Finite Group Databasebeta

← C2×#11744105 #14261506

Subgroups — C2×#11744105 #14261506

Order 1792.

6446 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic, complemented
2#11744105C2132yesmaximal, direct product factor
3C2×#90426C212yesmaximal, complemented
4C2×#90420C212yesmaximal, complemented
5C2×#90424C211yesmaximal, characteristic
6C2×#90413C211yesmaximal, characteristic, complemented
7C2×#90390C212yesmaximal, complemented
8C2×#90384C212yesmaximal, complemented
9C2×#90388C211yesmaximal, characteristic, complemented
10C2×#90376C211yesmaximal, characteristic, complemented
11C2×#90381C211yesmaximal, characteristic, complemented
12C2×#90387C212yesmaximal, complemented
13C2×#90387C212yesmaximal, complemented
14C2×#90382C211yesmaximal, characteristic
15C2×#90273C211yesmaximal, characteristic
16C2×#90274C211yesmaximal, characteristic, complemented
17C2×#90274C212yesmaximal, complemented
18C2×#90269C211yesmaximal, characteristic, complemented
19C2×#90269C211yesmaximal, characteristic, complemented
20C2×#90258C211yesmaximal, characteristic, complemented
21C2×#90259C211yesmaximal, characteristic, complemented
22C2×#90259C212yesmaximal, complemented
23C2×#90259C211yesmaximal, characteristic, complemented
24C2×#90275C211yesmaximal, characteristic, complemented
25C7×#557C22116yescomplemented
26C2×C7×C4⋊Q8C2211yescharacteristic
27C2×C7×C4⋊Q8C2212yes—
28C2×C7×#125C2211yescharacteristic
29C2×C7×#125C2212yes—
30C2×C7×#125C2212yes—
31C2×C7×#125C2211yescharacteristic
32C2×C4×C7×Q8C2211yescharacteristic
33C2×C4×C7×Q8C2211yescharacteristic
34C2×C4×C7×Q8C2211yescharacteristic
35C2×C4×C7×Q8C2212yes—
36C2×C4×C7×Q8C2211yescharacteristic
37C2×#6510C2212yes—
38C2×#6510C2211yescharacteristic
39C2×#6509C2212yes—
40C2×#6509C2212yes—
41C2×#6509C2211yescharacteristic
42C2×#6509C2211yescharacteristic
43C2×#6507C2212yes—
44C2×#6507C2212yes—
45C2×#6507C2211yescharacteristic
46C2×#6507C2211yescharacteristic
47C2×#6507C2211yescharacteristic
48#90426C22132yescomplemented
49#90424C22116yes—
50#90420C22132yescomplemented
51#90413C22116yescomplemented
52#90390C22132yescomplemented
53#90388C22116yescomplemented
54#90387C22132yescomplemented
55#90387C22132yescomplemented
56#90384C22132yescomplemented
57#90382C22116yes—
58#90381C22116yescomplemented
59#90376C22116yescomplemented
60#90275C22116yescomplemented
61#90274C22132yescomplemented
62#90274C22116yescomplemented
63#90273C22116yes—
64#90269C22116yescomplemented
65#90269C22116yescomplemented
66#90259C22116yescomplemented
67#90259C22132yescomplemented
68#90259C22116yescomplemented
69#90258C22116yescomplemented
70C2×#6461C2212yes—
71C2×#6461C2212yes—
72C2×#6461C2212yes—
73C2×#6461C2212yes—
74C2×#6461C2212yes—
75C2×#6461C2212yes—
76C2×#6461C2212yes—
77C2×#6461C2212yes—
78C2×#6461C2212yes—
79C2×#6460C2211yescharacteristic
80C2×#6460C2211yescharacteristic
81C2×#6460C2211yescharacteristic
82C2×#6460C2212yes—
83C2×#6459C2212yes—
84C2×#6459C2212yes—
85C2×#6459C2212yes—
86C2×#6459C2212yes—
87C2×#6459C2211yescharacteristic
88C2×#6459C2212yes—
89C2×#6459C2212yes—
90C2×#6459C2211yescharacteristic
91C2×#6458C2211yescharacteristic
92C2×#6457C2212yes—
93C2×#6457C2212yes—
94C2×#6457C2212yes—
95C2×#6456C2211yescharacteristic
96C2×#6456C2211yescharacteristic
97C2×#6456C2212yes—
98C2×#6455C2212yes—
99C2×#6455C2212yes—
100C2×D7×C4⋊C4C2212yes—
