Finite Group Databasebeta

← C109×#25148 #42143142

Subgroups — C109×#25148 #42143142

Order 27904.

1402 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C109C211yesmaximal, characteristic, complemented
2C2×#447×C109C211yesmaximal, characteristic, complemented
3C2×#447×C109C211yesmaximal, characteristic, complemented
4C2×C4×D8×C109C211yesmaximal, characteristic, complemented
5C109×#2428C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C109C211yesmaximal, characteristic, complemented
7C109×#2067C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#2033C211yesmaximal, characteristic, complemented
10C109×#2011C211yesmaximal, characteristic, complemented
11C109×#1970C211yesmaximal, characteristic, complemented
12C109×#1923C211yesmaximal, characteristic, complemented
13C109×#1879C211yesmaximal, characteristic, complemented
14C109×#1879C211yesmaximal, characteristic, complemented
15C109×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C22×D8×C109C2211yescharacteristic
18C22×D8×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C2×#127×C109C2211yescharacteristic, complemented
22C2×#121×C109—21no—
23C2×#121×C109C2211yescharacteristic
24C2×#121×C109C2211yescharacteristic
25C2×C4×D4×C109C2211yescharacteristic
26C2×C4×D4×C109C2211yescharacteristic
27C2×C4×D4×C109C2211yescharacteristic, complemented
28C22×C22⋊C4×C109—21no—
29#459×C109—24no—
30#447×C109—24no—
31#447×C109—24no—
32C4×D8×C109—24no—
33C2×#107×C109C2211yescharacteristic, complemented
34C2×#107×C109C2211yescharacteristic, complemented
35C2×C4⋊C8×C109C2211yescharacteristic, complemented
36C2×#102×C109C2211yescharacteristic
37C2×#102×C109C2211yescharacteristic
38C2×#102×C109C2211yescharacteristic
39C2×#102×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic, complemented
41C2×#102×C109C2211yescharacteristic, complemented
42C2×#102×C109C2211yescharacteristic, complemented
43C2×#102×C109C2211yescharacteristic, complemented
44C2×C22⋊C8×C109C2211yescharacteristic
45C2×C22⋊C8×C109C2211yescharacteristic
46C2×C4×C8×C109C2211yescharacteristic, complemented
47#394×C109—21no—
48#392×C109—21no—
49#390×C109C2211yescharacteristic
50#390×C109C2211yescharacteristic
51#390×C109C2211yescharacteristic, complemented
52#389×C109C2211yescharacteristic, complemented
53#386×C109—21no—
54#386×C109—21no—
55#386×C109—21no—
56#380×C109C2211yescharacteristic
57#379×C109—21no—
58C4×C22⋊C4×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic, complemented
60#340×C109C2211yescharacteristic, complemented
61#336×C109C2211yescharacteristic, complemented
62#336×C109C2211yescharacteristic, complemented
63C25×C109—21no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—22no—
68C22×D4×C109—21no—
69C22×D4×C109—21no—
70C22×D4×C109—21no—
71C22×D4×C109—21no—
72C22×D4×C109—21no—
73C22×D4×C109—41no—
74C22×D4×C109—41no—
75C22×D4×C109C2311yescharacteristic
76C22×D4×C109C2311yescharacteristic
77C22×D4×C109C2311yescharacteristic
78C22×D4×C109C2311yescharacteristic
79C23×C4×C109—21no—
80C23×C4×C109—21no—
81C23×C4×C109—21no—
82C23×C4×C109C2311yescharacteristic
83C2×D8×C109—22no—
84C2×D8×C109—22no—
85C2×D8×C109—22no—
86C2×D8×C109—22no—
87C2×D8×C109—22no—
