Finite Group Databasebeta

← C2×#11740292 #13521521

Subgroups — C2×#11740292 #13521521

Order 1792.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic, complemented
2C22×#6502C211yesmaximal, characteristic
3C22×D4×Dic7C211yesmaximal, characteristic, complemented
4C22×#6492C211yesmaximal, characteristic, complemented
5C22×C7⋊#95C211yesmaximal, characteristic, complemented
6#11740292C2116yesmaximal, direct product factor
7C2×#89766C211yesmaximal, characteristic, complemented
8C2×#89756C211yesmaximal, characteristic, complemented
9C2×#89744C211yesmaximal, characteristic, complemented
10C2×#89762C211yesmaximal, characteristic, complemented
11C2×#89731C211yesmaximal, characteristic, complemented
12C2×#89724C211yesmaximal, characteristic, complemented
13C2×#89730C211yesmaximal, characteristic, complemented
14C2×#89730C211yesmaximal, characteristic, complemented
15C2×#89718C211yesmaximal, characteristic, complemented
16C2×#89714C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C24×Dic7C2211yescharacteristic
23C24×Dic7C2211yescharacteristic
24C2×C7×#123—28no—
25C2×C7×#123C2218yescomplemented
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C2×#6502—28no—
35C2×#6502C2218yes—
36C2×D4×Dic7—28no—
37C2×D4×Dic7C2218yescomplemented
38C2×#6492—28no—
39C2×#6492C2218yescomplemented
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×(C2×D7)⋊C4C2211yescharacteristic
42C22×(C2×D7)⋊C4C2211yescharacteristic
43C22×(C2×D7)⋊C4C2211yescharacteristic
44C22×(C2×D7)⋊C4C2211yescharacteristic
45C22×C4⋊Dic7C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×Dic7⋊C4C2211yescharacteristic
50C22×Dic7⋊C4C2211yescharacteristic
51C22×C4×Dic7C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2218yescomplemented
61#89766C2218yescomplemented
62#89762C2218yescomplemented
63#89756C2218yescomplemented
64#89744C2218yescomplemented
65#89731C2218yescomplemented
66#89730C2218yescomplemented
67#89730C2218yescomplemented
68#89724C2218yescomplemented
69#89718C2218yescomplemented
70#89714C2218yescomplemented
71C2×#2425—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4D418yes—
78C22×C7×D4C2314yes—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—24no—
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2314yes—
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×Dic7—24no—
97C23×Dic7—24no—
98C23×Dic7—24no—
99C23×Dic7—24no—
100C23×Dic7—24no—
101C23×Dic7—24no—
102C23×Dic7—42no—
103C23×Dic7—42no—
104C23×Dic7—42no—
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2311yescharacteristic
108C23×Dic7C2314yes—
109C23×Dic7C2314yes—
110C23×Dic7C2314yes—
111C23×Dic7C2311yescharacteristic
112C23×Dic7C2311yescharacteristic
113C23×Dic7C2311yescharacteristic
114C23×Dic7C2311yescharacteristic
115C7×#123—232no—
116C2×C7×C4⋊C4—24no—
117C2×C7×C4⋊C4—24no—
118C2×C7×C4⋊C4C2314yes—
119C2×C7×C4⋊C4C2314yes—
120C2×C7×C22⋊C4—24no—
121C2×C7×C22⋊C4—24no—
122C2×C7×C22⋊C4—24no—
123C2×C7×C22⋊C4C2314yes—
124C2×C7×C22⋊C4C2314yes—
125C2×C7×C22⋊C4C2314yes—
126C2×C22⋊Dic7—24no—
127C2×C22⋊Dic7—24no—
128C2×C22⋊Dic7D418yescomplemented
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132#6502—232no—
133D4×Dic7—232no—
134#6492—232no—
135C2×(C2×D7)⋊C4—24no—
136C2×(C2×D7)⋊C4—24no—
137C2×(C2×D7)⋊C4—24no—
138C2×(C2×D7)⋊C4—24no—
139C2×(C2×D7)⋊C4—42no—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2314yes—
143C2×(C2×D7)⋊C4C2314yes—
144C2×(C2×D7)⋊C4C2314yes—
145C2×C4⋊Dic7—24no—
146C2×C4⋊Dic7C2314yes—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—24no—
150C2×Dic7⋊C4—24no—
151C2×Dic7⋊C4—42no—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×Dic7⋊C4C2314yes—
155C2×Dic7⋊C4C2314yes—
156C2×Dic7⋊C4C2314yes—
157C2×C4×Dic7—24no—
158C2×C4×Dic7C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#123—71no—
168C22×#123D711yescharacteristic, complemented
169C22×#121—71no—
170C22×C4×D4—71no—
171#2425—716no—