101C2×#6453C2212yes—
102C2×#6453C2212yes—
103C2×#6453C2211yescharacteristic
104C2×#6452C2212yes—
105C2×#6452C2212yes—
106C2×#6452C2212yes—
107C2×#6452C2212yes—
108C2×#6452C2211yescharacteristic
109C2×#6452C2211yescharacteristic
110C2×#6452C2212yes—
111C2×#6452C2212yes—
112C2×#6451C2211yescharacteristic
113C2×#6451C2211yescharacteristic
114C2×#6451C2212yes—
115C2×#6451C2212yes—
116C2×#6451C2211yescharacteristic
117C2×#6450C2211yescharacteristic
118C2×#6450C2211yescharacteristic
119C2×#6450C2212yes—
120C2×#6450C2211yescharacteristic
121C2×#6450C2212yes—
122C2×#6450C2211yescharacteristic
123C2×#6439C2212yes—
124C2×#6439C2212yes—
125C2×#6439C2212yes—
126C2×#6439C2212yes—
127C2×#6438C2211yescharacteristic
128C2×#6438C2211yescharacteristic
129C2×#6438C2212yes—
130C2×C4×D28C2211yescharacteristic
131C2×#6435C2211yescharacteristic
132C2×#6435C2212yes—
133C2×#6435C2212yes—
134C2×#6435C2212yes—
135C2×#6435C2211yescharacteristic
136C2×C42×D7C2211yescharacteristic
137C2×#6433C2212yes—
138C2×#6433C2212yes—
139C2×#6432C2211yescharacteristic
140C2×C4×Dic14C2211yescharacteristic
141C2×C4×Dic14C2211yescharacteristic
142C2×C4×Dic14C2211yescharacteristic
143C2×C4×Dic14C2212yes—
144C2×C4×Dic14C2211yescharacteristic
145C2×C4×Dic14C2211yescharacteristic
146C2×C4×Dic14C2212yes—
147C2×#3555—71nomaximal, Sylow
148C22×C7×Q8C2311yescharacteristic
149C22×C7×Q8C2312yes—
150C22×C7×Q8C2311yescharacteristic
151C22×D28C2311yescharacteristic
152C22×D28C2312yes—
153C22×C4×D7C2311yescharacteristic
154C22×C4×D7C2311yescharacteristic
155C22×C4×D7C2312yes—
156C22×C4×D7C2311yescharacteristic
157C22×C4×D7C2312yes—
158C22×C4×D7C2312yes—
159C22×Dic14C2311yescharacteristic
160C22×Dic14C2311yescharacteristic
161C22×Dic14C2311yescharacteristic
162C22×Dic14C2311yescharacteristic
163C22×Dic14C2311yescharacteristic
164C22×Dic14C2312yes—
165C22×Dic14C2312yes—
166C7×C4⋊Q8C2318yes—
167C7×C4⋊Q8C23116yes—
168C7×#125C2318yes—
169C7×#125C2318yes—
170C7×#125C23116yes—
171C7×#125C23116yes—
172C4×C7×Q8C2318yes—
173C4×C7×Q8C2318yes—
174C4×C7×Q8C2318yes—
175C4×C7×Q8C23116yes—
176C4×C7×Q8C2318yes—
177C2×C7×C4⋊C4C2311yescharacteristic
178C2×C7×C4⋊C4C2311yescharacteristic
179C2×C7×C4⋊C4C2312yes—
180C2×C7×C4⋊C4C2312yes—
181C2×C7×C4⋊C4C2311yescharacteristic
182C2×C7×C4⋊C4C2312yes—
183C2×C7×C4⋊C4C2311yescharacteristic
184C2×C7×C4⋊C4C2312yes—
185C2×C7×C4⋊C4C2311yescharacteristic
186C2×C7×C4⋊C4C2312yes—
187C2×C7×C4⋊C4C2311yescharacteristic
188C2×C7×C4⋊C4C2312yes—
189C2×C7×C4⋊C4C2312yes—
190C2×C7×C4⋊C4C2312yes—
191C2×C42×C7C2311yescharacteristic
192C2×C42×C7C2311yescharacteristic
193C2×C42×C7C2311yescharacteristic
194C2×C42×C7C2312yes—
195C2×C42×C7C2312yes—
196C2×C42×C7C2312yes—
197#6510C23116yes—
198#6510C2318yes—
199#6509C23116yes—
200#6509C23116yes—
201#6509C2318yes—
202#6509C2318yes—
203#6507C23116yes—
204#6507C23116yes—
205#6507C2318yes—
206#6507C2318yes—
207#6507C2318yes—
208C2×(C2×D7)⋊C4C2311yescharacteristic
209C2×(C2×D7)⋊C4C2312yes—
210C2×(C2×D7)⋊C4C2312yes—
211C2×(C2×D7)⋊C4C2312yes—
212C2×(C2×D7)⋊C4C2312yes—
213C2×(C2×D7)⋊C4C2312yes—
214C2×(C2×D7)⋊C4C2311yescharacteristic
215C2×(C2×D7)⋊C4C2311yescharacteristic
216C2×(C2×D7)⋊C4C2311yescharacteristic
217C2×(C2×D7)⋊C4C2312yes—
218C2×(C2×D7)⋊C4C2312yes—
219C2×(C2×D7)⋊C4C2312yes—
220C2×(C2×D7)⋊C4C2312yes—
221C2×(C2×D7)⋊C4C2312yes—
222C2×(C2×D7)⋊C4C2312yes—
223C2×(C2×D7)⋊C4C2312yes—