88C2×D8×C109—22no—
89C2×D8×C109—22no—
90C2×D8×C109—22no—
91C2×D8×C109—22no—
92C2×D8×C109—41no—
93C2×D8×C109—41no—
94C2×D8×C109D414yescomplemented
95C22×C8×C109C2311yescharacteristic
96C22×C8×C109C2311yescharacteristic
97C22×C8×C109C2311yescharacteristic
98C22×C8×C109C2311yescharacteristic
99#127×C109—22no—
100#127×C109—41no—
101#121×C109—22no—
102#121×C109—22no—
103#121×C109—41no—
104#121×C109—41no—
105#121×C109—44no—
106C4×D4×C109—22no—
107C4×D4×C109—22no—
108C4×D4×C109—22no—
109C4×D4×C109—41no—
110C4×D4×C109—41no—
111C4×D4×C109—41no—
112C2×C4⋊C4×C109—21no—
113C2×C4⋊C4×C109C2311yescharacteristic
114C2×C4⋊C4×C109C2311yescharacteristic
115C2×C4⋊C4×C109C2311yescharacteristic
116C2×C4⋊C4×C109C2311yescharacteristic
117C2×C22⋊C4×C109—21no—
118C2×C22⋊C4×C109—21no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
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—44no—
130C2×C22⋊C4×C109D411yescharacteristic
131C2×C22⋊C4×C109D411yescharacteristic
132C2×C42×C109C2311yescharacteristic
133C2×C42×C109C2311yescharacteristic
134#107×C109—22no—
135#107×C109—41no—
136C4⋊C8×C109—22no—
137#102×C109—22no—
138#102×C109—22no—
139#102×C109—22no—
140#102×C109—22no—
141#102×C109—22no—
142#102×C109—22no—
143#102×C109—41no—
144#102×C109D414yescomplemented
145C22⋊C8×C109—22no—
146C22⋊C8×C109—22no—
147C4×C8×C109—22no—
148#95×C109—21no—
149#95×C109—21no—
150#95×C109D411yescharacteristic
151#95×C109D411yescharacteristic
152C24×C109—21no—
153C24×C109—24no—
154C24×C109—21no—
155C24×C109—21no—
156C24×C109—21no—
157C24×C109—42no—
158C24×C109—42no—
159C24×C109—42no—
160C24×C109—42no—
161C24×C109—81no—
162C24×C109—81no—
163C24×C109C2×D411yescharacteristic
164C2×D4×C109—24no—
165C2×D4×C109—21no—
166C2×D4×C109—21no—
167C2×D4×C109—21no—
168C2×D4×C109—21no—
169C2×D4×C109—21no—
170C2×D4×C109—21no—
171C2×D4×C109—21no—
172C2×D4×C109—21no—
173C2×D4×C109—21no—
174C2×D4×C109—21no—
175C2×D4×C109—21no—
176C2×D4×C109—21no—
177C2×D4×C109—21no—
178C2×D4×C109—21no—
179C2×D4×C109—21no—
180C2×D4×C109—21no—
181C2×D4×C109—21no—
182C2×D4×C109—21no—
183C2×D4×C109—21no—
184C2×D4×C109—42no—
185C2×D4×C109—42no—
186C2×D4×C109—42no—
187C2×D4×C109—42no—
188C2×D4×C109—42no—
189C2×D4×C109—42no—
190C2×D4×C109—44no—
191C2×D4×C109—44no—
192C2×D4×C109—44no—
193C2×D4×C109—44no—
194C2×D4×C109—42no—
195C2×D4×C109—42no—
196C2×D4×C109—42no—
197C2×D4×C109—42no—
198C2×D4×C109—81no—
199C2×D4×C109—81no—
200C2×D4×C109—81no—
201C2×D4×C109—81no—
202C2×D4×C109C2×D412yes—
203C2×D4×C109C2×D412yes—
204C2×D4×C109C2×D412yes—
205C2×D4×C109#4112yes—
206C2×D4×C109#4112yes—
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—42no—
218C22×C4×C109—42no—
219C22×C4×C109—42no—
220C22×C4×C109—42no—
221C22×C4×C109—42no—
222C22×C4×C109—42no—
223C22×C4×C109—81no—
224C22×C4×C109—81no—
225C22×C4×C109—81no—
226C22×C4×C109C2×D411yescharacteristic
227C22×C4×C109C2×D411yescharacteristic
228C22×C4×C109C2×D411yescharacteristic
229C22×C4×C109C2×D411yescharacteristic
230C22×C4×C109C2×D411yescharacteristic
231C22×C4×C109C2411yescharacteristic
232D8×C109—28no—
233D8×C109—44no—
234D8×C109—44no—
235D8×C109—44no—
236C2×C8×C109—21no—
237C2×C8×C109—21no—
