Finite Group Databasebeta

← C109×#22424 #42140418

Subgroups — C109×#22424 #42140418

Order 27904.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C109C211yesmaximal, characteristic
2C2×#435×C109C211yesmaximal, characteristic, complemented
3C2×#418×C109C211yesmaximal, characteristic, complemented
4C2×#416×C109C211yesmaximal, characteristic, complemented
5C109×#2354C211yesmaximal, characteristic, complemented
6C109×#1983C211yesmaximal, characteristic, complemented
7C109×#1959C211yesmaximal, characteristic, complemented
8C109×#1894C211yesmaximal, characteristic, complemented
9C109×#1893C211yesmaximal, characteristic, complemented
10C109×#1875C211yesmaximal, characteristic, complemented
11C109×#1873C211yesmaximal, characteristic, complemented
12C109×#1802C211yesmaximal, characteristic, complemented
13C109×#1788C211yesmaximal, characteristic, complemented
14C109×#1786C211yesmaximal, characteristic, complemented
15C109×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C22×M16×C109C2211yescharacteristic
19C23×C8×C109C2211yescharacteristic, complemented
20#546×C109—24no—
21#546×C109C418yescomplemented
22C2×#124×C109C2211yescharacteristic
23C2×#123×C109—21no—
24C2×C22⋊Q8×C109C2211yescharacteristic
25C2×#121×C109—21no—
26C2×#121×C109C2211yescharacteristic
27C2×#120×C109—21no—
28C2×C4×D4×C109C2211yescharacteristic
29C2×C4×D4×C109C2211yescharacteristic
30C2×#117×C109C2211yescharacteristic
31C2×#117×C109C2211yescharacteristic, complemented
32C22×C22⋊C4×C109—21no—
33#435×C109—24no—
34C2×C4⋊C8×C109C2211yescharacteristic, complemented
35#418×C109—24no—
36#416×C109—24no—
37C2×#103×C109C2211yescharacteristic, complemented
38C2×#103×C109C2211yescharacteristic, complemented
39C2×#103×C109C2211yescharacteristic, complemented
40C2×#103×C109C2211yescharacteristic, complemented
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49C2×C22⋊C8×C109C2211yescharacteristic
50C2×C22⋊C8×C109C2211yescharacteristic, complemented
51C2×#97×C109C2211yescharacteristic, complemented
52#390×C109—21no—
53#388×C109—21no—
54#388×C109—21no—
55#384×C109C2211yescharacteristic, complemented
56#380×C109C2211yescharacteristic
57#380×C109C2211yescharacteristic, complemented
58C4×C4⋊C4×C109—21no—
59C4×C4⋊C4×C109C2211yescharacteristic, complemented
60#340×C109C2211yescharacteristic, complemented
61#340×C109C2211yescharacteristic, complemented
62#340×C109C2211yescharacteristic, complemented
63#340×C109C2211yescharacteristic, complemented
64C25×C109—21no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—41no—
69C2×#41×C109—41no—
70C2×#41×C109C2×C414yes—
71C22×Q8×C109C2311yescharacteristic
72C22×D4×C109—22no—
73C22×D4×C109—22no—
74C22×D4×C109—21no—
75C22×D4×C109—21no—
76C22×D4×C109—21no—
77C22×D4×C109—22no—
78C22×D4×C109—41no—
79C22×D4×C109—41no—
80C22×D4×C109C2×C414yes—
81C22×D4×C109D411yescharacteristic
82C22×D4×C109C2311yescharacteristic
83C22×D4×C109C2311yescharacteristic
84C23×C4×C109—21no—
85C23×C4×C109—21no—
86C23×C4×C109C2311yescharacteristic
87C23×C4×C109C2311yescharacteristic
88C2×M16×C109—22no—
89C2×M16×C109—22no—
90C2×M16×C109—41no—
91C22×C8×C109—22no—
92C22×C8×C109—22no—
93C22×C8×C109—41no—
94C22×C8×C109C2311yescharacteristic