224C2×(C2×D7)⋊C4C2312yes—
225C2×C4⋊Dic7C2311yescharacteristic
226C2×C4⋊Dic7C2312yes—
227C2×C4⋊Dic7C2311yescharacteristic
228C2×C4⋊Dic7C2311yescharacteristic
229C2×C4⋊Dic7C2311yescharacteristic
230C2×C4⋊Dic7C2312yes—
231C2×C4⋊Dic7C2312yes—
232C2×C4⋊Dic7C2312yes—
233C2×C4⋊Dic7C2312yes—
234C2×Dic7⋊C4C2312yes—
235C2×Dic7⋊C4C2312yes—
236C2×Dic7⋊C4C2312yes—
237C2×Dic7⋊C4C2311yescharacteristic
238C2×Dic7⋊C4C2312yes—
239C2×Dic7⋊C4C2311yescharacteristic
240C2×Dic7⋊C4C2311yescharacteristic
241C2×Dic7⋊C4C2312yes—
242C2×Dic7⋊C4C2311yescharacteristic
243C2×Dic7⋊C4C2312yes—
244C2×Dic7⋊C4C2311yescharacteristic
245C2×Dic7⋊C4C2311yescharacteristic
246C2×Dic7⋊C4C2312yes—
247C2×Dic7⋊C4C2311yescharacteristic
248C2×Dic7⋊C4C2312yes—
249C2×Dic7⋊C4C2312yes—
250C2×Dic7⋊C4C2311yescharacteristic
251C2×Dic7⋊C4C2312yes—
252C2×Dic7⋊C4C2311yescharacteristic
253C2×Dic7⋊C4C2311yescharacteristic
254C2×Dic7⋊C4C2312yes—
255C2×Dic7⋊C4C2312yes—
256C2×Dic7⋊C4C2312yes—
257C2×Dic7⋊C4C2312yes—
258C2×C4×Dic7C2311yescharacteristic
259C2×C4×Dic7C2311yescharacteristic
260C2×C4×Dic7C2311yescharacteristic
261C2×C4×Dic7C2312yes—
262C2×C4×Dic7C2311yescharacteristic
263C2×C4×Dic7C2312yes—
264C2×C4×Dic7C2312yes—
265C2×C4×Dic7C2312yes—
266C2×C4×Dic7C2311yescharacteristic
267C2×C4×Dic7C2312yes—
268C2×C4×Dic7C2312yes—
269#6461C23116yes—
270#6461C23116yes—
271#6461C23116yes—
272#6461C23116yes—
273#6461C23116yes—
274#6461C23116yes—
275#6461C23116yes—
276#6461C23116yes—
277#6461C23116yes—
278#6460C23116yes—
279#6460C2318yes—
280#6460C2318yes—
281#6460C2318yes—
282#6459C23116yes—
283#6459C23116yes—
284#6459C2318yes—
285#6459C23116yes—
286#6459C23116yes—
287#6459C23116yes—
288#6459C23116yes—
289#6459C2318yes—
290#6458C2318yes—
291#6457C23116yes—
292#6457C23116yes—
293#6457C23116yes—
294#6456C2318yes—
295#6456C2318yes—
296#6456C23116yes—
297#6455C23116yes—
298#6455C23116yes—
299D7×C4⋊C4C23116yes—
300#6453C2318yes—
301#6453C23116yes—
302#6453C23116yes—
303#6452C23116yes—
304#6452C23116yes—
305#6452C23116yes—
306#6452C2318yes—
307#6452C23116yes—
308#6452C23116yes—
309#6452C23116yes—
310#6452C2318yes—
311#6451C23116yes—
312#6451C2318yes—
313#6451C2318yes—
314#6451C2318yes—
315#6451C23116yes—
316#6450C23116yes—
317#6450C2318yes—
318#6450C2318yes—
319#6450C2318yes—
320#6450C23116yes—
321#6450C2318yes—
322#6439C23116yes—
323#6439C23116yes—
324#6439C23116yes—
325#6439C23116yes—
326#6438C2318yes—
327#6438C23116yes—
328#6438C2318yes—
329C4×D28C2318yes—
330#6435C23116yes—
331#6435C23116yes—
332#6435C2318yes—
333#6435C23116yes—
334#6435C2318yes—
335C42×D7C2318yes—
336#6433C23116yes—
337#6433C23116yes—
338#6432C2318yes—
339C4×Dic14C2318yes—
340C4×Dic14C2318yes—
341C4×Dic14C2318yes—
342C4×Dic14C23116yes—
343C4×Dic14C23116yes—
344C4×Dic14C2318yes—
345C4×Dic14C2318yes—
346#3555—732no—
347C2×#563—72no—
348C2×#563—72no—
349C2×Q82—71no—
350C2×#557—71no—
351C2×#557—71no—
352C2×#557D711yescharacteristic, complemented
353C2×#556—71no—
354C2×#556—72no—
355C2×#556—71no—
356C2×#556—71no—
357C2×#554—71no—
358C2×#552—72no—
359C2×#544—72no—
360C2×#542—71no—
361C2×#542—71no—
362C2×#541—72no—
363C2×#541—72no—
364C2×#541—71no—
365C2×#541—71no—
366C2×#541—72no—
367C2×#533—71no—
368C2×#533—71no—
369C2×#529—71no—
370C23×D7C2411yescharacteristic
371C23×D7C2412yes—
372C2×C7×Q8—24no—
373C2×C7×Q8—44no—
374C2×C7×Q8—42no—
375C2×C7×Q8C2414yes—