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×C109C2×D412yes—
247C2×C8×C109C2×D412yes—
248C4⋊C4×C109—21no—
249C4⋊C4×C109—21no—
250C4⋊C4×C109—21no—
251C4⋊C4×C109—21no—
252C4⋊C4×C109—21no—
253C4⋊C4×C109—21no—
254C4⋊C4×C109—21no—
255C4⋊C4×C109—42no—
256C4⋊C4×C109C2×D412yes—
257C22⋊C4×C109—41no—
258C22⋊C4×C109—42no—
259C22⋊C4×C109—42no—
260C22⋊C4×C109—42no—
261C22⋊C4×C109—42no—
262C22⋊C4×C109—42no—
263C22⋊C4×C109—42no—
264C22⋊C4×C109—42no—
265C22⋊C4×C109—42no—
266C22⋊C4×C109—42no—
267C22⋊C4×C109—81no—
268C22⋊C4×C109—81no—
269C22⋊C4×C109—81no—
270C22⋊C4×C109D814yescomplemented
271C42×C109—21no—
272C42×C109—21no—
273C42×C109—21no—
274C42×C109—21no—
275C23×C109—21no—
276C23×C109—22no—
277C23×C109—22no—
278C23×C109—22no—
279C23×C109—21no—
280C23×C109—21no—
281C23×C109—21no—
282C23×C109—21no—
283C23×C109—21no—
284C23×C109—22no—
285C23×C109—22no—
286C23×C109—48no—
287C23×C109—48no—
288C23×C109—41no—
289C23×C109—41no—
290C23×C109—41no—
291C23×C109—41no—
292C23×C109—41no—
293C23×C109—41no—
294C23×C109—41no—
295C23×C109—41no—
296C23×C109—41no—
297C23×C109—41no—
298C23×C109—41no—
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—84no—
312C23×C109—84no—
313C23×C109—84no—
314C23×C109—84no—
315C23×C109—84no—
316C23×C109C2×D812yes—
317C23×C109C22×D411yescharacteristic
318D4×C109—22no—
319D4×C109—22no—
320D4×C109—22no—
321D4×C109—22no—
322D4×C109—22no—
323D4×C109—22no—
324D4×C109—22no—
325D4×C109—48no—
326D4×C109—41no—
327D4×C109—41no—
328D4×C109—41no—
329D4×C109—41no—
330D4×C109—41no—
331D4×C109—41no—
332D4×C109—41no—
333D4×C109—41no—
334D4×C109—84no—
335D4×C109—84no—
336D4×C109—84no—
337D4×C109—84no—
338D4×C109#12114yescomplemented
339C2×C4×C109—21no—
340C2×C4×C109—21no—
341C2×C4×C109—21no—
342C2×C4×C109—21no—
343C2×C4×C109—21no—
344C2×C4×C109—21no—
345C2×C4×C109—21no—
346C2×C4×C109—22no—
347C2×C4×C109—21no—
348C2×C4×C109—21no—
349C2×C4×C109—21no—
350C2×C4×C109—21no—
351C2×C4×C109—21no—
352C2×C4×C109—21no—
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×C109—84no—
370C2×C4×C109—84no—
371C2×C4×C109C2×D812yes—
372C2×C4×C109C2×D812yes—
373C2×C4×C109C22×D411yescharacteristic
374C2×C4×C109C22×D411yescharacteristic
375C2×C4×C109C2×#4111yescharacteristic
376C2×C4×C109C2×#4111yescharacteristic
377C2×C4×C109H(5,𝔽2)11yescharacteristic
378C2×C4×C109H(5,𝔽2)11yescharacteristic
379C8×C109—22no—
380C8×C109—22no—
381C8×C109—41no—
382C8×C109—41no—
383C22×C109—22no—
384C22×C109—24no—
385C22×C109—22no—
386C22×C109—22no—
387C22×C109—42no—
388C22×C109—41no—
389C22×C109—42no—
390C22×C109—41no—
391C22×C109—41no—
392C22×C109—42no—
393C22×C109—41no—
394C22×C109—42no—
395C22×C109—42no—
396C22×C109—42no—
397C22×C109—42no—
398C22×C109—42no—
399C22×C109—42no—
400C22×C109—42no—
401C22×C109—42no—
402C22×C109—42no—
403C22×C109—816no—
404C22×C109—81no—
405C22×C109—81no—
406C22×C109—81no—
407C22×C109—81no—
408C22×C109—81no—
409C22×C109—81no—
410C22×C109—81no—
411C22×C109—81no—
412C22×C109—81no—
413C22×C109—81no—
414C22×C109—81no—
415C22×C109—81no—
416C22×C109—81no—
417C22×C109—81no—
418C22×C109—81no—
419C22×C109#52511yescharacteristic
420C22×C109D4211yescharacteristic
421C22×C109D4211yescharacteristic
422C22×C109C22×D811yescharacteristic
