Finite Group Databasebeta

← C2×#11732163 #13521661

Subgroups — C2×#11732163 #13521661

Order 1792.

3786 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
1C22×#6487C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D7C211yesmaximal, characteristic, complemented
3C22×#6446C211yesmaximal, characteristic, complemented
4C22×#6448C211yesmaximal, characteristic, complemented
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C2×#89995C211yesmaximal, characteristic
7C2×#89993C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89720C211yesmaximal, characteristic, complemented
10C2×#89717C211yesmaximal, characteristic, complemented
11C2×#89723C211yesmaximal, characteristic, complemented
12#11732163C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89428C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C2×C4×C22⋊D7—28no—
33C2×C4×C22⋊D7C2218yescomplemented
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C2×#6487—28no—
42C2×#6487C2218yescomplemented
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C22×C4×Dic7C2211yescharacteristic
49C22×C4×Dic7C2211yescharacteristic
50C2×#6448—28no—
51C2×#6448C2218yescomplemented
52C2×#6446—28no—
53C2×#6446C2218yescomplemented
54C7×#386C2218yescomplemented
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57#89995C2218yes—
58#89993C2218yescomplemented
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62C2×C7⋊#95C2211yescharacteristic
63#89731C2218yescomplemented
64#89723C2218yescomplemented
65#89720C2218yescomplemented
66#89717C2218yescomplemented
67#89442C2218yescomplemented
68#89440C2218yescomplemented
69#89428C2218yescomplemented
70#89421C2218yescomplemented
71C2×#2461—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—42no—
78C22×C7×D4C2314yes—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—42no—
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2314yes—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—24no—
91C22×C22⋊D7—24no—
92C22×C22⋊D7—24no—
93C22×C22⋊D7—42no—
94C22×C22⋊D7C2314yes—
95C22×C22⋊D7C2314yes—
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C22×C4×D7—24no—
104C22×C4×D7—24no—
105C22×C4×D7—42no—
106C22×C4×D7C2314yes—
107C22×Dic14—24no—
108C22×Dic14—24no—
109C22×Dic14—42no—
110C22×Dic14C2314yes—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C4×C22⋊D7—232no—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—24no—
133C2×(C2×D7)⋊C4D418yescomplemented
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×C4⋊Dic7—24no—
139C2×C4⋊Dic7—24no—
140C2×C4⋊Dic7—42no—
141C2×C4⋊Dic7C2314yes—
142C2×C4⋊Dic7C2314yes—
143C2×C4⋊Dic7C2314yes—
144#6487—232no—
145C2×Dic7⋊C4—24no—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4D418yescomplemented
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2314yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×C4×Dic7—24no—
154C2×C4×Dic7—24no—
155C2×C4×Dic7—24no—
156C2×C4×Dic7C2314yes—
157C2×C4×Dic7C2314yes—
158C2×C4×Dic7C2314yes—
159#6448—232no—
160#6446—232no—
161C7×#95C2314yes—
162C7×#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#124—71no—
168C22×#123—71no—
169C22×C22⋊Q8—71no—
170C22×C4×D4—71no—
171#2461—716no—
172C2×#396—71no—
173C2×#395—71no—
174C2×#394—71no—
175C2×#392—71no—
176C2×#390—71no—
177C2×#388—71no—
178C2×#388—71no—
179C2×#388—71no—
180C2×#386D711yescharacteristic, complemented
181C2×#385—71no—
182C2×C4×C4⋊C4—71no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7—22no—
196C24×C7#4114yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7—22no—
206C23×D7C2×D414yes—
207C23×D7C2412yes—
208C2×C7×D4—28no—
209C2×C7×D4—28no—
210C2×C7×D4—44no—
211C2×C7×D4—416no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—28no—
225C22×C4×C7—28no—
226C22×C4×C7—44no—
227C22×C4×C7—416no—
228C22×C4×C7C2×D414yes—
229C22×C4×C7C2×D414yes—
230C22×C4×C7#4114yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
236C2×C22⋊D7—232no—
237C2×C22⋊D7—28no—
238C2×C22⋊D7—28no—
239C2×C22⋊D7—28no—
240C2×C22⋊D7—28no—
241C2×C22⋊D7—28no—
242C2×C22⋊D7—44no—
243C2×C22⋊D7—416no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7C2×D414yes—
262C22×Dic7C2×D414yes—
263C22×Dic7C2×D414yes—
264C22×Dic7#4114yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C2×C4×D7—28no—
273C2×C4×D7—28no—
274C2×C4×D7—44no—
275C2×C4×D7—416no—
276C2×Dic14—28no—
277C2×Dic14—28no—
278C2×Dic14—44no—
279C2×Dic14—416no—
280C7×C22⋊C4—28no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—28no—
283C22⋊Dic7—28no—
284C22⋊Dic7—28no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—28no—