376C2×C7×Q8C2418yes—
377C2×C7×Q8C2414yes—
378C22×C4×C7C2411yescharacteristic
379C22×C4×C7C2412yes—
380C22×C4×C7C2411yescharacteristic
381C22×C4×C7C2412yes—
382C22×C4×C7C2411yescharacteristic
383C22×C4×C7C2412yes—
384C22×C4×C7C2412yes—
385C22×C4×C7C2411yescharacteristic
386C22×C4×C7C2411yescharacteristic
387C22×C4×C7C2411yescharacteristic
388C22×C4×C7C2411yescharacteristic
389C22×Dic7C2411yescharacteristic
390C22×Dic7C2411yescharacteristic
391C22×Dic7C2412yes—
392C22×Dic7C2412yes—
393C22×Dic7C2411yescharacteristic
394C22×Dic7C2411yescharacteristic
395C22×Dic7C2411yescharacteristic
396C22×Dic7C2412yes—
397C22×Dic7C2411yescharacteristic
398C22×Dic7C2411yescharacteristic
399C2×D28—24no—
400C2×D28—44no—
401C2×D28C2414yes—
402C2×D28C2418yes—
403C2×C4×D7—24no—
404C2×C4×D7—24no—
405C2×C4×D7—28no—
406C2×C4×D7—42no—
407C2×C4×D7—44no—
408C2×C4×D7—44no—
409C2×C4×D7C2414yes—
410C2×C4×D7C2414yes—
411C2×C4×D7C2418yes—
412C2×C4×D7C2414yes—
413C2×C4×D7C2418yes—
414C2×C4×D7C2418yes—
415C2×Dic14—24no—
416C2×Dic14—24no—
417C2×Dic14—24no—
418C2×Dic14—24no—
419C2×Dic14—44no—
420C2×Dic14—42no—
421C2×Dic14—44no—
422C2×Dic14C2414yes—
423C2×Dic14C2414yes—
424C2×Dic14C2414yes—
425C2×Dic14C2414yes—
426C2×Dic14C2414yes—
427C2×Dic14C2418yes—
428C2×Dic14C2418yes—
429C7×C4⋊C4C2414yes—
430C7×C4⋊C4C2414yes—
431C7×C4⋊C4C2418yes—
432C7×C4⋊C4C2418yes—
433C7×C4⋊C4C2414yes—
434C7×C4⋊C4C2418yes—
435C7×C4⋊C4C2414yes—
436C7×C4⋊C4C2418yes—
437C7×C4⋊C4C2414yes—
438C7×C4⋊C4C2418yes—
439C7×C4⋊C4C2414yes—
440C7×C4⋊C4C2418yes—
441C7×C4⋊C4C2418yes—
442C7×C4⋊C4C2418yes—
443C42×C7C2414yes—
444C42×C7C2414yes—
445C42×C7C2414yes—
446C42×C7C2418yes—
447C42×C7C2418yes—
448C42×C7C2418yes—
449(C2×D7)⋊C4C2414yes—
450(C2×D7)⋊C4C2418yes—
451(C2×D7)⋊C4C2418yes—
452(C2×D7)⋊C4C2418yes—
453(C2×D7)⋊C4C2418yes—
454(C2×D7)⋊C4C2418yes—
455(C2×D7)⋊C4C2414yes—
456(C2×D7)⋊C4C2414yes—
457(C2×D7)⋊C4C2414yes—
458(C2×D7)⋊C4C2418yes—
459(C2×D7)⋊C4C2418yes—
460(C2×D7)⋊C4C2418yes—
461(C2×D7)⋊C4C2418yes—
462(C2×D7)⋊C4C2418yes—
463(C2×D7)⋊C4C2418yes—
464(C2×D7)⋊C4C2418yes—
465(C2×D7)⋊C4C2418yes—
466C4⋊Dic7C2414yes—
467C4⋊Dic7C2418yes—
468C4⋊Dic7C2414yes—
469C4⋊Dic7C2414yes—
470C4⋊Dic7C2414yes—
471C4⋊Dic7C2418yes—
472C4⋊Dic7C2418yes—
473C4⋊Dic7C2418yes—
474C4⋊Dic7C2418yes—
475Dic7⋊C4C2418yes—
476Dic7⋊C4C2418yes—
477Dic7⋊C4C2418yes—
478Dic7⋊C4C2414yes—
479Dic7⋊C4C2418yes—
480Dic7⋊C4C2414yes—
481Dic7⋊C4C2414yes—
482Dic7⋊C4C2418yes—
483Dic7⋊C4C2414yes—
484Dic7⋊C4C2418yes—
485Dic7⋊C4C2414yes—
486Dic7⋊C4C2414yes—
487Dic7⋊C4C2418yes—
488Dic7⋊C4C2414yes—
489Dic7⋊C4C2418yes—
490Dic7⋊C4C2418yes—
491Dic7⋊C4C2414yes—
492Dic7⋊C4C2418yes—
493Dic7⋊C4C2414yes—
494Dic7⋊C4C2414yes—
495Dic7⋊C4C2418yes—
496Dic7⋊C4C2418yes—
497Dic7⋊C4C2418yes—
498Dic7⋊C4C2418yes—
499C4×Dic7C2414yes—
500C4×Dic7C2414yes—
501C4×Dic7C2414yes—
502C4×Dic7C2418yes—
503C4×Dic7C2414yes—
504C4×Dic7C2418yes—
505C4×Dic7C2418yes—
506C4×Dic7C2418yes—
507C4×Dic7C2414yes—
508C4×Dic7C2418yes—
509C4×Dic7C2418yes—
510#563—732no—
511#563—732no—
512Q82—716no—
513#557—716no—
514#557—716no—
515#557C2×D7116yescomplemented
516#556—732no—
517#556—716no—
518#556—716no—
519#556—716no—
520#554—716no—
521#552—732no—
522#544—732no—
523#542—716no—
524#542—716no—
525#541—732no—
526#541—732no—
527#541—716no—
528#541—716no—
529#541—732no—
530#533—716no—
531#533—716no—
532C2×C4⋊Q8—71no—
533C2×C4⋊Q8—71no—