95C22×C8×C109C2311yescharacteristic
96C22×C8×C109C2311yescharacteristic
97C22×C8×C109C2311yescharacteristic
98#124×C109—22no—
99#124×C109C2×C414yes—
100#123×C109—28no—
101C22⋊Q8×C109—22no—
102C22⋊Q8×C109C2×C414yes—
103#121×C109—22no—
104#121×C109—28no—
105#121×C109C2×C414yes—
106#120×C109—28no—
107C4×D4×C109—22no—
108C4×D4×C109C2×C414yes—
109C4×D4×C109C2×C414yes—
110C4×D4×C109D414yes—
111#117×C109—22no—
112#117×C109—22no—
113#117×C109—41no—
114#117×C109—41no—
115C2×C4⋊C4×C109—21no—
116C2×C4⋊C4×C109—21no—
117C2×C4⋊C4×C109—21no—
118C2×C4⋊C4×C109D411yescharacteristic
119C2×C4⋊C4×C109C2311yescharacteristic
120C2×C4⋊C4×C109C2311yescharacteristic
121C2×C4⋊C4×C109C2311yescharacteristic
122C2×C4⋊C4×C109C2311yescharacteristic
123C2×C4⋊C4×C109C2311yescharacteristic
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109—21no—
129C2×C22⋊C4×C109—28no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—21no—
134C2×C22⋊C4×C109D411yescharacteristic
135C2×C22⋊C4×C109D411yescharacteristic
136C2×C42×C109—21no—
137C2×C42×C109—21no—
138C2×C42×C109—21no—
139C2×C42×C109C2311yescharacteristic
140C4⋊C8×C109—22no—
141#103×C109—22no—
142#103×C109—22no—
143#103×C109—41no—
144#103×C109—41no—
145#102×C109—22no—
146#102×C109—22no—
147#102×C109—22no—
148#102×C109—22no—
149#102×C109—22no—
150#102×C109—41no—
151#102×C109—41no—
152#102×C109D414yescomplemented
153C22⋊C8×C109—22no—
154C22⋊C8×C109—22no—
155#97×C109—22no—
156#95×C109—21no—
157#95×C109—21no—
158#95×C109—21no—
159C24×C109—21no—
160C24×C109—21no—
161C24×C109—24no—
162C24×C109—42no—
163C24×C109—42no—
164C24×C109—42no—
165C24×C109—42no—
166C24×C109—81no—
167C24×C109—81no—
168C24×C109C2×D411yescharacteristic
169C24×C109C2×D411yescharacteristic
170#41×C109—28no—
171#41×C109—44no—
172#41×C109—44no—
173#41×C109—44no—
174C2×Q8×C109—21no—
175C2×Q8×C109—21no—
176C2×Q8×C109—21no—
177C2×Q8×C109—21no—
178C2×Q8×C109—21no—
179C2×Q8×C109C22×C412yes—
180C2×D4×C109—28no—
181C2×D4×C109—24no—
182C2×D4×C109—24no—
183C2×D4×C109—24no—
184C2×D4×C109—21no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—21no—
189C2×D4×C109—21no—
190C2×D4×C109—21no—
191C2×D4×C109—21no—
192C2×D4×C109—44no—
193C2×D4×C109—44no—
194C2×D4×C109—44no—
195C2×D4×C109—41no—
196C2×D4×C109—41no—
197C2×D4×C109—42no—
198C2×D4×C109—42no—
199C2×D4×C109—42no—
200C2×D4×C109—42no—
201C2×D4×C109—81no—
202C2×D4×C109—81no—
203C2×D4×C109C22⋊C414yes—
204C2×D4×C109C22×C412yes—
205C2×D4×C109C22×C412yes—
206C2×D4×C109C2×D412yes—
207C2×D4×C109#4112yes—
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—24no—
220C22×C4×C109—24no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—42no—
225C22×C4×C109—42no—
226C22×C4×C109—81no—
227C22×C4×C109—81no—
228C22×C4×C109C22×C412yes—
229C22×C4×C109C22×C412yes—
230C22×C4×C109C2×D411yescharacteristic
231C22×C4×C109C2×D411yescharacteristic
232C22×C4×C109C2×D411yescharacteristic
233C22×C4×C109C2×D411yescharacteristic
234C22×C4×C109C2×D412yes—
235C22×C4×C109C2×D412yes—
236C22×C4×C109C2411yescharacteristic
237M16×C109—44no—
238C2×C8×C109—21no—
239C2×C8×C109—21no—
240C2×C8×C109—21no—
241C2×C8×C109—21no—
242C2×C8×C109—21no—
243C2×C8×C109—21no—
244C2×C8×C109—21no—
245C2×C8×C109—21no—