423C22×C109#57511yescharacteristic
424C22×C109#57611yescharacteristic
425C22×C109#57611yescharacteristic
426C4×C109—22no—
427C4×C109—22no—
428C4×C109—41no—
429C4×C109—41no—
430C4×C109—41no—
431C4×C109—42no—
432C4×C109—81no—
433C4×C109—81no—
434C4×C109—81no—
435C4×C109C2×#12111yescharacteristic
436C4×C109#53811yescharacteristic
437C4×C109#54611yescharacteristic
438C4×C109#54611yescharacteristic
439#25148C10911yesmaximal, characteristic, direct product factor, Sylow
440C2×C109—42no—
441C2×C109—44no—
442C2×C109—82no—
443C2×C109—82no—
444C2×C109—161no—
445C2×C109#242411yescharacteristic
446C2×C109#310011yescharacteristic
447C2×C109#312211yescharacteristic
448C2×C109#326811yescharacteristic
449C2×C109#327311yescharacteristic
450C2×C109D4×D811yescharacteristic
451C2×C109D4×D811yescharacteristic
452C2×#459C2×C10911yescharacteristic, complemented
453C2×#447C2×C10911yescharacteristic, complemented
454C2×#447C2×C10911yescharacteristic, complemented
455C2×C4×D8C2×C10911yescharacteristic, complemented
456#2428C2×C10911yescharacteristic, complemented
457D4×C22⋊C4C2×C10911yescharacteristic, complemented
458#2067C2×C10911yescharacteristic, complemented
459#2033C2×C10911yescharacteristic, complemented
460#2033C2×C10911yescharacteristic, complemented
461#2011C2×C10911yescharacteristic, complemented
462#1970C2×C10911yescharacteristic, complemented
463#1923C2×C10911yescharacteristic, complemented
464#1879C2×C10911yescharacteristic, complemented
465#1879C2×C10911yescharacteristic, complemented
466#1862C2×C10911yescharacteristic, complemented
467C109#2514811yescharacteristic, direct product factor, Sylow
468C23×D4C22×C10911yescharacteristic
469C22×D8C22×C10911yescharacteristic
470C22×D8C22×C10911yescharacteristic
471C22×D8C22×C10911yescharacteristic
472C22×D8C22×C10911yescharacteristic
473C2×#127C22×C10911yescharacteristic, complemented
474C2×#121—21no—
475C2×#121C22×C10911yescharacteristic
476C2×#121C22×C10911yescharacteristic
477C2×C4×D4C22×C10911yescharacteristic
478C2×C4×D4C22×C10911yescharacteristic
479C2×C4×D4C22×C10911yescharacteristic, complemented
480C22×C22⋊C4—21no—
481#459—24no—
482#447—24no—
483#447—24no—
484C4×D8—24no—
485C2×#107C22×C10911yescharacteristic, complemented
486C2×#107C22×C10911yescharacteristic, complemented
487C2×C4⋊C8C22×C10911yescharacteristic, complemented
488C2×#102C22×C10911yescharacteristic
489C2×#102C22×C10911yescharacteristic
490C2×#102C22×C10911yescharacteristic
491C2×#102C22×C10911yescharacteristic
492C2×#102C22×C10911yescharacteristic, complemented
493C2×#102C22×C10911yescharacteristic, complemented
494C2×#102C22×C10911yescharacteristic, complemented
495C2×#102C22×C10911yescharacteristic, complemented
496C2×C22⋊C8C22×C10911yescharacteristic
497C2×C22⋊C8C22×C10911yescharacteristic
498C2×C4×C8C22×C10911yescharacteristic, complemented
499#394—21no—
500#392—21no—
501#390C22×C10911yescharacteristic
502#390C22×C10911yescharacteristic
503#390C22×C10911yescharacteristic, complemented
504#389C22×C10911yescharacteristic, complemented
505#386—21no—
506#386—21no—
507#386—21no—
508#380C22×C10911yescharacteristic
509#379—21no—
510C4×C22⋊C4C22×C10911yescharacteristic