534C2×C4⋊Q8—71no—
535C2×C4⋊Q8—72no—
536C2×C4⋊Q8—72no—
537C2×C4⋊Q8—71no—
538C2×C4⋊Q8—71no—
539C2×C4⋊Q8—72no—
540C2×C4⋊Q8—71no—
541C2×C4⋊Q8—72no—
542C2×C4⋊Q8—71no—
543C2×C4⋊Q8C2×D711yescharacteristic
544C2×C4⋊Q8C2×D712yes—
545#529—716no—
546C2×#126—72no—
547C2×#126—72no—
548C2×#126—72no—
549C2×#126—72no—
550C2×#126—72no—
551C2×#126—72no—
552C2×#126—72no—
553C2×#126—72no—
554C2×#126—72no—
555C2×#126—72no—
556C2×#126—72no—
557C2×#126—72no—
558C2×#126—72no—
559C2×#125—71no—
560C2×#125—71no—
561C2×#125—72no—
562C2×#125—72no—
563C2×#125—72no—
564C2×#125—72no—
565C2×#125—72no—
566C2×#125—72no—
567C2×#125—72no—
568C2×#125—72no—
569C2×#125—71no—
570C2×#125—72no—
571C2×#125—72no—
572C2×#125C2×D711yescharacteristic
573C2×#125C2×D712yes—
574C2×#125C2×D711yescharacteristic
575C2×#125C2×D712yes—
576C2×#124—71no—
577C2×#124—72no—
578C2×#124—71no—
579C2×#124—71no—
580C2×#124—72no—
581C2×#123—72no—
582C2×#123—72no—
583C2×#123—72no—
584C2×C22⋊Q8—71no—
585C2×C22⋊Q8—71no—
586C2×C22⋊Q8—72no—
587C2×C22⋊Q8—72no—
588C2×C22⋊Q8—71no—
589C2×C22⋊Q8—71no—
590C2×C22⋊Q8—72no—
591C2×C22⋊Q8—72no—
592C2×C22⋊Q8—72no—
593C2×C22⋊Q8—72no—
594C2×C22⋊Q8—72no—
595C2×C22⋊Q8—72no—
596C2×C22⋊Q8—71no—
597C2×C22⋊Q8—71no—
598C2×C22⋊Q8—71no—
599C2×C22⋊Q8—72no—
600C2×#121—71no—
601C2×C4×Q8—71no—
602C2×C4×Q8—72no—
603C2×C4×Q8—72no—
604C2×C4×Q8—71no—
605C2×C4×Q8—71no—
606C2×C4×Q8—71no—
607C2×C4×Q8—72no—
608C2×C4×Q8—71no—
609C2×C4×Q8—71no—
610C2×C4×Q8—71no—
611C2×C4×Q8—71no—
612C2×C4×Q8—72no—
613C2×C4×Q8—71no—
614C2×C4×Q8C2×D711yescharacteristic
615C2×C4×Q8C2×D711yescharacteristic
616C2×C4×Q8C2×D712yes—
617C2×C4×Q8C2×D711yescharacteristic
618C2×C4×Q8C2×D711yescharacteristic
619C2×C4×D4—72no—
620C2×C4×D4—71no—
621C2×C4×D4—71no—
622C2×C4×D4—71no—
623C2×#117—72no—
624C2×#117—72no—
625C2×#117—71no—
626C2×#117—71no—
627C2×#117—72no—
628C2×#117—72no—
629C2×#117—72no—
630C22×C4⋊C4—72no—
631C22×C42—71no—
632C23×C7C2511yescharacteristic
633C22×D7—22no—
634C22×D7—22no—
635C22×D7—24no—
636C22×D7—24no—
637C22×D7—24no—
638C22×D7—22no—
639C22×D7C2512yes—
640C22×D7C2514yes—
641C7×Q8—28no—
642C7×Q8—48no—
643C7×Q8—44no—
644C2×C4×C7—22no—
645C2×C4×C7—22no—
646C2×C4×C7—22no—
647C2×C4×C7—24no—
648C2×C4×C7—24no—
649C2×C4×C7—22no—
650C2×C4×C7—24no—
651C2×C4×C7—24no—
652C2×C4×C7—22no—
653C2×C4×C7—22no—
654C2×C4×C72−1+414yes—
655C2×C4×C7C2512yes—
656C2×C4×C7C2514yes—
657C2×C4×C7C2512yes—
658C2×C4×C7C2514yes—
659C2×C4×C7C2512yes—
660C2×C4×C7C2514yes—
661C2×C4×C7C2514yes—
662C2×C4×C7C2512yes—
663C2×C4×C7C2512yes—
664C2×C4×C7C2512yes—
665C2×C4×C7C2512yes—
666C2×Dic7—24no—
667C2×Dic7—24no—
668C2×Dic7—22no—
669C2×Dic7—22no—
670C2×Dic7—22no—
671C2×Dic7—22no—
672C2×Dic7—24no—
673C2×Dic7—22no—
674C2×Dic7—22no—
675C2×Dic72−1+414yes—
676C2×Dic7C2512yes—
677C2×Dic7C2512yes—
678C2×Dic7C2514yes—
679C2×Dic7C2514yes—
680C2×Dic7C2512yes—
681C2×Dic7C2512yes—
682C2×Dic7C2512yes—
683C2×Dic7C2514yes—
684C2×Dic7C2512yes—
685C2×Dic7C2512yes—
686D28—28no—
687D28—48no—
688C4×D7—28no—
689C4×D7—28no—
690C4×D7—216no—
691C4×D7—44no—
692C4×D7—48no—
693C4×D7—48no—
694Dic14—28no—
695Dic14—28no—
696Dic14—28no—
697Dic14—28no—
698Dic14—48no—
699Dic14—44no—
700Dic14—48no—
701C22×Q8—71no—
702C22×Q8—71no—
703C22×Q8—71no—
704C22×Q8—71no—
705C22×Q8—71no—
706C22×Q8—72no—
707C22×Q8—72no—
708C22×Q8C22×D711yescharacteristic
709C22×Q8C22×D711yescharacteristic
710C22×Q8C22×D712yes—