246C2×C8×C109—21no—
247C2×C8×C109—21no—
248C2×C8×C109—21no—
249C2×C8×C109—44no—
250C2×C8×C109C2×D412yes—
251C4⋊C4×C109—24no—
252C4⋊C4×C109—21no—
253C4⋊C4×C109—21no—
254C4⋊C4×C109—21no—
255C4⋊C4×C109—21no—
256C4⋊C4×C109—21no—
257C4⋊C4×C109—21no—
258C4⋊C4×C109—21no—
259C4⋊C4×C109—21no—
260C4⋊C4×C109—42no—
261C4⋊C4×C109—81no—
262C4⋊C4×C109C22⋊C414yes—
263C4⋊C4×C109C22×C412yes—
264C4⋊C4×C109C2×D412yes—
265C22⋊C4×C109—24no—
266C22⋊C4×C109—24no—
267C22⋊C4×C109—24no—
268C22⋊C4×C109—24no—
269C22⋊C4×C109—24no—
270C22⋊C4×C109—42no—
271C22⋊C4×C109—42no—
272C22⋊C4×C109—81no—
273C22⋊C4×C109—81no—
274C22⋊C4×C109C22⋊C414yes—
275C22⋊C4×C109C22⋊C414yes—
276C42×C109—42no—
277C42×C109—42no—
278C42×C109—42no—
279C42×C109C22×C412yes—
280C42×C109C2×D412yes—
281C23×C109—22no—
282C23×C109—21no—
283C23×C109—21no—
284C23×C109—22no—
285C23×C109—21no—
286C23×C109—21no—
287C23×C109—22no—
288C23×C109—21no—
289C23×C109—21no—
290C23×C109—21no—
291C23×C109—21no—
292C23×C109—21no—
293C23×C109—21no—
294C23×C109—21no—
295C23×C109—21no—
296C23×C109—22no—
297C23×C109—48no—
298C23×C109—48no—
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—84no—
310C23×C109—84no—
311C23×C109—84no—
312C23×C109—84no—
313C23×C109—84no—
314C23×C109C2×C22⋊C412yes—
315C23×C109C2×C22⋊C412yes—
316C23×C109C22×D411yescharacteristic
317Q8×C109—22no—
318Q8×C109—22no—
319Q8×C109—41no—
320Q8×C109—41no—
321D4×C109—22no—
322D4×C109—22no—
323D4×C109—22no—
324D4×C109—22no—
325D4×C109—22no—
326D4×C109—44no—
327D4×C109—48no—
328D4×C109—48no—
329D4×C109—41no—
330D4×C109—41no—
331D4×C109—84no—
332D4×C109C4×D414yes—
333C2×C4×C109—21no—
334C2×C4×C109—21no—
335C2×C4×C109—21no—
336C2×C4×C109—21no—
337C2×C4×C109—21no—
338C2×C4×C109—21no—
339C2×C4×C109—21no—
340C2×C4×C109—21no—
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—48no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—41no—
356C2×C4×C109—41no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109—41no—
360C2×C4×C109—41no—
361C2×C4×C109—41no—
362C2×C4×C109—41no—
363C2×C4×C109—41no—
364C2×C4×C109—41no—
365C2×C4×C109—41no—
366C2×C4×C109—41no—
367C2×C4×C109—41no—
368C2×C4×C109—84no—
369C2×C4×C109C2×C22⋊C412yes—
370C2×C4×C109C2×C22⋊C412yes—
371C2×C4×C109C2×C22⋊C412yes—
372C2×C4×C109C2×C22⋊C412yes—
373C2×C4×C109C23×C411yescharacteristic
374C2×C4×C109C22×D411yescharacteristic
375C2×C4×C109C22×D411yescharacteristic
376C2×C4×C109C2×#4111yescharacteristic
377C2×C4×C109H(5,𝔽2)11yescharacteristic
378C2×C4×C109H(5,𝔽2)11yescharacteristic
379C8×C109—22no—
380C8×C109—41no—
381C8×C109—41no—
382C8×C109—41no—
383C22×C109—22no—
384C22×C109—22no—
385C22×C109—24no—
386C22×C109—22no—
387C22×C109—22no—
388C22×C109—22no—
389C22×C109—22no—
390C22×C109—42no—
391C22×C109—42no—
392C22×C109—41no—
393C22×C109—41no—
394C22×C109—42no—
395C22×C109—41no—
396C22×C109—41no—
397C22×C109—42no—
398C22×C109—41no—
399C22×C109—41no—
400C22×C109—42no—
401C22×C109—41no—
402C22×C109—41no—
403C22×C109—42no—
404C22×C109—42no—
405C22×C109—42no—
406C22×C109—42no—
407C22×C109—816no—
408C22×C109—81no—
409C22×C109—81no—
410C22×C109—81no—
411C22×C109—81no—
412C22×C109C22×C22⋊C411yescharacteristic
413C22×C109D4211yescharacteristic