172C2×#398—71no—
173C2×#397—71no—
174C2×#396—71no—
175C2×#394—71no—
176C2×#389—71no—
177C2×#388—71no—
178C2×#386—71no—
179C2×#386—71no—
180C2×#385—71no—
181C2×#380—71no—
182C22×#95—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×C7C2×D414yes—
194C24×C7C2×D414yes—
195C24×C7C2×D414yes—
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×D7—22no—
207C23×D7C2412yes—
208C2×C7×D4—232no—
209C2×C7×D4—28no—
210C2×C7×D4—28no—
211C2×C7×D4C2×D4116yes—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—28no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—28no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—28no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—416no—
230C22×C4×C7C2×D414yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
236C2×C22⋊D7—28no—
237C2×C22⋊D7—28no—
238C2×C22⋊D7—28no—
239C2×C22⋊D7—28no—
240C2×C22⋊D7—28no—
241C2×C22⋊D7—44no—
242C2×C22⋊D7—416no—
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—28no—
257C22×Dic7—28no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—28no—
264C22×Dic7—28no—
265C22×Dic7—28no—
266C22×Dic7—28no—
267C22×Dic7—44no—
268C22×Dic7—44no—
269C22×Dic7—44no—
270C22×Dic7—416no—
271C22×Dic7—416no—
272C22×Dic7—416no—
273C22×Dic7C2×D414yes—
274C22×Dic7C2×D414yes—
275C22×Dic7#4114yes—
276C22×Dic7#4114yes—
277C22×Dic7C2412yes—
278C22×Dic7C2412yes—
279C22×Dic7C2412yes—
280C22×Dic7C2412yes—
281C22×Dic7C2412yes—
282C22×Dic7C2412yes—
283C22×Dic7C2412yes—
284C7×C4⋊C4—28no—
285C7×C4⋊C4—28no—
286C7×C22⋊C4—28no—
287C7×C22⋊C4—28no—
288C7×C22⋊C4—28no—
289C22⋊Dic7—28no—
290C22⋊Dic7—28no—
291C22⋊Dic7C2×D4116yescomplemented
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—28no—
295(C2×D7)⋊C4—28no—
296(C2×D7)⋊C4—44no—
297C4⋊Dic7—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4—28no—
300Dic7⋊C4—28no—
301Dic7⋊C4—28no—
302Dic7⋊C4—44no—
303C4×Dic7—28no—
304C23×D4—71no—
305C23×D4—71no—
306C23×D4C2×D711yescharacteristic
307C24×C4—71no—
308C24×C4—71no—
309C24×C4—71no—
310C24×C4C2×D711yescharacteristic
311C2×#123—28no—
312C2×#123—78no—
313C2×#123—148no—
314C2×#123C2×D718yescomplemented
315C2×#121—78no—
316C2×#121—148no—
317C2×C4×D4—78no—
318C2×C4×D4—148no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4C2×D711yescharacteristic
326C22×C4⋊C4C2×D711yescharacteristic
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⋊C4—71no—
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C22⋊C4C2×D711yescharacteristic
338C22×C42—71no—
339#398—78no—
340#397—78no—
341#396—78no—
342#394—78no—
343#389—78no—
344#388—78no—
345#386—78no—
346#386—78no—
347#385—78no—
348#380—78no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—78no—
355C2×#95—71no—
356C2×#95—71no—
357C2×#95—71no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—28no—
361C23×C7—28no—
362C23×C7—28no—
363C23×C7—28no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—28no—
369C23×C7—28no—
370C23×C7—28no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7#121116yes—
382C23×C7C22×D414yes—
383C23×C7C22×D412yes—
384C23×C7C22×D414yes—
385C23×C7C22×D414yes—
386C23×C7C22×D412yes—
387C23×C7C2×#4114yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7C2×#4112yes—
391C23×C7H(5,𝔽2)12yes—
392C23×C72−1+412yes—
393C23×C7C2511yescharacteristic
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—44no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7—44no—
407C22×D7—44no—
408C7×D4—232no—
409C2×C4×C7—28no—
410C2×C4×C7—22no—
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—22no—
424C2×C4×C7—416no—
425C2×C4×C7—44no—
426C2×C4×C7—44no—
427C2×C4×C7—44no—
428C2×C4×C7—44no—
429C2×C4×C7C22×D414yes—
430C22⋊D7—416no—
431C22⋊D7—416no—
432C2×Dic7—28no—
433C2×Dic7—28no—
434C2×Dic7—28no—
435C2×Dic7—28no—
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—22no—
453C2×Dic7—416no—
454C2×Dic7—416no—
455C2×Dic7—416no—
456C2×Dic7—44no—
457C2×Dic7—44no—
458C2×Dic7—44no—
459C2×Dic7C22×D414yes—