711C22×D4—71no—
712C22×D4—72no—
713C23×C4—72no—
714C23×C4—71no—
715C23×C4—71no—
716C23×C4—72no—
717C23×C4—72no—
718C23×C4—71no—
719C4⋊Q8—78no—
720C4⋊Q8—78no—
721C4⋊Q8—78no—
722C4⋊Q8—716no—
723C4⋊Q8—716no—
724C4⋊Q8—78no—
725C4⋊Q8—78no—
726C4⋊Q8—716no—
727C4⋊Q8—78no—
728C4⋊Q8—716no—
729C4⋊Q8—78no—
730C4⋊Q8C22×D718yes—
731C4⋊Q8C22×D7116yes—
732#126—716no—
733#126—716no—
734#126—716no—
735#126—716no—
736#126—716no—
737#126—716no—
738#126—716no—
739#126—716no—
740#126—716no—
741#126—716no—
742#126—716no—
743#126—716no—
744#126—716no—
745#125—78no—
746#125—78no—
747#125—716no—
748#125—716no—
749#125—716no—
750#125—716no—
751#125—716no—
752#125—78no—
753#125—716no—
754#125—716no—
755#125—716no—
756#125—716no—
757#125—716no—
758#125C22×D718yes—
759#125C22×D7116yes—
760#125C22×D718yes—
761#125C22×D7116yes—
762#124—78no—
763#124—716no—
764#124—78no—
765#124—78no—
766#124—716no—
767#123—716no—
768#123—716no—
769#123—716no—
770C22⋊Q8—78no—
771C22⋊Q8—78no—
772C22⋊Q8—716no—
773C22⋊Q8—716no—
774C22⋊Q8—78no—
775C22⋊Q8—78no—
776C22⋊Q8—78no—
777C22⋊Q8—78no—
778C22⋊Q8—716no—
779C22⋊Q8—78no—
780C22⋊Q8—716no—
781C22⋊Q8—716no—
782C22⋊Q8—716no—
783C22⋊Q8—716no—
784C22⋊Q8—716no—
785C22⋊Q8—716no—
786#121—78no—
787C4×Q8—78no—
788C4×Q8—716no—
789C4×Q8—716no—
790C4×Q8—78no—
791C4×Q8—78no—
792C4×Q8—78no—
793C4×Q8—716no—
794C4×Q8—78no—
795C4×Q8—78no—
796C4×Q8—78no—
797C4×Q8—78no—
798C4×Q8—716no—
799C4×Q8—78no—
800C4×Q8C22×D718yes—
801C4×Q8C22×D718yes—
802C4×Q8C22×D7116yes—
803C4×Q8C22×D718yes—
804C4×Q8C22×D718yes—
805C4×D4—716no—
806C4×D4—78no—
807C4×D4—78no—
808C4×D4—78no—
809#117—716no—
810#117—716no—
811#117—78no—
812#117—78no—
813#117—716no—
814#117—716no—
815#117—716no—
816C2×C4⋊C4—71no—
817C2×C4⋊C4—72no—
818C2×C4⋊C4—72no—
819C2×C4⋊C4—71no—
820C2×C4⋊C4—72no—
821C2×C4⋊C4—71no—
822C2×C4⋊C4—71no—
823C2×C4⋊C4—71no—
824C2×C4⋊C4—72no—
825C2×C4⋊C4—72no—
826C2×C4⋊C4—72no—
827C2×C4⋊C4—71no—
828C2×C4⋊C4—71no—
829C2×C4⋊C4—71no—
830C2×C4⋊C4—71no—
831C2×C4⋊C4—71no—
832C2×C4⋊C4—71no—
833C2×C4⋊C4—72no—
834C2×C4⋊C4—72no—
835C2×C4⋊C4—72no—
836C2×C4⋊C4—72no—
837C2×C4⋊C4—72no—
838C2×C4⋊C4—72no—
839C2×C4⋊C4—72no—
840C2×C4⋊C4—71no—
841C2×C4⋊C4—72no—
842C2×C4⋊C4—71no—
843C2×C4⋊C4—72no—
844C2×C4⋊C4—71no—
845C2×C4⋊C4—72no—
846C2×C4⋊C4—72no—
847C2×C4⋊C4—72no—
848C2×C4⋊C4—72no—
849C2×C4⋊C4—716no—
850C2×C4⋊C4C22×D712yes—
851C2×C4⋊C4C22×D711yescharacteristic
852C2×C4⋊C4C22×D712yes—
853C2×C4⋊C4C22×D711yescharacteristic
854C2×C4⋊C4C22×D711yescharacteristic
855C2×C4⋊C4C22×D712yes—
856C2×C4⋊C4C22×D711yescharacteristic
857C2×C4⋊C4C22×D712yes—
858C2×C4⋊C4C22×D711yescharacteristic
859C2×C4⋊C4C22×D712yes—
860C2×C4⋊C4C22×D712yes—
861C2×C4⋊C4C22×D712yes—
862C2×C4⋊C4C22×D712yes—
863C2×C4⋊C4C22×D711yescharacteristic
864C2×C22⋊C4—72no—
865C2×C22⋊C4—72no—
866C2×C22⋊C4—71no—
867C2×C22⋊C4—71no—
868C2×C22⋊C4—72no—
869C2×C22⋊C4—72no—
870C2×C22⋊C4—72no—
871C2×C22⋊C4—71no—
872C2×C22⋊C4—72no—
873C2×C22⋊C4—72no—
874C2×C22⋊C4—71no—
875C2×C22⋊C4—72no—
876C2×C22⋊C4—72no—
877C2×C22⋊C4—72no—
878C2×C22⋊C4—72no—
879C2×C22⋊C4—72no—
880C2×C22⋊C4—72no—
881C2×C42—72no—
882C2×C42—71no—
883C2×C42—72no—
884C2×C42—71no—
885C2×C42—71no—
886C2×C42—72no—
887C2×C42—72no—
888C2×C42—72no—
889C2×C42—71no—
890C2×C42—72no—
891C2×C42—71no—
892C2×C42—78no—
893C2×C42C22×D712yes—
894C2×C42C22×D711yescharacteristic
895C2×C42C22×D711yescharacteristic