414C22×C109#54611yescharacteristic
415C22×C109#57511yescharacteristic
416C22×C109#57511yescharacteristic
417C22×C109#57611yescharacteristic
418C22×C109#57711yescharacteristic
419C4×C109—22no—
420C4×C109—22no—
421C4×C109—22no—
422C4×C109—22no—
423C4×C109—42no—
424C4×C109—42no—
425C4×C109—42no—
426C4×C109—81no—
427C4×C109—81no—
428C4×C109—81no—
429C4×C109C2×C4×D411yescharacteristic
430C4×C109#51811yescharacteristic
431C4×C109D4211yescharacteristic
432C4×C109#54611yescharacteristic
433#22424C10911yesmaximal, characteristic, direct product factor, Sylow
434C2×C109—42no—
435C2×C109—42no—
436C2×C109—44no—
437C2×C109—82no—
438C2×C109D4×C22⋊C411yescharacteristic
439C2×C109#289611yescharacteristic
440C2×C109#289711yescharacteristic
441C2×C109#326711yescharacteristic
442C2×C109#326811yescharacteristic
443C2×C109#331111yescharacteristic
444C2×C109#331911yescharacteristic
445C2×#546C2×C10911yescharacteristic
446C2×#435C2×C10911yescharacteristic, complemented
447C2×#418C2×C10911yescharacteristic, complemented
448C2×#416C2×C10911yescharacteristic, complemented
449#2354C2×C10911yescharacteristic, complemented
450#1983C2×C10911yescharacteristic, complemented
451#1959C2×C10911yescharacteristic, complemented
452#1894C2×C10911yescharacteristic, complemented
453#1893C2×C10911yescharacteristic, complemented
454#1875C2×C10911yescharacteristic, complemented
455#1873C2×C10911yescharacteristic, complemented
456#1802C2×C10911yescharacteristic, complemented
457#1788C2×C10911yescharacteristic, complemented
458#1786C2×C10911yescharacteristic, complemented
459#1762C2×C10911yescharacteristic, complemented
460C109#2242411yescharacteristic, direct product factor, Sylow
461C22×#41C22×C10911yescharacteristic
462C23×D4C22×C10911yescharacteristic
463C22×M16C22×C10911yescharacteristic
464C23×C8C22×C10911yescharacteristic, complemented
465#546—24no—
466#546C4×C10918yescomplemented
467C2×#124C22×C10911yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C22×C10911yescharacteristic
470C2×#121—21no—
471C2×#121C22×C10911yescharacteristic
472C2×#120—21no—
473C2×C4×D4C22×C10911yescharacteristic
474C2×C4×D4C22×C10911yescharacteristic
475C2×#117C22×C10911yescharacteristic
476C2×#117C22×C10911yescharacteristic, complemented
477C22×C22⋊C4—21no—
478#435—24no—
479C2×C4⋊C8C22×C10911yescharacteristic, complemented
480#418—24no—
481#416—24no—
482C2×#103C22×C10911yescharacteristic, complemented
483C2×#103C22×C10911yescharacteristic, complemented
484C2×#103C22×C10911yescharacteristic, complemented
485C2×#103C22×C10911yescharacteristic, complemented
486C2×#102C22×C10911yescharacteristic
487C2×#102C22×C10911yescharacteristic
488C2×#102C22×C10911yescharacteristic
489C2×#102C22×C10911yescharacteristic
490C2×#102C22×C10911yescharacteristic
491C2×#102C22×C10911yescharacteristic
492C2×#102C22×C10911yescharacteristic
493C2×#102C22×C10911yescharacteristic
494C2×C22⋊C8C22×C10911yescharacteristic
495C2×C22⋊C8C22×C10911yescharacteristic, complemented
496C2×#97C22×C10911yescharacteristic, complemented
497#390—21no—
498#388—21no—
499#388—21no—
500#384C22×C10911yescharacteristic, complemented
501#380C22×C10911yescharacteristic
502#380C22×C10911yescharacteristic, complemented
