×#14412
C109×#14392
C109×#14362
C109×C4⋊#952
C109×C22⋊#952
#14403109