896C2×C42C22×D712yes—
897C2×C42C22×D711yescharacteristic
898C2×C42C22×D712yes—
899C22×C7C2×2−1+412yes—
900C22×C7C2×2−1+412yes—
901C22×C7#58512yes—
902C22×C7C2611yescharacteristic
903C2×D7—22no—
904C2×D7—22no—
905C2×D7—24no—
906C2×D7—24no—
907C2×D7—24no—
908C2×D7—22no—
909C2×D7—44no—
910C2×D7—48no—
911C4×C7—22no—
912C4×C7—22no—
913C4×C7—22no—
914C4×C7—24no—
915C4×C7—24no—
916C4×C7—22no—
917C4×C7—24no—
918C4×C7—24no—
919C4×C7—22no—
920C4×C7—22no—
921C4×C7C2×2−1+414yes—
922Dic7—24no—
923Dic7—24no—
924Dic7—22no—
925Dic7—22no—
926Dic7—22no—
927Dic7—22no—
928Dic7—24no—
929Dic7—22no—
930Dic7—22no—
931Dic7C2×2−1+414yes—
932C24—71no—
933C24—72no—
934C2×Q8—24no—
935C2×Q8—42no—
936C2×Q8—44no—
937C2×Q8—74no—
938C2×Q8—74no—
939C2×Q8—74no—
940C2×Q8—74no—
941C2×Q8—74no—
942C2×Q8—78no—
943C2×Q8—78no—
944C2×Q8—144no—
945C2×Q8—144no—
946C2×Q8—144no—
947C2×Q8—144no—
948C2×Q8—282no—
949C2×Q8—284no—
950C2×Q8—284no—
951C2×Q8C23×D714yes—
952C2×Q8C23×D714yes—
953C2×Q8C23×D718yes—
954C2×D4—74no—
955C2×D4—78no—
956C2×D4—144no—
957C2×D4—284no—
958C22×C4—71no—
959C22×C4—72no—
960C22×C4—72no—
961C22×C4—71no—
962C22×C4—71no—
963C22×C4—71no—
964C22×C4—71no—
965C22×C4—72no—
966C22×C4—71no—
967C22×C4—71no—
968C22×C4—74no—
969C22×C4—74no—
970C22×C4—78no—
971C22×C4—74no—
972C22×C4—78no—
973C22×C4—78no—
974C22×C4—148no—
975C22×C4—144no—
976C22×C4—144no—
977C22×C4—284no—
978C22×C4—284no—
979C22×C4—282no—
980C22×C4C23×D711yescharacteristic
981C22×C4C23×D711yescharacteristic
982C22×C4C23×D712yes—
983C22×C4C23×D712yes—
984C22×C4C23×D711yescharacteristic
985C22×C4C23×D712yes—
986C22×C4C23×D712yes—
987C22×C4C23×D711yescharacteristic
988C22×C4C23×D711yescharacteristic
989C22×C4C23×D711yescharacteristic
990C22×C4C23×D711yescharacteristic
991C4⋊C4—74no—
992C4⋊C4—78no—
993C4⋊C4—74no—
994C4⋊C4—78no—
995C4⋊C4—74no—
996C4⋊C4—74no—
997C4⋊C4—74no—
998C4⋊C4—78no—
999C4⋊C4—74no—
1000C4⋊C4—74no—
1001C4⋊C4—74no—
1002C4⋊C4—74no—
1003C4⋊C4—78no—
1004C4⋊C4—78no—
1005C4⋊C4—78no—
1006C4⋊C4—78no—
1007C4⋊C4—78no—
1008C4⋊C4—78no—
1009C4⋊C4—78no—
1010C4⋊C4—78no—
1011C4⋊C4—74no—
1012C4⋊C4—78no—
1013C4⋊C4—78no—
1014C4⋊C4—78no—
1015C4⋊C4—78no—
1016C4⋊C4—78no—
1017C4⋊C4—78no—
1018C4⋊C4—74no—
1019C4⋊C4—74no—
1020C4⋊C4—78no—
1021C4⋊C4—74no—
1022C4⋊C4—74no—
1023C4⋊C4—78no—
1024C4⋊C4C23×D718yes—
1025C4⋊C4C23×D714yes—
1026C4⋊C4C23×D718yes—
1027C4⋊C4C23×D714yes—
1028C4⋊C4C23×D714yes—
1029C4⋊C4C23×D718yes—
1030C4⋊C4C23×D714yes—
1031C4⋊C4C23×D718yes—
1032C4⋊C4C23×D714yes—
1033C4⋊C4C23×D718yes—
1034C4⋊C4C23×D718yes—
1035C4⋊C4C23×D718yes—
1036C4⋊C4C23×D718yes—
1037C4⋊C4C23×D714yes—
1038C22⋊C4—78no—
1039C22⋊C4—78no—
1040C22⋊C4—74no—
1041C22⋊C4—74no—
1042C22⋊C4—78no—
1043C22⋊C4—78no—
1044C22⋊C4—78no—
1045C22⋊C4—78no—
1046C22⋊C4—74no—
1047C22⋊C4—78no—
1048C22⋊C4—74no—
1049C22⋊C4—78no—
1050C22⋊C4—78no—
1051C22⋊C4—78no—
1052C22⋊C4—78no—
1053C22⋊C4—78no—
1054C22⋊C4—78no—
1055C42—74no—
1056C42—74no—
1057C42—74no—
1058C42—78no—
1059C42—78no—
1060C42—74no—
1061C42—74no—
1062C42—78no—
1063C42—78no—
1064C42—78no—
1065C42—78no—
1066C42C23×D714yes—
1067C42C23×D718yes—
1068C42C23×D714yes—
1069C42C23×D714yes—
1070C42C23×D718yes—
1071C42C23×D718yes—
1072C2×C7#355514yescomplemented
1073C2×C7C22×2−1+411yescharacteristic
1074C2×C7C22×2−1+411yescharacteristic
1075C2×C7C2×#58511yescharacteristic
1076D7—42no—
1077D7—44no—
1078C23—72no—
1079C23—74no—