503C4×C4⋊C4—21no—
504C4×C4⋊C4C22×C10911yescharacteristic, complemented
505#340C22×C10911yescharacteristic, complemented
506#340C22×C10911yescharacteristic, complemented
507#340C22×C10911yescharacteristic, complemented
508#340C22×C10911yescharacteristic, complemented
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C10914yes—
516C22×Q8C23×C10911yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×C4×C10914yes—
526C22×D4D4×C10911yescharacteristic
527C22×D4C23×C10911yescharacteristic
528C22×D4C23×C10911yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C23×C10911yescharacteristic
532C23×C4C23×C10911yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8C23×C10911yescharacteristic
540C22×C8C23×C10911yescharacteristic
541C22×C8C23×C10911yescharacteristic
542C22×C8C23×C10911yescharacteristic
543#124—22no—
544#124C2×C4×C10914yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×C4×C10914yes—
548#121—22no—
549#121—28no—
550#121C2×C4×C10914yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×C4×C10914yes—
554C4×D4C2×C4×C10914yes—
555C4×D4D4×C10914yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C10911yescharacteristic
564C2×C4⋊C4C23×C10911yescharacteristic
565C2×C4⋊C4C23×C10911yescharacteristic
566C2×C4⋊C4C23×C10911yescharacteristic
567C2×C4⋊C4C23×C10911yescharacteristic
568C2×C4⋊C4C23×C10911yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C10911yescharacteristic
580C2×C22⋊C4D4×C10911yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C10911yescharacteristic
585C4⋊C8—22no—
586#103—22no—
587#103—22no—
588#103—41no—
589#103—41no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102—41no—
597#102D4×C10914yescomplemented
598C22⋊C8—22no—
599C22⋊C8—22no—
600#97—22no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C10911yescharacteristic
614C24C2×D4×C10911yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C10912yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C10914yes—
649C2×D4C22×C4×C10912yes—
650C2×D4C22×C4×C10912yes—
651C2×D4C2×D4×C10912yes—
652C2×D4#41×C10912yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4C22×C4×C10912yes—
674C22×C4C22×C4×C10912yes—
675C22×C4C2×D4×C10911yescharacteristic
676C22×C4C2×D4×C10911yescharacteristic
677C22×C4C2×D4×C10911yescharacteristic
678C22×C4C2×D4×C10911yescharacteristic
679C22×C4C2×D4×C10912yes—
680C22×C4C2×D4×C10912yes—
681C22×C4C24×C10911yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8C2×D4×C10912yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—81no—
707C4⋊C4C22⋊C4×C10914yes—
708C4⋊C4C22×C4×C10912yes—
709C4⋊C4C2×D4×C10912yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4C22⋊C4×C10914yes—
720C22⋊C4C22⋊C4×C10914yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C22×C4×C10912yes—
725C42C2×D4×C10912yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊C4×C10912yes—
760C23C2×C22⋊C4×C10912yes—
761C23C22×D4×C10911yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4C4×D4×C10914yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4C2×C22⋊C4×C10912yes—
815C2×C4C2×C22⋊C4×C10912yes—
816C2×C4C2×C22⋊C4×C10912yes—
817C2×C4C2×C22⋊C4×C10912yes—
818C2×C4C23×C4×C10911yescharacteristic
819C2×C4C22×D4×C10911yescharacteristic