511#340C22×C10911yescharacteristic, complemented
512#340C22×C10911yescharacteristic, complemented
513#336C22×C10911yescharacteristic, complemented
514#336C22×C10911yescharacteristic, complemented
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C23×C10911yescharacteristic
528C22×D4C23×C10911yescharacteristic
529C22×D4C23×C10911yescharacteristic
530C22×D4C23×C10911yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C23×C10911yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8D4×C10914yescomplemented
547C22×C8C23×C10911yescharacteristic
548C22×C8C23×C10911yescharacteristic
549C22×C8C23×C10911yescharacteristic
550C22×C8C23×C10911yescharacteristic
551#127—22no—
552#127—41no—
553#121—22no—
554#121—22no—
555#121—41no—
556#121—41no—
557#121—44no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C2×C4⋊C4—21no—
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—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—44no—
582C2×C22⋊C4D4×C10911yescharacteristic
583C2×C22⋊C4D4×C10911yescharacteristic
584C2×C42C23×C10911yescharacteristic
585C2×C42C23×C10911yescharacteristic
586#107—22no—
587#107—41no—
588C4⋊C8—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102D4×C10914yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—21no—
601#95—21no—
602#95D4×C10911yescharacteristic
603#95D4×C10911yescharacteristic
604C24—21no—
605C24—24no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C10911yescharacteristic
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4C2×D4×C10912yes—
655C2×D4C2×D4×C10912yes—
656C2×D4C2×D4×C10912yes—
657C2×D4#41×C10912yes—
658C2×D4#41×C10912yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—81no—
678C22×C4C2×D4×C10911yescharacteristic
679C22×C4C2×D4×C10911yescharacteristic
680C22×C4C2×D4×C10911yescharacteristic
681C22×C4C2×D4×C10911yescharacteristic
682C22×C4C2×D4×C10911yescharacteristic
683C22×C4C24×C10911yescharacteristic
684D8—28no—
685D8—44no—
686D8—44no—
687D8—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8C2×D4×C10912yes—
699C2×C8C2×D4×C10912yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4C2×D4×C10912yes—
709C22⋊C4—41no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C22⋊C4D8×C10914yescomplemented
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—22no—
738C23—48no—
739C23—48no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23C2×D8×C10912yes—
769C23C22×D4×C10911yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4#121×C10914yescomplemented
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
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—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4C2×D8×C10912yes—
824C2×C4C2×D8×C10912yes—
825C2×C4C22×D4×C10911yescharacteristic
826C2×C4C22×D4×C10911yescharacteristic
827C2×C4C2×#41×C10911yescharacteristic
828C2×C4C2×#41×C10911yescharacteristic
829C2×C4H(5,𝔽2)×C10911yescharacteristic
830C2×C4H(5,𝔽2)×C10911yescharacteristic
831C8—22no—
832C8—22no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—24no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—816no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22#525×C10911yescharacteristic