460C2×Dic7C22×D414yes—
461C2×Dic7C2×#4114yes—
462C2×Dic7C2×#4114yes—
463C25—71no—
464C25C22×D711yescharacteristic
465C25C22×D711yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—74no—
469C22×D4—74no—
470C22×D4—144no—
471C22×D4—144no—
472C22×D4—144no—
473C22×D4—144no—
474C22×D4—144no—
475C22×D4—282no—
476C22×D4C22⋊D718yes—
477C22×D4C22×D714yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—74no—
489C23×C4—74no—
490C23×C4—74no—
491C23×C4—144no—
492C23×C4—144no—
493C23×C4—144no—
494C23×C4—144no—
495C23×C4—144no—
496C23×C4—144no—
497C23×C4—282no—
498C23×C4—282no—
499C23×C4—282no—
500C23×C4C22×D714yes—
501C23×C4C22×D711yescharacteristic
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506#123—232no—
507#123—1432no—
508#121—1432no—
509C4×D4—1432no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—74no—
513C2×C4⋊C4—74no—
514C2×C4⋊C4—74no—
515C2×C4⋊C4—74no—
516C2×C4⋊C4—74no—
517C2×C4⋊C4—74no—
518C2×C4⋊C4—144no—
519C2×C4⋊C4—144no—
520C2×C4⋊C4—144no—
521C2×C4⋊C4—144no—
522C2×C4⋊C4—144no—
523C2×C4⋊C4—282no—
524C2×C4⋊C4C22×D714yes—
525C2×C4⋊C4C22×D714yes—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—78no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—74no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—144no—
539C2×C22⋊C4—144no—
540C2×C22⋊C4—144no—
541C2×C22⋊C4—144no—
542C2×C22⋊C4—144no—
543C2×C22⋊C4—144no—
544C2×C22⋊C4—282no—
545C2×C22⋊C4C22×D714yes—
546C2×C22⋊C4C22×D714yes—
547C2×C22⋊C4C22×D714yes—
548C2×C42—74no—
549C2×C42—144no—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95—74no—
556#95—74no—
557#95—74no—
558C22×C7—24no—
559C22×C7—232no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—24no—
563C22×C7—24no—
564C22×C7—24no—
565C22×C7—24no—
566C22×C7—24no—
567C22×C7—24no—
568C22×C7—42no—
569C22×C7—416no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7C2×#12118yes—
574C22×C7C2×#12114yes—
575C22×C7#52914yes—
576C22×C7#53914yes—
577C22×C7#54614yes—
578C22×C7#54614yes—
579C22×C7#54714yes—
580C22×C7#54714yes—
581C22×C7C23×D411yescharacteristic
582C22×C7C23×D411yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C22×#4111yescharacteristic
585C22×C7C22×#4111yescharacteristic
586C22×C7C2×H(5,𝔽2)11yescharacteristic
587C22×C7C2×2−1+411yescharacteristic
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—42no—
594C2×D7—42no—
595C2×D7—88no—
596C4×C7—24no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600C4×C7—42no—
601Dic7—24no—
602Dic7—24no—
603Dic7—24no—
604Dic7—24no—
605Dic7—42no—
606Dic7—42no—
607Dic7—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—72no—
619C24—142no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24D4×D714yes—
627C24#115914yes—
628C24C2×C22⋊D714yes—
629C24C2×C22⋊D714yes—
630C24C23×D712yes—
631C24C23×D712yes—
632C24C23×D711yescharacteristic
633C2×D4—232no—
634C2×D4—28no—
635C2×D4—28no—
636C2×D4—148no—
637C2×D4—148no—
638C2×D4—148no—
639C2×D4—148no—
640C2×D4—148no—
641C2×D4—284no—
642C2×D4—2816no—
643C2×D4—2816no—
644C2×D4C2×C22⋊D7116yes—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—28no—
650C22×C4—28no—
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—22no—
660C22×C4—22no—
661C22×C4—28no—
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—148no—
676C22×C4—148no—
677C22×C4—148no—
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—148no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—142no—
695C22×C4—142no—
696C22×C4—148no—
697C22×C4—284no—
698C22×C4—284no—
699C22×C4—284no—
700C22×C4—2816no—
701C22×C4—2816no—
702C22×C4—2816no—
703C22×C4C2×C22⋊D714yes—
704C22×C4C23×D712yes—
705C22×C4C23×D712yes—
706C22×C4C23×D712yes—
707C22×C4C23×D712yes—
708C22×C4C23×D712yes—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—148no—
712C4⋊C4—148no—
713C4⋊C4—148no—
714C4⋊C4—148no—
715C4⋊C4—148no—
716C4⋊C4—284no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—716no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C22⋊C4—148no—