820C2×C4C22×D4×C10911yescharacteristic
821C2×C4C2×#41×C10911yescharacteristic
822C2×C4H(5,𝔽2)×C10911yescharacteristic
823C2×C4H(5,𝔽2)×C10911yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊C4×C10911yescharacteristic
858C22D42×C10911yescharacteristic
859C22#546×C10911yescharacteristic
860C22#575×C10911yescharacteristic
861C22#575×C10911yescharacteristic
862C22#576×C10911yescharacteristic
863C22#577×C10911yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4C2×C4×D4×C10911yescharacteristic
875C4#518×C10911yescharacteristic
876C4D42×C10911yescharacteristic
877C4#546×C10911yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊C4×C10911yescharacteristic
883C2C109×#289611yescharacteristic
884C2C109×#289711yescharacteristic
885C2C109×#326711yescharacteristic
886C2C109×#326811yescharacteristic
887C2C109×#331111yescharacteristic
888C2C109×#331911yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutatorC2×C4C23×C4×C109
Frattini, cosocleC22×C4C24×C109
prime radicalC2×#546×C109C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#435×C109C2semidirect
3. C2×#418×C109C2semidirect
4. C2×#416×C109C2semidirect
5. C109×#2354C2semidirect
6. C109×#1983C2semidirect
7. C109×#1959C2semidirect
8. C109×#1894C2semidirect
9. C109×#1893C2semidirect
10. C109×#1875C2semidirect
11. C109×#1873C2semidirect
12. C109×#1802C2semidirect
13. C109×#1788C2semidirect
14. C109×#1786C2semidirect
15. C109×#1762C2semidirect
19. C23×C8×C109C22semidirect
21. #546×C109C4semidirect
31. C2×#117×C109C22semidirect
34. C2×C4⋊C8×C109C22semidirect
37. C2×#103×C109C22semidirect
38. C2×#103×C109C22semidirect
39. C2×#103×C109C22semidirect
40. C2×#103×C109C22semidirect
50. C2×C22⋊C8×C109C22semidirect
51. C2×#97×C109C22semidirect
55. #384×C109C22semidirect
57. #380×C109C22semidirect
59. C4×C4⋊C4×C109C22semidirect
60. #340×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
63. #340×C109C22semidirect
152. #102×C109D4semidirect
433. #22424C109direct (N × H)
446. C2×#435C2×C109semidirect
447. C2×#418C2×C109semidirect
448. C2×#416C2×C109semidirect
449. #2354C2×C109semidirect
450. #1983C2×C109semidirect
451. #1959C2×C109semidirect
452. #1894C2×C109semidirect
453. #1893C2×C109semidirect
454. #1875C2×C109semidirect
455. #1873C2×C109semidirect
456. #1802C2×C109semidirect
457. #1788C2×C109semidirect
458. #1786C2×C109semidirect
459. #1762C2×C109semidirect
460. C109#22424direct (N × H)
464. C23×C8C22×C109semidirect
466. #546C4×C109semidirect
476. C2×#117C22×C109semidirect
479. C2×C4⋊C8C22×C109semidirect
482. C2×#103C22×C109semidirect
483. C2×#103C22×C109semidirect
484. C2×#103C22×C109semidirect
485. C2×#103C22×C109semidirect
495. C2×C22⋊C8C22×C109semidirect
496. C2×#97C22×C109semidirect
500. #384C22×C109semidirect
502. #380C22×C109semidirect
504. C4×C4⋊C4C22×C109semidirect
505. #340C22×C109semidirect
506. #340C22×C109semidirect
507. #340C22×C109semidirect
508. #340C22×C109semidirect
597. #102D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1092
C2×#435×C1092
C2×#418×C1092
C2×#416×C1092
C109×#23542
C109×#19832
C109×#19592
C109×#18942
C109×#18932
C109×#18752
C109×#18732
C109×#18022
C109×#17882
C109×#17862
C109×#17622
#22424109