289(C2×D7)⋊C4—28no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4C2×D4116yescomplemented
293C4⋊Dic7—28no—
294C4⋊Dic7—28no—
295C4⋊Dic7—44no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4C2×D4116yescomplemented
300C4×Dic7—28no—
301C4×Dic7—28no—
302C4×Dic7—28no—
303C23×Q8—71no—
304C23×D4—71no—
305C23×D4—71no—
306C23×D4C2×D711yescharacteristic
307C24×C4—71no—
308C24×C4C2×D711yescharacteristic
309C2×#124—78no—
310C2×#124—148no—
311C2×#123—78no—
312C2×#123—148no—
313C2×C22⋊Q8—78no—
314C2×C22⋊Q8—148no—
315C2×C4×D4—78no—
316C2×C4×D4—148no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C42—71no—
338C22×C42—71no—
339C22×C42—71no—
340#396—78no—
341#395—78no—
342#394—78no—
343#392—78no—
344#390—78no—
345#388—78no—
346#388—78no—
347#388—78no—
348#386C2×D718yescomplemented
349#385—78no—
350C4×C4⋊C4—78no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95C2×D711yescharacteristic
356C2×#95C2×D711yescharacteristic
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7—44no—
384C23×C7C22×D412yes—
385C23×C7C22×D412yes—
386C23×C7C2×#4112yes—
387C23×C7C2×#4114yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C72−1+412yes—
392C23×C7C2511yescharacteristic
393C22×D7—28no—
394C22×D7—28no—
395C22×D7—28no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7C22×D414yes—
407C7×D4—416no—
408C2×C4×C7—28no—
409C2×C4×C7—28no—
410C2×C4×C7—28no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—416no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7C22×D414yes—
427C2×C4×C7C22×D414yes—
428C2×C4×C7C2×#4114yes—
429C22⋊D7—232no—
430C22⋊D7—416no—
431C2×Dic7—28no—
432C2×Dic7—28no—
433C2×Dic7—28no—
434C2×Dic7—28no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—44no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455C2×Dic7C22×D414yes—
456C2×Dic7C22×D414yes—
457C2×Dic7C22×D414yes—
458C2×Dic7C2×#4114yes—
459C4×D7—416no—
460Dic14—416no—
461C25—71no—
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C22×Q8—74no—
465C22×Q8—144no—
466C22×Q8—144no—
467C22×Q8—282no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—42no—
471C22×D4—74no—
472C22×D4—74no—
473C22×D4—144no—
474C22×D4—144no—
475C22×D4—144no—
476C22×D4—144no—
477C22×D4—144no—
478C22×D4—282no—
479C22×D4C22×D714yes—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—42no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—74no—
491C23×C4—144no—
492C23×C4—144no—
493C23×C4—282no—
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D714yes—
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500#124—1432no—
501#123—1432no—
502C22⋊Q8—1432no—
503C4×D4—1432no—
504C2×C4⋊C4—78no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—74no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—144no—
513C2×C4⋊C4—144no—
514C2×C4⋊C4—144no—
515C2×C4⋊C4—144no—
516C2×C4⋊C4—144no—
517C2×C4⋊C4—282no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—78no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—144no—
533C2×C22⋊C4—144no—
534C2×C22⋊C4—144no—
535C2×C22⋊C4—144no—
536C2×C22⋊C4—144no—
537C2×C22⋊C4—144no—
538C2×C22⋊C4—144no—
539C2×C22⋊C4—144no—
540C2×C22⋊C4—144no—
541C2×C22⋊C4C22×D714yes—
542C2×C22⋊C4C22×D714yes—
543C2×C22⋊C4C22×D714yes—
544C2×C42—74no—
545C2×C42—74no—
546C2×C42—74no—
547C2×C42—144no—
548C2×C42—144no—
549C2×C42—144no—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95C22×D714yes—
555#95C22×D714yes—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—24no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—416no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—88no—
572C22×C7#52514yes—
573C22×C7#53214yes—
574C22×C7#54214yes—
575C22×C7D4214yes—
576C22×C7#54714yes—
577C22×C7#54814yes—
578C22×C7#55114yes—
579C22×C7C23×D411yescharacteristic
580C22×C7C23×D411yescharacteristic
581C22×C7C22×#4111yescharacteristic
582C22×C7C22×#4111yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C2×H(5,𝔽2)11yescharacteristic
585C22×C7C2×2−1+411yescharacteristic
586C2×D7—24no—
587C2×D7—24no—
588C2×D7—24no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—416no—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—24no—
597C4×C7—42no—
598C4×C7—42no—
599Dic7—24no—
600Dic7—24no—
601Dic7—24no—
602Dic7—24no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—74no—
620C24—72no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24—142no—
627C24#115914yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×Q8—148no—
632C2×Q8—148no—
633C2×Q8—284no—
634C2×Q8—2816no—
635C2×D4—28no—
636C2×D4—28no—
637C2×D4—44no—
638C2×D4—416no—
639C2×D4—148no—
640C2×D4—148no—
641C2×D4—148no—