724C22⋊C4—148no—
725C22⋊C4—148no—
726C22⋊C4—148no—
727C22⋊C4—284no—
728C42—148no—
729C2×C7—28no—
730C2×C7—44no—
731C2×C7#242518yescomplemented
732C2×C7C22×#12111yescharacteristic
733C2×C7C2×#52911yescharacteristic
734C2×C7C2×#53911yescharacteristic
735C2×C7C2×#54611yescharacteristic
736C2×C7C2×#54611yescharacteristic
737C2×C7C2×#54711yescharacteristic
738C2×C7C2×#54711yescharacteristic
739D7—82no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—284no—
771C23—284no—
772C23—284no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23#6502116yes—
778C23C2×D4×D714yes—
779C23C2×D4×D712yes—
780C23C2×#115914yes—
781C23C2×#115912yes—
782C23D7×#4112yes—
783C23D7×#4112yes—
784C23#655312yes—
785C23#655412yes—
786C23C22×C22⋊D714yes—
787C23C22×C22⋊D714yes—
788C23C22×C22⋊D712yes—
789C23C24×D711yescharacteristic
790D4—232no—
791D4—2816no—
792D4—2816no—
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—22no—
807C2×C4—22no—
808C2×C4—416no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—74no—
814C2×C4—74no—
815C2×C4—74no—
816C2×C4—74no—
817C2×C4—148no—
818C2×C4—148no—
819C2×C4—148no—
820C2×C4—148no—
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—142no—
835C2×C4—142no—
836C2×C4—142no—
837C2×C4—142no—
838C2×C4—2816no—
839C2×C4—2816no—
840C2×C4—2816no—
841C2×C4—284no—
842C2×C4—284no—
843C2×C4—284no—
844C2×C4C22×C22⋊D714yes—
845C7C2×#242511yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—232no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—416no—
861C22—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—282no—
866C22—282no—
867C22—282no—
868C22—568no—
869C22#9034014yes—
870C22#9034514yes—
871C22#9034614yes—
872C22#9035614yes—
873C22C2×#650218yes—
874C22C2×#650214yes—
875C22#9051514yes—
876C22#9052014yes—
877C22C22×D4×D711yescharacteristic
878C22C22×#115911yescharacteristic
879C22C2×D7×#4111yescharacteristic
880C22C2×D7×#4111yescharacteristic
881C22C2×#655311yescharacteristic
882C22C2×#655411yescharacteristic
883C22C23×C22⋊D711yescharacteristic
884C4—24no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—144no—
890C4—144no—
891C4—144no—
892C4—144no—
893C4—282no—
894C4—282no—
895C4—282no—
896C2—28no—
897C2—44no—
898C2—562no—
899C2#1174029218yesdirect product factor
900C2C2×#9034011yescharacteristic
901C2C2×#9035611yescharacteristic
902C2C2×#9034511yescharacteristic
903C2C2×#9034611yescharacteristic
904C2C22×#650211yescharacteristic
905C2C2×#9051511yescharacteristic
906C2C2×#9052011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#123C2
socleC24×C7C24
prime radicalC22×#6502C2
hypercenterC22×#123D7
hypocenterC7C2×#2425
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C7×#123C2semidirect
3. C22×D4×Dic7C2semidirect
4. C22×#6492C2semidirect
5. C22×C7⋊#95C2semidirect
6. #11740292C2direct (N × H)
7. C2×#89766C2semidirect
8. C2×#89756C2semidirect
9. C2×#89744C2semidirect
10. C2×#89762C2semidirect
11. C2×#89731C2semidirect
12. C2×#89724C2semidirect
13. C2×#89730C2semidirect
14. C2×#89730C2semidirect
15. C2×#89718C2semidirect
16. C2×#89714C2semidirect
25. C2×C7×#123C22semidirect
37. C2×D4×Dic7C22semidirect
39. C2×#6492C22semidirect
60. C2×C7⋊#95C22semidirect
61. #89766C22semidirect
62. #89762C22semidirect
63. #89756C22semidirect
64. #89744C22semidirect
65. #89731C22semidirect
66. #89730C22semidirect
67. #89730C22semidirect
68. #89724C22semidirect
69. #89718C22semidirect
70. #89714C22semidirect
128. C2×C22⋊Dic7D4semidirect
168. C22×#123D7semidirect
291. C22⋊Dic7C2×D4semidirect
314. C2×#123C2×D7semidirect
731. C2×C7#2425semidirect
845. C7C2×#2425semidirect
899. C2#11740292direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C22×#65022
C22×D4×Dic72
C22×#64922
C22×C7⋊#952
#117402922
C2×#897662
C2×#897562
C2×#897442
C2×#897622
C2×#897312
C2×#897242
C2×#897302
C2×#897182
C2×#897142
C2×#24257