872C22D42×C10911yescharacteristic
873C22D42×C10911yescharacteristic
874C22C22×D8×C10911yescharacteristic
875C22#575×C10911yescharacteristic
876C22#576×C10911yescharacteristic
877C22#576×C10911yescharacteristic
878C4—22no—
879C4—22no—
880C4—41no—
881C4—41no—
882C4—42no—
883C4—41no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4C2×#121×C10911yescharacteristic
888C4#538×C10911yescharacteristic
889C4#546×C10911yescharacteristic
890C4#546×C10911yescharacteristic
891C2—42no—
892C2—44no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2C109×#242411yescharacteristic
897C2C109×#310011yescharacteristic
898C2C109×#312211yescharacteristic
899C2C109×#326811yescharacteristic
900C2C109×#327311yescharacteristic
901C2D4×D8×C10911yescharacteristic
902C2D4×D8×C10911yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C22⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C109C2semidirect
2. C2×#447×C109C2semidirect
3. C2×#447×C109C2semidirect
4. C2×C4×D8×C109C2semidirect
5. C109×#2428C2semidirect
6. D4×C22⋊C4×C109C2semidirect
7. C109×#2067C2semidirect
8. C109×#2033C2semidirect
9. C109×#2033C2semidirect
10. C109×#2011C2semidirect
11. C109×#1970C2semidirect
12. C109×#1923C2semidirect
13. C109×#1879C2semidirect
14. C109×#1879C2semidirect
15. C109×#1862C2semidirect
21. C2×#127×C109C22semidirect
27. C2×C4×D4×C109C22semidirect
33. C2×#107×C109C22semidirect
34. C2×#107×C109C22semidirect
35. C2×C4⋊C8×C109C22semidirect
40. C2×#102×C109C22semidirect
41. C2×#102×C109C22semidirect
42. C2×#102×C109C22semidirect
43. C2×#102×C109C22semidirect
46. C2×C4×C8×C109C22semidirect
51. #390×C109C22semidirect
52. #389×C109C22semidirect
59. #340×C109C22semidirect
60. #340×C109C22semidirect
61. #336×C109C22semidirect
62. #336×C109C22semidirect
94. C2×D8×C109D4semidirect
144. #102×C109D4semidirect
270. C22⋊C4×C109D8semidirect
338. D4×C109#121semidirect
439. #25148C109direct (N × H)
452. C2×#459C2×C109semidirect
453. C2×#447C2×C109semidirect
454. C2×#447C2×C109semidirect
455. C2×C4×D8C2×C109semidirect
456. #2428C2×C109semidirect
457. D4×C22⋊C4C2×C109semidirect
458. #2067C2×C109semidirect
459. #2033C2×C109semidirect
460. #2033C2×C109semidirect
461. #2011C2×C109semidirect
462. #1970C2×C109semidirect
463. #1923C2×C109semidirect
464. #1879C2×C109semidirect
465. #1879C2×C109semidirect
466. #1862C2×C109semidirect
467. C109#25148direct (N × H)
473. C2×#127C22×C109semidirect
479. C2×C4×D4C22×C109semidirect
485. C2×#107C22×C109semidirect
486. C2×#107C22×C109semidirect
487. C2×C4⋊C8C22×C109semidirect
492. C2×#102C22×C109semidirect
493. C2×#102C22×C109semidirect
494. C2×#102C22×C109semidirect
495. C2×#102C22×C109semidirect
498. C2×C4×C8C22×C109semidirect
503. #390C22×C109semidirect
504. #389C22×C109semidirect
511. #340C22×C109semidirect
512. #340C22×C109semidirect
513. #336C22×C109semidirect
514. #336C22×C109semidirect
546. C2×D8D4×C109semidirect
596. #102D4×C109semidirect
722. C22⋊C4D8×C109semidirect
790. D4#121×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1092
C2×#447×C1092
C2×C4×D8×C1092
C109×#24282
D4×C22⋊C4×C1092
C109×#20672
C109×#20332
C109×#20112
C109×#19702
C109×#19232
C109×#18792
C109×#18622
#25148109