1080C23—142no—
1081C23—144no—
1082C23—144no—
1083C23—142no—
1084C23—142no—
1085C23—144no—
1086C23C24×D711yescharacteristic
1087Q8—28no—
1088Q8—44no—
1089Q8—48no—
1090Q8—148no—
1091Q8—148no—
1092Q8—148no—
1093Q8—148no—
1094Q8—284no—
1095Q8—288no—
1096Q8—288no—
1097D4—148no—
1098D4—288no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—72no—
1110C2×C4—74no—
1111C2×C4—74no—
1112C2×C4—74no—
1113C2×C4—72no—
1114C2×C4—72no—
1115C2×C4—72no—
1116C2×C4—72no—
1117C2×C4—72no—
1118C2×C4—74no—
1119C2×C4—72no—
1120C2×C4—148no—
1121C2×C4—1416no—
1122C2×C4—142no—
1123C2×C4—144no—
1124C2×C4—144no—
1125C2×C4—142no—
1126C2×C4—144no—
1127C2×C4—142no—
1128C2×C4—142no—
1129C2×C4—142no—
1130C2×C4—142no—
1131C2×C4—148no—
1132C2×C4—288no—
1133C2×C4—288no—
1134C2×C4—284no—
1135C2×C4#655114yes—
1136C2×C4C24×D712yes—
1137C2×C4C24×D712yes—
1138C2×C4C24×D714yes—
1139C2×C4C24×D714yes—
1140C2×C4C24×D712yes—
1141C2×C4C24×D714yes—
1142C2×C4C24×D714yes—
1143C2×C4C24×D712yes—
1144C2×C4C24×D712yes—
1145C2×C4C24×D712yes—
1146C2×C4C24×D712yes—
1147C7C2×#355511yescharacteristic, complemented, Sylow
1148C22—142no—
1149C22—144no—
1150C22—144no—
1151C22—142no—
1152C22—142no—
1153C22—144no—
1154C22—284no—
1155C22—288no—
1156C22C2×#655112yes—
1157C22#9061612yes—
1158C22D7×2−1+412yes—
1159C22C25×D711yescharacteristic
1160C4—24no—
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—24no—
1165C4—22no—
1166C4—22no—
1167C4—24no—
1168C4—22no—
1169C4—22no—
1170C4—74no—
1171C4—142no—
1172C4—144no—
1173C4—144no—
1174C4—142no—
1175C4—142no—
1176C4—144no—
1177C4—142no—
1178C4—142no—
1179C4—142no—
1180C4C2×#655114yes—
1181C2—282no—
1182C2—284no—
1183C2#1174410514yesdirect product factor
1184C2C22×#655111yescharacteristic
1185C2C2×#9061611yescharacteristic
1186C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#557C2
socleC23×C7C25
prime radicalC2×#6458C22
hypercenterC2×#557D7
hypocenterC7C2×#3555
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
2. #11744105C2direct (N × H)
3. C2×#90426C2semidirect
4. C2×#90420C2semidirect
6. C2×#90413C2semidirect
7. C2×#90390C2semidirect
8. C2×#90384C2semidirect
9. C2×#90388C2semidirect
10. C2×#90376C2semidirect
11. C2×#90381C2semidirect
12. C2×#90387C2semidirect
13. C2×#90387C2semidirect
16. C2×#90274C2semidirect
17. C2×#90274C2semidirect
18. C2×#90269C2semidirect
19. C2×#90269C2semidirect
20. C2×#90258C2semidirect
21. C2×#90259C2semidirect
22. C2×#90259C2semidirect
23. C2×#90259C2semidirect
24. C2×#90275C2semidirect
25. C7×#557C22semidirect
48. #90426C22semidirect
50. #90420C22semidirect
51. #90413C22semidirect
52. #90390C22semidirect
53. #90388C22semidirect
54. #90387C22semidirect
55. #90387C22semidirect
56. #90384C22semidirect
58. #90381C22semidirect
59. #90376C22semidirect
60. #90275C22semidirect
61. #90274C22semidirect
62. #90274C22semidirect
64. #90269C22semidirect
65. #90269C22semidirect
66. #90259C22semidirect
67. #90259C22semidirect
68. #90259C22semidirect
69. #90258C22semidirect
352. C2×#557D7semidirect
515. #557C2×D7semidirect
1072. C2×C7#3555semidirect
1147. C7C2×#3555semidirect
1183. C2#11744105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
#117441052
C2×#904262
C2×#904202
C2×#904242
C2×#904132
C2×#903902
C2×#903842
C2×#903882
C2×#903762
C2×#903812
C2×#903872
C2×#903822
C2×#902732
C2×#902742
C2×#902692
C2×#902582
C2×#902592
C2×#902752
C2×#35557