642C2×D4—1432no—
643C2×D4—148no—
644C2×D4—148no—
645C2×D4—284no—
646C2×D4—2816no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—44no—
662C22×C4—416no—
663C22×C4—74no—
664C22×C4—74no—
665C22×C4—74no—
666C22×C4—74no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—148no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—148no—
693C22×C4—284no—
694C22×C4—2816no—
695C22×C4#115714yes—
696C22×C4D4×D714yes—
697C22×C4D4×D714yes—
698C22×C4C23×D712yes—
699C22×C4C23×D712yes—
700C22×C4C23×D712yes—
701C22×C4C23×D712yes—
702C22×C4C23×D712yes—
703C4⋊C4—716no—
704C4⋊C4—148no—
705C4⋊C4—148no—
706C4⋊C4—148no—
707C4⋊C4—148no—
708C4⋊C4—148no—
709C4⋊C4—284no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
713C22⋊C4—716no—
714C22⋊C4—148no—
715C22⋊C4—148no—
716C22⋊C4—148no—
717C22⋊C4—148no—
718C22⋊C4—148no—
719C22⋊C4—148no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C42—148no—
724C42—148no—
725C42—148no—
726C2×C7—44no—
727C2×C7—82no—
728C2×C7#246118yescomplemented
729C2×C7C2×#52511yescharacteristic
730C2×C7C2×#53211yescharacteristic
731C2×C7C2×#54211yescharacteristic
732C2×C7C2×D4211yescharacteristic
733C2×C7C2×#54711yescharacteristic
734C2×C7C2×#54811yescharacteristic
735C2×C7C2×#55111yescharacteristic
736D7—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—74no—
765C23—148no—
766C23—148no—
767C23—148no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—142no—
773C23—142no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23—284no—
778C23C2×#115712yes—
779C23C2×D4×D712yes—
780C23C2×D4×D712yes—
781C23C2×#115914yes—
782C23C2×#115912yes—
783C23#654812yes—
784C23D7×#4112yes—
785C23#655412yes—
786C23C24×D711yescharacteristic
787Q8—2816no—
788D4—416no—
789D4—1432no—
790D4—2816no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—416no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—74no—
812C2×C4—74no—
813C2×C4—148no—
814C2×C4—148no—
815C2×C4—148no—
816C2×C4—148no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—142no—
834C2×C4—2816no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4C2×#115714yes—
839C2×C4C2×D4×D714yes—
840C2×C4C2×D4×D714yes—
841C7C2×#246111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—416no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—88no—
858C22—144no—
859C22—144no—
860C22—144no—
861C22—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—2816no—
866C22#9018614yes—
867C22#9023914yes—
868C22#9024214yes—
869C22#9028114yes—
870C22#9028914yes—
871C22#9029714yes—
872C22#9035314yes—
873C22C22×#115711yescharacteristic
874C22C22×D4×D711yescharacteristic
875C22C22×D4×D711yescharacteristic
876C22C22×#115911yescharacteristic
877C22C2×#654811yescharacteristic
878C22C2×D7×#4111yescharacteristic
879C22C2×#655411yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—144no—
886C4—144no—
887C4—144no—
888C4—144no—
889C4—282no—
890C4—282no—
891C4—282no—
892C2—44no—
893C2—82no—
894C2—284no—
895C2#1173216318yesdirect product factor
896C2C2×#9018611yescharacteristic
897C2C2×#9023911yescharacteristic
898C2C2×#9024211yescharacteristic
899C2C2×#9028111yescharacteristic
900C2C2×#9029711yescharacteristic
901C2C2×#9028911yescharacteristic
902C2C2×#9035311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#386D7
hypocenterC7C2×#2461
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#6487C2semidirect
2. C22×C4×C22⋊D7C2semidirect
3. C22×#6446C2semidirect
4. C22×#6448C2semidirect
5. C2×C7×#386C2semidirect
7. C2×#89993C2semidirect
8. C2×#89731C2semidirect
9. C2×#89720C2semidirect
10. C2×#89717C2semidirect
11. C2×#89723C2semidirect
12. #11732163C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89428C2semidirect
15. C2×#89442C2semidirect
16. C2×#89421C2semidirect
33. C2×C4×C22⋊D7C22semidirect
42. C2×#6487C22semidirect
51. C2×#6448C22semidirect
53. C2×#6446C22semidirect
54. C7×#386C22semidirect
58. #89993C22semidirect
63. #89731C22semidirect
64. #89723C22semidirect
65. #89720C22semidirect
66. #89717C22semidirect
67. #89442C22semidirect
68. #89440C22semidirect
69. #89428C22semidirect
70. #89421C22semidirect
133. C2×(C2×D7)⋊C4D4semidirect
148. C2×Dic7⋊C4D4semidirect
180. C2×#386D7semidirect
292. (C2×D7)⋊C4C2×D4semidirect
299. Dic7⋊C4C2×D4semidirect
348. #386C2×D7semidirect
728. C2×C7#2461semidirect
841. C7C2×#2461semidirect
895. C2#11732163direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64872
C22×C4×C22⋊D72
C22×#64462
C22×#64482
C2×C7×#3862
C2×#899952
C2×#899932
C2×#897312
C2×#897202
C2×#897172
C2×#897232
#117321632
C2×#894402
C2×#894282
C2×#894422
C2×#894212
C2×#24617